Department of Mathematics at UTSA - User contributions [en]

The Divergence and Integral Tests

2020-09-19T00:34:39Z

James.kercheville: Added video links

[https://youtu.be/4vGr104Qpj4 Infinite Series: The Nth Term Divergent Test] by James Sousa

[https://youtu.be/DcduHCJuiWk Test for Divergence for Series, Two Examples] by patrickJMT

[https://youtu.be/e50wqj2Y-18 nth term test, divergence test, zero test] by Krista King

[https://youtu.be/nC_IU1IzzS4 Divergence Test For Series - Calculus 2] by The Organic Chemistry Tutor

[https://youtu.be/qQlnPrpwKY8 The Integral Test] by James Sousa

[https://youtu.be/Lla2xi6W8cQ Infinite Series: The Integral Test] by James Sousa

[https://youtu.be/1riNZY-8ATM Ex: Infinite Series - Integral Test Requiring Integration by Parts (Convergent)] by James Sousa

[https://youtu.be/gvZ7UIaC50M Integral Test - Basic Idea] by patrickJMT

[https://youtu.be/XHUxLLu_c_0 Integral Test for Series Example 1] by patrickJMT

[https://youtu.be/f0hGrW6_weo Integral Test for Series - Example 2] by patrickJMT

[https://youtu.be/TZAmpPZ4DH4 Integral Test to Evaluate Series, Ex 1] by patrickJMT

[https://youtu.be/QQBtF7_KJrE Interval and Radius of Convergence for a Series, Ex 2] by patrickJMT

[https://youtu.be/xHaV9Ambgqc Integral Test to Evaluate Series, Ex 3] by patrickJMT

[https://youtu.be/_KDtZ5wRq8Q Integral Test to Evaluate Series, Ex 4.] by patrickJMT

[https://youtu.be/qiwGXzbans4 How to use the INTEGRAL TEST for series] by Krista King

[https://youtu.be/f9SJz4-UaQQ Calculus 2 - Integral Test For Convergence and Divergence of Series] by The Organic Chemistry Tutor

Infinite Series

2020-09-17T17:14:02Z

James.kercheville: Added additional video links

[https://youtu.be/jPx2S4mSZWc Introduction to Infinite Series] by James Sousa

[https://youtu.be/LPFSQoozBL0 Calculating the first terms in a series of partial sums] by Krista King

[https://youtu.be/wpB7nk5J0AA Sum of the series of partial sums] by Krista King

[https://youtu.be/-wvF8OQSMx8 Convergence & Divergence - Geometric Series, Telescoping Series, Harmonic Series, Divergence Test] by The Organic Chemistry Tutor

[https://youtu.be/6LfoMmCckFY Telescoping Series] by James Sousa

[https://youtu.be/cyoiIBs7kIg Finding a Formula for a Partial Sum of a Telescoping Series] by patrickJMT

[https://youtu.be/xmyLUFv2mDM Telescoping Series ,Showing Divergence Using Partial Sums] by patrickJMT

[https://youtu.be/H8HVYiEqzBo Telescoping Series , Finding the Sum, Example 1] by patrickJMT

[https://youtu.be/pFcJZnxqzNc Infinite Geometric Series] by James Sousa

[https://youtu.be/xjmy5hkZccY Geometric Series and the Test for Divergence - Part 1] by patrickJMT

[https://youtu.be/C8piSCOdo1Y Geometric Series and the Test for Divergence - Part 2] by patrickJMT

[https://youtu.be/LhO7i3RFri0 Convergence of a geometric series] by Krista King

[https://youtu.be/1eInMsp20cI Values for which the geometric series converges] by Kritsa King

[https://youtu.be/-5kIBPR2Npk Geometric Series and Geometric Sequences - Basic Introduction] by The Organic Chemistry Tutor

[https://youtu.be/jxRqRLMliPc Finding The Sum of an Infinite Geometric Series] by The Organic Chemistry Tutor

Infinite Series

2020-09-15T21:54:13Z

James.kercheville: Added video links

Sequences

2020-09-11T15:43:32Z

James.kercheville: Added additional video links

[https://youtu.be/p-rc5mTDt9E Introduction to Sequences] by James Sousa

[https://youtu.be/Kxh7yJC9Jr0 What is a Sequence? Basic Sequence Info] by patrickJMT

[https://youtu.be/XdoqvWxTVEw Calculating the first terms of the sequence ] by Krista King

[https://youtu.be/0aCpT3dalh8 Ex: Find the General Formula For a Sequence in Fraction Form (Arithmetic/Geometric)] by James Sousa

[https://youtu.be/zoP3UnulRcA Geometric Sequences: A Formula for the' n - th ' Term , Part 1] by patrickJMT

[https://youtu.be/INjRH9h3oxA Finding the nth Term of the Sequence] by Krista King

[https://youtu.be/hc64LUtPjP0 Limits of a Sequence] by James Sousa

[https://youtu.be/9K1xx6wfN-U Sequences - Examples showing convergence or divergence] by patrickJMT

[https://youtu.be/0piu2uP4zr4 Finding the Limit of a Sequence, 3 more examples] by patrickJMT

[https://youtu.be/BknXGSoCNB0 Does the sequence converge or diverge?] by Krista King

[https://youtu.be/bvPxNhs-yrI Intro to Monotonic and Bounded Sequences, Ex 1] by patrickJMT

[https://youtu.be/npboNfgQff8 Increasing, decreasing and not monotonic sequences] by Krista King

[https://youtu.be/tHy3TXmZpF0 Monotonic Sequences and Bounded Sequences] by The Organic Chemistry Tutor

[https://youtu.be/RjsyEWDEQe0 Ex: Finding Terms in a Sequence Given a Recursive Formula] by James Sousa

[https://youtu.be/IEyojX9jzv0 Recursive Sequences] by patrickJMT

[https://youtu.be/IFHZQ6MaG6w Recursive Formulas For Sequences] by The Organic Chemistry Tutor

Sequences

2020-09-09T20:47:43Z

James.kercheville: Added additional video links

Derivatives Rates of Change

2020-09-03T20:58:58Z

James.kercheville: Added video links

* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Derivatives%20as%20Rates%20of%20Change/MAT1214-3.4TheDerivativeAsARateOfChangePwPt.pptx Derivatives as Rates of Change ] PowerPoint file created by Dr. Sara Shirinkam, UTSA.

* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Derivatives%20as%20Rates%20of%20Change/MAT1214-3.4TheDerivativeAsARateOfChangeWS1.pdf Derivatives as Rates of Change Worksheet]

* [https://youtu.be/4Up5gsDeluw Average and Instantaneous Rate of Change of a function over an interval & a point - Calculus] by The Organic Chemistry Tutor

* [https://youtu.be/jlihNi_Mkos Finding Instantaneous Rates of Change Using Def'n of Derivative] by patrickJMT

Differentiation Rules

2020-09-03T20:55:39Z

James.kercheville: Added video links

* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Differentiation%20Rules/MAT1214-3.3DifferentiationRulesPwPt.pptx Differentiation Rules] PowerPoint file created by Dr. Sara Shirinkam, UTSA.

* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Differentiation%20Rules/MAT1214-3.3DifferentiationRulesWS1.pdf Differentiation Rules Worksheet 1]

* [https://youtu.be/IvLpN1G1Ncg Basic Differentiation Rules For Derivatives] by The Organic Chemistry Tutor

* [https://youtu.be/_e0gqRYpCWs Power rule for derivatives] by Krista King

* [https://youtu.be/uPCjqfT0Ixg The Product Rule for Derivatives] by patrickJMT

* [https://youtu.be/YxxGmeV_Dm0 Product rule - 3+ functions] by Krista King

* [https://youtu.be/K3MxofAF-9o The Quotient Rule] by patrickJMT

The Derivative as a Function

2020-08-28T18:10:44Z

James.kercheville: Added video link

* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/The%20Derivative%20as%20a%20Function/MAT1214-3.2TheDerivativeAsAFunctionPwPt.pptx The Derivative as a Function] PowerPoint file created by Dr. Sara Shirinkam, UTSA.

* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/The%20Derivative%20as%20a%20Function/MAT1214-3.2TheDerivAsFunctionNotes.pdf The Derivative as a Function Notes] created by Instructor Sean Beatty, UTSA.

* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/The%20Derivative%20as%20a%20Function/MAT1214-3.2TheDerivativeAsAFunctionWS1.pdf The Derivative as a Function Worksheet 1]

* [https://youtu.be/vzDYOHETFlo Finding a Derivative Using the Definition of a Derivative] by patrickJMT

* [https://youtu.be/3bmw9UQxbRI Derivative of Root Function Using Definition of a Derivative] by patrickJMT

* [https://youtu.be/WERgBgi4hg4 Derivative Using the Definition, Example 2] by patrickJMT

* [https://youtu.be/-aTLjoDT1GQ Definition of the Derivative] by The Organic Chemistry Tutor

* [https://youtu.be/fml0-ELYLaE Continuity and Differentiability] by The Organic Chemistry Tutor

The Derivative as a Function

2020-08-28T18:08:48Z

James.kercheville: Added video links

Sequences

2020-08-28T18:02:33Z

James.kercheville: Added video links

The Logistic Equation

2020-08-28T17:59:07Z

James.kercheville: Added video links

[https://youtu.be/zkAPudy52U4 Ex: Logistic Growth Differential Equation] by James Sousa

[https://youtu.be/vsYWMEmNmZo The Logistic Equation and the Analytic Solution] by patrickJMT

[https://youtu.be/MIOj-W-jY-k The Logistic Equation and Models for Population - Example 1, part 1] by patrickJMT

[https://youtu.be/n0gIf8xEkVA The Logistic Equation and Models for Population - Example 1, part 2] by patrickJMT

[https://youtu.be/uemhtqZHnak Logistic growth model of a population] by Krista King

[https://youtu.be/JgMvB22XQs0 Logistic Growth Function and Differential Equations] by The Organic Chemistry Tutor

Exponential Growth and Decay

2020-08-27T19:34:29Z

James.kercheville: Added video links

[https://youtu.be/KCDtss0pT_c Ex: Exponential Growth Function - Population] by James Sousa

[https://youtu.be/D1mnrvbJEWs Ex: Exponential Decay Function - Half Life] by James Sousa

[https://youtu.be/63udRYh04sY Exponential Growth / Population Growth Problem.] by patrickJMT

[https://youtu.be/K8IaH3adKz8 Radioactive Decay and Exponential Growth] by patrickJMT

[https://youtu.be/T7ivdB2qQyo Exponential Decay / Finding Half Life] by patrickJMT

[https://youtu.be/Pm-sAbnChF4 Population Growth] by Krista King

[https://youtu.be/6io7id17smM Finding HALF LIFE] by Krista King

[https://youtu.be/M9rcYTuFG4w Exponential Growth and Decay Calculus, Relative Growth Rate, Differential Equations, Word Problems] by The Organic Chemistry Tutor

Separation of Variables

2020-08-26T17:50:41Z

James.kercheville: Added video links

[https://youtu.be/nzqLplhh0DU Differential Equations: Separation of Variables] by James Sousa

[https://youtu.be/OF9K9MK0Yvg Ex.1 Differential Equations: Separation of Variables] by James Sousa

[https://youtu.be/A_RdFJJUyEg Ex.2 Differential Equations: Separation of Variables] by James Sousa

[https://youtu.be/0-dy9aaNdZ8 Ex.3 Differential Equations: Separation of Variables] by James Sousa

[https://youtu.be/KNQFAusQ_KM Ex 1: Initial Value Problem - Separation of Variables] by James Sousa

[https://youtu.be/fBb68MsuAAk Ex 2: Initial Value Problem - Separation of Variables] by James Sousa

[https://youtu.be/nNHlSB6b1HU Solving Separable First Order Differential Equations - Ex 1] by patrickJMT

[https://youtu.be/XExEixAPK6s Solving Separable First Order Differential Equations - Ex 2] by patrickJMT

[https://youtu.be/uS_5bmRUYEI Solving a Separable Differential Equation, Another Example #1] by patrickJMT

[https://youtu.be/Vc6MwLVdCuM Solving a Separable Differential Equation, Another Example #2] by patrickJMT

The Limit of a Function

2020-08-25T18:45:41Z

James.kercheville: minor edit

* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Limits%20of%20Functions/MAT1214_2.2TheLimitOfAFunctionPwPt.pptx The Limit of a Function] PowerPoint file created by Dr. Sara Shirinkam, UTSA.

* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Limits%20of%20Functions/MAT1214-2.2TheLimitOfAFunctionNotes1.pdf The Limit of a Function] notes created by Instructor Beatty, UTSA.

* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Limits%20of%20Functions/MAT1214_2.2TheLimitOfAFunctionNotes.pdf The Left and Right Hand Limit] notes created by Instructor Beatty, UTSA.

* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Limits%20of%20Functions/MAT1214-2.2TheLimitOfAFunctionWS1.pdf The Limit of a Function Worksheet 1]

* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Limits%20of%20Functions/MAT1214_2.2TheLimitOfAFunctionWS2.pdf The Limit of a Function Worksheet 2]

* [https://youtu.be/QfPqRMqP5kU Calculus 1 - Introduction to Limits] by The Organic Chemistry Tutor

* [https://youtu.be/HYSI-AHUqRM What is a Limit? Basic Idea of Limits] by patrickJMT

* [https://youtu.be/kG_p2vKApOE Lots of Limit Examples, Part 1] by patrickJMT

Improper Integrals

2020-08-25T18:44:49Z

James.kercheville: Added video links

[https://youtu.be/F19y9IiH-cM Improper Integrals] by James Sousa

[https://youtu.be/qWMJpYajOww Ex 1: Improper Integral - Infinite Interval (-inf,+inf)] by James Sousa

[https://youtu.be/q-l1WbnjKhw Ex 2: Improper Integral - Infinite Interval (-inf, constant)] by James Sousa

[https://youtu.be/8cc720Y_UWU Ex 3: Improper Integral - Infinite Interval (-inf,+inf)] by James Sousa

[https://youtu.be/85-HNJyuyrU Improper Integral - Basic Idea and Example] by patrickJMT

[https://youtu.be/KvC4XyayEC0 Improper Integral - More Complicated Example] by patrickJMT

[https://youtu.be/f6cGotvktxs Improper Integral - Infinity in Upper and Lower Limits] by patrickJMT

[https://youtu.be/GZ-vy0bApWc What makes an integral improper?] by Krista King

[https://youtu.be/f6cGotvktxs What makes an integral improper?] by Krista King

[https://youtu.be/DUowajlKIKA Improper Integrals] by Krista King

[https://youtu.be/266JzwOkSJs Improper Integral Example 2 PART 1/2 ] by Krista King

[https://youtu.be/6fVgBQMvVJY Improper Integral Example 2 PART 2/2 ] by Krista King

Partial Fractions

2020-08-24T18:14:51Z

James.kercheville: Added video links

[https://youtu.be/8MMALX7mUqQ Integration Using Partial Fraction Decomposition Part 1] by James Sousa

[https://youtu.be/BgVNLWLJmMs Integration Using Partial Fraction Decomposition Part 2] by James Sousa

[https://youtu.be/c2oLHtPA03U Partial Fraction Decomposition Part 1 (Linear)] by James Sousa

[https://youtu.be/SQ4l8yDlBVE Partial Fraction Decomposition - Part 2 of 2] by James Sousa

[https://youtu.be/HZTv4zCgEnA Partial Fraction Decomposition - Example 1] by patrickJMT

[https://youtu.be/hnIs8uwAT3U Partial Fraction Decomposition - Example 2] by patrickJMT

[https://youtu.be/lH9Mw65vAIA Partial Fraction Decomposition - Example 4] by patrickJMT

[https://youtu.be/Slfrb8aEj08 Partial Fraction Decomposition - Example 5] by patrickJMT

[https://youtu.be/_YMG5mQTAOg Partial Fraction Decomposition - Example 6] by patrickJMT

[https://youtu.be/7GcSOjLitF8 Partial Fraction Decompositions] by patrickJMT

The Limit of a Function

2020-08-24T18:06:51Z

James.kercheville: Added notes links

* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Limits%20of%20Functions/MAT1214_2.2TheLimitOfAFunctionPwPt.pptx The Limit of a Function] PowerPoint file created by Dr. Sara Shirinkam, UTSA.

* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Limits%20of%20Functions/MAT1214-2.2TheLimitOfAFunctionNotes1.pdf The Limit of a Function] notes created by Instructor Beatty,UTSA.

* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Limits%20of%20Functions/MAT1214_2.2TheLimitOfAFunctionNotes.pdf The Left and Right Hand Limit] notes created by Instructor Beatty,UTSA.

* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Limits%20of%20Functions/MAT1214-2.2TheLimitOfAFunctionWS1.pdf The Limit of a Function Worksheet 1]

* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Limits%20of%20Functions/MAT1214_2.2TheLimitOfAFunctionWS2.pdf The Limit of a Function Worksheet 2]

* [https://youtu.be/QfPqRMqP5kU Calculus 1 - Introduction to Limits] by The Organic Chemistry Tutor

* [https://youtu.be/HYSI-AHUqRM What is a Limit? Basic Idea of Limits] by patrickJMT

* [https://youtu.be/kG_p2vKApOE Lots of Limit Examples, Part 1] by patrickJMT

Limits at Infinity and Asymptotes

2020-08-24T18:02:43Z

James.kercheville: Added notes link

* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Limits%20at%20Infinity/MAT1214-4.6LimitsAtInfinityPwPt.pptx Limits at Infinity and Asymptotes] PowerPoint file created by Dr. Sara Shirinkam, UTSA.

* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Limits%20at%20Infinity/MAT1214-4.6LimitsAtInfinityWS1.pdf Limits at Infinity and Asymptotes Worksheet 1]

* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Limits%20at%20Infinity/MAT1214-4.6LimitsAtInfinityNotes.pdf Limits at Infinity and Asymptotes] notes created by Instructor Beatty,UTSA.

* [https://youtu.be/FVJNuukADeQ Limits at Infinity - Basic Idea and Shortcuts!] by patrickJMT

* [https://youtu.be/-vwcLvb9A0s Calculus - Infinite Limits] by patrickJMT

* [https://youtu.be/NmLljBAg82o How To Find The Limit At Infinity] by the Organic Chemistry Tutor

* [https://youtu.be/sjLFl7Z8W_Io Limits at Infinity & Horizontal Asymptotes] by the Organic Chemistry Tutor

The Limit of a Function

2020-08-24T13:15:32Z

James.kercheville: removed links due to student name

The Limit of a Function

2020-08-24T13:10:50Z

James.kercheville:

* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Limits%20of%20Functions/MAT1214_2.2TheLimitOfAFunctionPwPt.pptx The Limit of a Function] PowerPoint file created by Dr. Sara Shirinkam, UTSA.

* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Limits%20of%20Functions/MAT1214-2.2TheLimitOfAFunctionWS1.pdf The Limit of a Function Worksheet 1]

* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Limits%20of%20Functions/MAT1214_2.2TheLimitOfAFunctionWS2.pdf The Limit of a Function Worksheet 2]

* [https://youtu.be/sdwbppTH0Do The Limit of a Function Part 1] Video Lecture by Instructor Sharon, UTSA.

* [https://youtu.be/QlxNdVIRxe4 The Limit of a Function Part 2] Video Lecture by Instructor Sharon, UTSA.

* [https://youtu.be/BeyZNXTLels The Limit of a Function Part 3] Video Lecture by Instructor Sharon, UTSA.

* [https://youtu.be/HsmId5dqXkQ The Limit of a Function Part 4] Video Lecture by Instructor Sharon, UTSA.

* [https://youtu.be/QfPqRMqP5kU Calculus 1 - Introduction to Limits] by The Organic Chemistry Tutor

* [https://youtu.be/HYSI-AHUqRM What is a Limit? Basic Idea of Limits] by patrickJMT

* [https://youtu.be/kG_p2vKApOE Lots of Limit Examples, Part 1] by patrickJMT

The Limit of a Function

2020-08-24T13:03:42Z

James.kercheville: Added video links again

* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Limits%20of%20Functions/MAT1214_2.2TheLimitOfAFunctionPwPt.pptx The Limit of a Function] PowerPoint file created by Dr. Sara Shirinkam, UTSA.

* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Limits%20of%20Functions/MAT1214-2.2TheLimitOfAFunctionWS1.pdf The Limit of a Function Worksheet 1]

* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Limits%20of%20Functions/MAT1214_2.2TheLimitOfAFunctionWS2.pdf The Limit of a Function Worksheet 2]

* [https://youtu.be/sdwbppTH0Do The Limit of a Function Part 1] Video Lecture by Instructor Sharon, UTSA.

* [https://youtu.be/QlxNdVIRxe4 The Limit of a Function Part 2] Video Lecture by Instructor Sharon, UTSA.

* [https://youtu.be/sdwbppTH0Do The Limit of a Function Part 3] Video Lecture by Instructor Sharon, UTSA.

* [https://youtu.be/sdwbppTH0Do The Limit of a Function Part 4] Video Lecture by Instructor Sharon, UTSA.

* [https://youtu.be/QfPqRMqP5kU Calculus 1 - Introduction to Limits] by The Organic Chemistry Tutor

* [https://youtu.be/HYSI-AHUqRM What is a Limit? Basic Idea of Limits] by patrickJMT

* [https://youtu.be/kG_p2vKApOE Lots of Limit Examples, Part 1] by patrickJMT

Defining the Derivative

2020-08-24T02:34:54Z

James.kercheville: Added video links

* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Defining%20the%20Derivative/MAT1214-3.1DefiningTheDerivativePwPt.pptx Defining the Derivative] PowerPoint file created by Dr. Sara Shirinkam, UTSA.

* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Defining%20the%20Derivative/MAT1214-DefiningTheDerivative_RateOfChangeWS.pdf Defining the Derivative Worksheet 1]

* [https://youtu.be/2wH-g60EJ18 Understanding the Definition of the Derivative] by patrickJMT

* [https://youtu.be/vzDYOHETFlo Finding a Derivative Using the Definition of a Derivative] by patrickJMT

* [https://youtu.be/-aTLjoDT1GQ Definition of the Derivative] by The Organic Chemistry Tutor

* [https://youtu.be/5yfh5cf4-0w Calculus 1 - Derivatives] by The Organic Chemistry Tutor

Limits at Infinity and Asymptotes

2020-08-24T02:31:19Z

James.kercheville: Added video links

* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Limits%20at%20Infinity/MAT1214-4.6LimitsAtInfinityPwPt.pptx Limits at Infinity and Asymptotes] PowerPoint file created by Dr. Sara Shirinkam, UTSA.

* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Limits%20at%20Infinity/MAT1214-4.6LimitsAtInfinityWS1.pdf Limits at Infinity and Asymptotes Worksheet 1]

* [https://youtu.be/FVJNuukADeQ Limits at Infinity - Basic Idea and Shortcuts!] by patrickJMT

* [https://youtu.be/-vwcLvb9A0s Calculus - Infinite Limits] by patrickJMT

* [https://youtu.be/NmLljBAg82o How To Find The Limit At Infinity] by the Organic Chemistry Tutor

* [https://youtu.be/sjLFl7Z8W_Io Limits at Infinity & Horizontal Asymptotes] by the Organic Chemistry Tutor

Trigonometric Substitution

2020-08-23T18:29:43Z

James.kercheville: Added video links

[https://youtu.be/BVn8x7wCa3A Ex 1: Integration Using Trigonometric Substitution] by James Sousa

[https://youtu.be/a-f63vZVuBQ Ex 2: Integration Using Trigonometric Substitution] by James Sousa

[https://youtu.be/jZa4FM6l6pM Ex 3: Integration Using Trigonometric Substitution] by James Sousa

[https://youtu.be/ObxsrPx44nw Ex 4: Integration Using Trigonometric Substitution] by James Sousa

[https://youtu.be/OnT7Ub68FWg Ex 5: Integration Using Trigonometric Substitution] by James Sousa

[https://youtu.be/3lC5AuCFK4c Trigonometric Substitution - Example 1] by patrickJMT

[https://youtu.be/GVL4lHX6DgM Trigonometric Substitution - Example 2] by patrickJMT

[https://youtu.be/yW6Odu0YHL0 Trigonometric Substitution - Example 3 Part 1] by patrickJMT

[https://youtu.be/4QNntd_KZbc Trigonometric Substitution - Example 4 Rational Powers] by patrickJMT

[https://youtu.be/wuRNmNDLanc Trigonometric Substitution More Examples] by patrickJMT

Trigonometric Integrals

2020-08-23T14:24:04Z

James.kercheville: Added video links

[https://youtu.be/Sv-bSbAQeXc Trigonometric Integrals Involving Powers of Sine and Cosine - Part 1] by James Sousa

[https://youtu.be/vPnuigP8I6I Trigonometric Integrals Involving Powers of Sine and Cosine - Part 2] by James Sousa

[https://youtu.be/RGaDMqhOg8Y Trigonometric Integrals Involving Powers of Secant and Tangent - Part 1] by James Sousa

[https://youtu.be/o8sIHlS17qc Trigonometric Integrals Involving Powers of Secant and Tangent - Part 1] by James Sousa

[https://youtu.be/lTqnlihOC4o Trigonometric Integrals - Part 1 of 6] by patrickJMT

[https://youtu.be/zyg9k1je7Fg Trigonometric Integrals - Part 2 of 6] by patrickJMT

[https://youtu.be/BhJ4soojyAQ Trigonometric Integrals - Part 3 of 6] by patrickJMT

[https://youtu.be/8CHHY-2Ctug Trigonometric Integrals - Part 4 of 6] by patrickJMT

[https://youtu.be/QdNScjd5bno Trigonometric Integrals - Part 5 of 6] by patrickJMT

[https://youtu.be/m3zG7c52QR4 Trigonometric Integrals - Part 6 of 6] by patrickJMT

[https://youtu.be/WYhyq_mTCZs Trigonometric integrals - sin^mcos^n, odd m] by Kriata King

[https://youtu.be/RRDiT-djQPk Trigonometric integrals - sin^mcos^n, odd n] by Kriata King

[https://youtu.be/rpbr2nH7lNY Trigonometric integrals - sin^mcos^n, m and n even] by Kriata King

[https://youtu.be/CK2SfrzF_c4 Integrals of trigonometric functions, tan^msec^n, even n] by Krista King

[https://youtu.be/0TuZSSah5hc Integrals of trigonometric functions, tan^msec^n, odd m] by Krista King

Continuity

2020-08-23T01:18:17Z

James.kercheville: Added video links

* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Continuity/MAT1214-2.4ContinuityPwPt.pptx Continuity] PowerPoint file created by Dr. Sara Shirinkam, UTSA.

* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Continuity/MAT1214-2.4ContinuityWS1.pdf Continuity Worksheet 1]

* [https://youtu.be/hlorAjS0xWE Continuity and Limits Made Easy - Part 1 of 2] by patrickJMT

* [https://youtu.be/VUEM6vWJvE4 Continuity - Part 2 of 2] by patrickJMT

* [https://youtu.be/9brk313DjV8 Limits and Continuity] by The Organic Chemistry Tutor

* [https://youtu.be/joewRl1CTL8 Continuity Basic Introduction, Point, Infinite, & Jump Discontinuity, Removable & Nonremovable] by The Organic Chemistry Tutor

Integration by Parts

2020-08-23T01:13:38Z

James.kercheville: Added video links

[https://youtu.be/815s-YB9X44 Integration by Parts: The Basics] by James Sousa

[https://youtu.be/hfJ1zPizj_s Integration by Parts (After Integration by Parts Basics)] by James Sousa

[https://youtu.be/_kJNhoTJ4D4 Integration by Parts - Additional Examples] by James Sousa

[https://youtu.be/815s-YB9X44 Integration by Parts: The Basics] by James Sousa

[https://youtu.be/q_BP4LyvdOA Deriving the Integration by Parts Formula - Easy!] by patrickJMT

[https://youtu.be/dqaDSlYdRcs Integration by Parts Made Easy! ] by patrickJMT

[https://youtu.be/97RasvYIvl4 Integration by Parts - Indefinite Integral] by patrickJMT

[https://youtu.be/_MuKOm8IHBA Integration By Parts - Using IBP's Twice] by patrickJMT

[https://youtu.be/L8HoALsls-E Integration by Parts - A Loopy Example!] by patrickJMT

[https://youtu.be/zGGI4PkHzhI Integration by Parts - Definite Integral] by patrickJMT

[https://youtu.be/Eb5EDMHDnx8 How does integration by parts work?] by Krista King

[https://youtu.be/SlBp9hZBqaQ Integration by Parts] by Krista King

[https://youtu.be/s8l1vs4gjtY Integration by Parts Example 2] by Krista King

[https://youtu.be/0clmZGVl0ss Integration by Parts Example 3] by Krista King

[https://youtu.be/CxV5HE6chSY Integration by Parts Example 4 ] by Krista King

Applied Optimization Problems

2020-08-21T22:25:45Z

James.kercheville: Added video links

* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Applied%20Optimization/MAT1214-5.1AppliedOptimizationPwPt.pptx Applied Optimization] PowerPoint file created by Dr. Sara Shirinkam, UTSA.

* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Applied%20Optimization/MAT1214-5.1AppliedOptimizationWS1.pdf Applied Optimization Worksheet]

[https://youtu.be/p1R0yiMl1Ag Cal1 Applied Optimization Part1] video lecture by Instructor Beatty

[https://youtu.be/y92f_F_EuKo Cal1 Applied Optimization Part2] video lecture by Instructor Beatty

Derivatives and the Shape of a Graph

2020-08-21T22:24:13Z

James.kercheville: Added video links

* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Derivatives%20and%20the%20Shape%20of%20a%20Graph_/MAT1214-4.5DerivativesShapeOfGraphsPwPt.pptx Derivatives and the Shape of a Graph] PowerPoint file created by Dr. Sara Shirinkam, UTSA.

* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Derivatives%20and%20the%20Shape%20of%20a%20Graph_/MAT1214-4.5DerivativesShapeOfGraphsWS1.pdf Derivatives and the Shape of a Graph Worksheet]

[https://youtu.be/rPMfVi-FiuE Cal1 Intervals of Increase and Decrease Part1] video lecture by Instructor Beatty

[https://youtu.be/9ZP6VxofDaY Cal1 Intervals of Increase and Decrease Part2] video lecture by Instructor Beatty

[https://youtu.be/6dQY7j5vGT4 Cal1 Intervals of Concavity Part1] video lecture by Instructor Beatty

[https://youtu.be/BCb8KYhgR3Y Cal1 Intervals of Increase and Decrease and Concavity] video lecture by Instructor Beatty

[https://youtu.be/lM8Ej8VqKkw Cal1 Intervals of Increase Decrease and Concavity Part2] video lecture by Instructor Beatty

Maxima and Minima

2020-08-21T22:20:20Z

James.kercheville: Added video links

* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Maxima%20and%20Minima/MAT1214-4.3MaximaAndMinimaPwPt.pptx Maxima and Minima] PowerPoint file created by Dr. Sara Shirinkam, UTSA.

* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Maxima%20and%20Minima/MAT1214-4.3MaximaAndMinimaWS1.pdf Maxima and Minima Worksheet 1]

* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Maxima%20and%20Minima/MAT1214-4.3MaximaAndMinimaWS2.pdf Maxima and Minima Worksheet 2]

[https://youtu.be/50AeGk8ri9c Cal1 Extreme Values of Functions Part1] video lecture by Instructor Beatty

[https://youtu.be/vIywMukQmWM Cal1 Extreme Values of Functions Part2] video lecture by Instructor Beatty

Linear Approximations and Differentials

2020-08-21T22:18:18Z

James.kercheville: Added video links

* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Linear%20Approximation%20and%20Differentials/MAT1214-4.2LinearizationAndDifferentialsPwPt.pptx Linearization and Differentials] PowerPoint file created by Dr. Sara Shirinkam, UTSA.

* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Linear%20Approximation%20and%20Differentials/MAT1214-4.2LinearizationAndDifferentialsWS1.pdf Linearization and Differentials Worksheet 1]

* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Linear%20Approximation%20and%20Differentials/MAT1214-4.2LinearizationAndDifferentialsWS2.pdf Linearization and Differentials Worksheet 2]

* [https://youtu.be/9fW2QX-ik2I Cal1 Linearization Part1] video lecture by Instructor Beatty, UTSA.

* [https://youtu.be/72LAzx9dGXw Cal1 Differentials Part1] video lecture by Instructor Beatty, UTSA.

* [https://youtu.be/FYKY-3JSzfw Cal1 Differentials Part2] video lecture by Instructor Beatty, UTSA.

* [https://youtu.be/3hoiQJhzH3Y Cal1 Differentials Part3] video lecture by Instructor Beatty, UTSA.

Related Rates

2020-08-21T22:15:44Z

James.kercheville: Added video link

* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Related%20Rates/MAT1214-4.1RelatedRatesPwPt.pptx Related Rates] PowerPoint file created by Dr. Sara Shirinkam, UTSA.

* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Related%20Rates/MAT1214-4.1RelatedRatesWS1.pdf Related Rates Worksheet]

* [https://youtu.be/YRM-x3lZELs Cal1 Related Rates Part1] video lecture by Instructor Beatty, UTSA.

The Limit Laws

2020-08-21T20:29:51Z

James.kercheville: changed video links

* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/The%20Limit%20Laws/MAT1214-2.3TheLimitLawsPwPt.pptx The Limit Laws] PowerPoint file created by Dr. Sara Shirinkam, UTSA.

* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/The%20Limit%20Laws/MAT1214_2.3TheLimitLawsWS1.pdf The Limit Laws Worksheet]

* [https://youtu.be/P7G7F3NzPw0 Properties of Limits] by The Organic Chemistry Tutor

* [https://youtu.be/v_Nz6UUQ4HQ Limit Laws to Evaluate a Limit , Example 1] by patrickJMT

* [https://youtu.be/3d7qLvgZp0s Limit Laws to Evaluate a Limit , Example 2] by patrickJMT

* [https://youtu.be/KeAgfb3NZLc Limit Laws to Evaluate a Limit , Example 3] by patrickJMT

The Limit of a Function

2020-08-21T20:25:49Z

James.kercheville: changed video links

Moments and Center of Mass

2020-08-21T20:21:26Z

James.kercheville: Added video links

[https://youtu.be/-ICxOk6KINQ Moments and Center of Mass of a Discrete Set of Objects] by patrickJMT

[https://youtu.be/NYUyHj3c1Xg Centroids / Centers of Mass - Part 1 of 2] by patrickJMT

[https://youtu.be/H5RcfMIZ_yw Centroids / Centers of Mass - Part 2 of 2] by patrickJMT

[https://youtu.be/H46E5yKFfNE Center of mass of the system, x-axis] by Krista King

[https://youtu.be/xf2sa5Fr1fM Center of mass of the system] by Krista King

[https://youtu.be/zuSkFdzyCO4 Centroids of Plane Regions] by Krista King

[https://youtu.be/Z3pYtlhLXBk Moments of the system] by Krista King

[https://youtu.be/JSGlBHAGvy4 Moment, Center of Mass, and Centroid - Calculus Problems] by The Organic Chemistry Tutor

[https://youtu.be/SWu_i-19Rn0 Center of Mass & Centroid Problems - Calculus] by The Organic Chemistry Tutor

Physical Applications

2020-08-21T15:39:21Z

James.kercheville: Added video links

<strong>Work Done by a Variable Force</strong>

[https://youtu.be/KRKWJre--6U Work Done by a Variable Force] by Krista King

[https://youtu.be/LbAxcMQ7J6c Work Done By a Variable Force Physics Problems, Force Displacement Graphs - Calculus] by The Organic Chemistry Tutor

[https://youtu.be/TLw8xbmnY3c Work Problems - Calculus] by The Organic Chemistry Tutor

<strong>Work (Rope/Cable Problems)</strong>

[https://youtu.be/YMaR5KJj2zQ Ex 1: Integration Application - Work Lifting an Object] by James Sousa

[https://youtu.be/pKZzfYIgq1Q Ex 2: Integration Application - Work Lifting an Object and Cable] by James Sousa

[https://youtu.be/XEwdZqz93z4 Ex: Find the Work Lifting a Leaking Bucket of Sand and Rope Given Mass] by James Sousa

[https://youtu.be/oWcN96kcbkM Finding Work using Calculus - The Cable/Rope Problem - Part b] by patrickJMT

[https://youtu.be/UJF_34TSAwQ Work done using a rope to lift a weight] by patrickJMT

[https://youtu.be/TLw8xbmnY3c Work Problems - Calculus] by The Organic Chemistry Tutor

<strong>Work (Spring Problem)</strong>

[https://youtu.be/Fd65ZxqpktE Ex: Find the Force Required to Stretch a Spring (Integration App)] by James Sousa

[https://youtu.be/x_0YWeHXZFE Work and Hooke's Law - Ex 1] by patrickJMT

[https://youtu.be/_YXA8JeGLjo Work and Hooke's Law - Ex 2] by patrickJMT

[https://youtu.be/ZKfYUxzlLx8 Work Done on Elastic Springs] by Krista King

[https://youtu.be/D5vnqohxEOI Hooke's Law Physics, Basic Introduction, Restoring Force, Spring Constant, Practice Problems] by The Organic Chemistry Tutor
[https://youtu.be/TLw8xbmnY3c Work Problems - Calculus] by The Organic Chemistry Tutor

<strong>Work (Pumping Fluid Out of a Tank)</strong>

[https://youtu.be/1x-xMf4TFNM Ex: Determine the Work Required to Pump Water Out of Trough (Isosceles Triangle)] by James Sousa

[https://youtu.be/1x-xMf4TFNM Ex: Determine the Work Required to Pump Water Out of a Circular Cylinder] by James Sousa

[https://youtu.be/fJtxJv5sdqo Calculating the Work Required to Drain a Tank] by patrickJMT

[https://youtu.be/TLw8xbmnY3c Work Problems - Calculus] by The Organic Chemistry Tutor

<strong>Hydrostatic Pressure and Force</strong>

[https://youtu.be/zSyh3IzQMdc Ex: Find the Hydrostatic Force on a Horizontal Plate (No Calculus)] by James Sousa

[https://youtu.be/Ntk9RpCCSeM Ex: Find the Hydrostatic Force on a Semicircle Window Submerged in Water] by James Sousa

[https://youtu.be/8i7xOtAo6ws Ex: Find the Hydrostatic Force on a Dam in the Shape of a Degree 4 Polynomial] by James Sousa

[https://youtu.be/12MhraQo0TY Hydrostatic Force - Basic Idea / Deriving the Formula] by patrickJMT

[https://youtu.be/cXNmCaTod58 Hydrostatic Force - Complete Example #1] by patrickJMT

[https://youtu.be/h8kMaW2q9EM Hydrostatic Force - Complete Example #2, Part 1 of 2] by patrickJMT

[https://youtu.be/F2poHPZZBhE Hydrostatic Force - Complete Example #2, Part 2 of 2] by patrickJMT

[https://youtu.be/xTDA3H6-FAY Hydrostatic pressure] by Krista King

[https://youtu.be/FgwWPlYiZgY Hydrostatic force] by Krista King

[https://youtu.be/kkq8ruV8_Jw Introduction to Pressure & Fluids - Physics Practice Problems] by The Organic Chemistry Tutor

[https://youtu.be/3jG-hWgUJko Hydrostatic Force Problems - Calculus 2] by The Organic Chemistry Tutor

Physical Applications

2020-08-21T02:45:12Z

James.kercheville: Added video links

Integrals Resulting in Inverse Trigonometric Functions

2020-08-20T23:43:47Z

James.kercheville: Added video links

[https://youtu.be/AE-0gXXx_j0 Integration into Inverse trigonometric functions using Substitution] by The Organic Chemistry Tutor

[https://youtu.be/MdsAvt9y5ds Integrating using Inverse Trigonometric Functions] by patrickJMT

Integrals Involving Exponential and Logarithmic Functions

2020-08-20T23:41:51Z

James.kercheville: Added video link

[https://youtu.be/D9dqdbCgJQM Integrating Exponential Functions By Substitution - Antiderivatives - Calculus] by The Organic Chemistry Tutor

MAT1214

2020-08-20T23:40:36Z

James.kercheville: changed title for consistency

The textbook for this course is
[https://openstax.org/details/calculus-volume-1 Calculus (Volume 1) by Gilbert Strang, Edwin Herman, et al.]

A comprehensive list of all undergraduate math courses at UTSA can be found [https://catalog.utsa.edu/undergraduate/coursedescriptions/mat/ here].

The Wikipedia summary of [https://en.wikipedia.org/wiki/Calculus calculus and its history].

==Topics List==
{| class="wikitable sortable"
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes

|-

|Week 1

||

<div style="text-align: center;">2.2</div>

||

[[The Limit of a Function]]

||

* [[Functions|Evaluation of a function]]  including the [[Absolute Value Functions| Absolute Value]] , [[Rational Functions|Rational]] , and [[Piecewise Functions|Piecewise]] functions 
* [[Functions|Domain and Range of a Function]] 

||

*Describe the limit of a function using correct notation.
*Use a table of values to estimate the limit of a function or to identify when the limit does not exist.
*Use a graph to estimate the limit of a function or to identify when the limit does not exist.
*Define one-sided limits and provide examples.
*Explain the relationship between one-sided and two-sided limits.
*Describe an infinite limit using correct notation.
*Define a vertical asymptote.

|-

|Week 1/2

||

<div style="text-align: center;">2.3</div>

||

[[The Limit Laws]]

||

*[[FactoringPolynomials|Factoring Polynomials]] 
*[[Radicals|Identifying conjugate radical expressions]] 
*[[RationalFunctions|Simplifying rational expressions]] 
*[[Domain of a Function|Evaluating piecewise functions]] 
*[[Trigonometric Functions|The trigonometric functions]] 

||

*Recognize the basic limit laws.
*Use the limit laws to evaluate the limit of a function.
*Evaluate the limit of a function by factoring.
*Use the limit laws to evaluate the limit of a polynomial or rational function.
*Evaluate the limit of a function by factoring or by using conjugates.
*Evaluate the limit of a function by using the squeeze theorem.
*Evaluate left, right, and two sided limits of piecewise defined functions.
*Evaluate limits of the form K/0, K≠0.
*Establish and use this to evaluate other limits involving trigonometric functions.

|-

|Week 2/3

||

<div style="text-align: center;">2.4</div>

||

[[Continuity]]

||

* [[Functions|Domain and Range of a Function]] 
* [[Inequalities|Interval Notation]] 
* [[Limits of Functions|Evaluate limits]] 
* [[Limit Laws]] 
* '''[[Finding Roots of an Equation]]''' 

||

* Continuity at a point.
* Describe three kinds of discontinuities.
* Define continuity on an interval.
* State the theorem for limits of composite functions and use the theorem to evaluate limits.
* Provide an example of the intermediate value theorem.

|-

|Week 3

||

<div style="text-align: center;">4.6</div>

||

[[Limits at Infinity and Asymptotes]]

||

* [[Rational Functions|Horizontal asymptote of a function]] 
* [[Limit Laws]] 
* [[Continuity]] 

||

* Calculate the limit of a function that is unbounded.
* Identify a horizontal asymptote for the graph of a function.

||

|-

|Week 3/4

||

<div style="text-align: center;">3.1</div>

||

[[Defining the Derivative]]

||

* [[Functions|Evaluation of a function at a value]] 
* [[Linear Functions and Slope|The equation of a line and its slope]] 
* [[Limits of Functions|Evaluating limits]] 
* [[Continuity]] 

||

* Recognize the meaning of the tangent to a curve at a point.
* Calculate the slope of a secant line (average rate of change of a function over an interval).
* Calculate the slope of a tangent line.
* Find the equation of the line tangent to a curve at a point.
* Identify the derivative as the limit of a difference quotient.
* Calculate the derivative of a given function at a point.

||

|-

|Week 4

||

<div style="text-align: center;">3.2</div>

||

[[The Derivative as a Function]]

||

* [[Graphs of Equations|Graphing Functions]] 
* [[Continuity|Continuity of a function at a point]] 
* [[Defining the Derivative|The derivative represents the slope of the curve at a point]] 
* [[The Limit of Functions|When a limit fails to exist]] 
* [[Limit Laws]] 

||

* Define the derivative function of a given function.
* Graph a derivative function from the graph of a given function.
* State the connection between derivatives and continuity.
* Describe three conditions for when a function does not have a derivative.
* Explain the meaning of and compute a higher-order derivative.

||

|-

|Week 4/5

||

<div style="text-align: center;">3.3</div>

||

[[Differentiation Rules]]

||

* [[Simplifying Radicals|Radical & Rational Exponents]] 
* [[Simplifying Exponents|Re-write negative exponents]] 
* [[Limit Laws]] 
* [[The Derivative as a Function]] 

||

* State the constant, constant multiple, and power rules.
* Apply the sum and difference rules to combine derivatives.
* Use the product rule for finding the derivative of a product of functions.
* Use the quotient rule for finding the derivative of a quotient of functions.
* Extend the power rule to functions with negative exponents.
* Combine the differentiation rules to find the derivative of a polynomial or rational function.

||

|-

|Week 5

||

<div style="text-align: center;">3.4</div>

||

[[Derivatives_Rates_of_Change|Derivatives as Rates of Change]]

||

* [[Functions|Function evaluation at a value]] 
* [[Solving Equations|Solving an algebraic equation]] 
* '''[[Understanding of Velocity and Acceleration]]''' 
* [[Differentiation Rules]] 

||

* Determine a new value of a quantity from the old value and the amount of change.
* Calculate the average rate of change and explain how it differs from the instantaneous rate of change.
* Apply rates of change to displacement, velocity, and acceleration of an object moving along a straight line.
* Predict the future population from the present value and the population growth rate.
* Use derivatives to calculate marginal cost and revenue in a business situation.

||

|-

|Week 5

||

<div style="text-align: center;">3.5</div>

||

[[Derivatives of the Trigonometric Functions]]

||

* [[Trigonometric identities]] 
* [[Trigonometric Functions| Graphs of the Trigonometric Functions]] 
* [[Differentiation Rules|Rules for finding Derivatives]] 

||

* Find the derivatives of the sine and cosine function.
* Find the derivatives of the standard trigonometric functions.
* Calculate the higher-order derivatives of the sine and cosine.

||

|-

|Week 6

||

<div style="text-align: center;">3.6</div>
||

[[Chain_Rule|The Chain Rule]]

||

* [[Composition of Functions]] 
* [[Trigonometric Equations|Solve Trigonometric Equations]] 
* [[Differentiation Rules|Rules for finding Derivatives]] 
* [[Derivatives of the Trigonometric Functions]] 

||

* State the chain rule for the composition of two functions.
* Apply the chain rule together with the power rule.
* Apply the chain rule and the product/quotient rules correctly in combination when both are necessary.
* Recognize and apply the chain rule for a composition of three or more functions.
* Use interchangeably the Newton and Leibniz Notation for the Chain Rule.

||

|-

|Week 6

||

<div style="text-align: center;">3.7</div>

||

[[Derivatives of Inverse Functions]]

||

* [[Inverse Functions|Injective Functions]] 
* [[Inverse Functions]] 
* [[Inverse Trigonometric Functions|Customary domain restrictions for Trigonometric Functions]] 
* [[Differentiation Rules]] 
* [[The Chain Rule]] 

||

* State the Inverse Function Theorem for Derivatives.
* Apply the Inverse Function Theorem to find the derivative of a function at a point given its inverse and a point on its graph.
* Derivatives of the inverse trigonometric functions.

|-

|Week 6/7

||

<div style="text-align: center;">3.8</div>

||

[[Implicit Differentiation]]

||

* '''[[Implicit and explicit equations]]''' 
* [[Linear Equations|Linear Functions and Slope]] 
* [[Functions|Function evaluation]] 
* [[Differentiation Rules]] 
* [[The Chain Rule]] 

||

* Assuming, for example, y is implicitly a function of x, find the derivative of y with respect to x.
* Assuming, for example, y is implicitly a function of x, and given an equation relating y to x, find the derivative of y with respect to x.
* Find the equation of a line tangent to an implicitly defined curve at a point.

|-

|Week 7

||

<div style="text-align: center;">3.9</div>

||

[[Derivatives of Exponential and Logarithmic Functions]]

||

* [[Logarithmic Functions|Properties of logarithms]] 
* [[The Limit of a Function]] 
* [[Differentiation Rules]] 
* [[The Chain Rule]] 
* [[Implicit Differentiation]] 

||

* Find the derivative of functions that involve exponential functions.
* Find the derivative of functions that involve logarithmic functions.
* Use logarithmic differentiation to find the derivative of functions containing combinations of powers, products, and quotients.

|-

|Week 7/8

||

<div style="text-align: center;">4.1</div>

||

[[Related Rates]]

||

* '''Formulas for area, volume, etc''' 
* '''Similar triangles to form proportions''' 
* [[Trigonometric Functions]] 
* [[Trigonometric Identities]] 
* [[Differentiation Rules]] 
* [[Implicit Differentiation]] 

||

* Express changing quantities in terms of derivatives.
* Find relationships among the derivatives in a given problem.
* Use the chain rule to find the rate of change of one quantity that depends on the rate of change of other quantities.

|-

|Week 8

||

<div style="text-align: center;">4.2</div>

||

[[Linear Approximations and Differentials]]

||

* [[Absolute Value Function| Definition of Error in mathematics]] 
* [[Linear Equations|Slope of a Line]] 
* [[Defining the Derivative|Equation of the tangent line]] 
* [[Derivatives as Rates of Change|Leibnitz notation of the derivative]] 

||

* Approximate the function value close to the center of the linear approximation using the linearization.
* Given an expression to be evaluated/approximated, come up with the function and its linearization
* Understand the formula for the differential; how it can be used to estimate the change in the dependent variable quantity, given the small change in the independent variable quantity.
* Use the information above to estimate potential relative (and percentage) error

|-

|Week 8/9

||

<div style="text-align: center;">4.3</div>

||

[[Maxima and Minima]]

||

* '''[[Increasing and a decreasing functions]]''' 
* [[Solving Equations|Solve an algebraic equation]] 
* [[Solving Inequalities|Interval notation]] 
* [[Trigonometric Equations]] 
* [[Differentiation Rules]] 
* [[Derivatives of the Trigonometric Functions]] 
* [[Derivatives of Exponential and Logarithmic Functions]] 
* [[Continuity]] 

||
*
* Know the definitions of absolute and local extrema.
* Know what a critical point is and locate it (them).
* Use the Extreme Value Theorem to find the absolute extrema of a continuous function on a closed interval.

|-

|Week 9

||

<div style="text-align: center;">4.4</div>

||

[[Mean Value Theorem]]

||

* [[Functions|Evaluating Functions]] 
* [[Continuity]] 
* [[Defining the Derivative|Slope of a Line]] 

||

* Determine if the MVT applies given a function on an interval.
* Find c in the conclusion of the MVT (if algebraically feasible)
* Know the first 3 Corollaries of MVT (especially the 3rd)

|-

|Week 9

||

<div style="text-align: center;">4.5</div>

||

[[Derivatives and the Shape of a Graph]]

||

* [[Functions|Evaluating Functions]] 
* [[Maxima and Minima|Critical Points of a Function]] 
* [[Derivatives and the Shape of a Graph|Second Derivatives]] 

||

* Use the First Derivative Test to find intervals on which the function is increasing and decreasing and the local extrema and their type
* Use the Concavity Test (aka the Second Derivative Test for Concavity) to find the intervals on which the function is concave up and down, and point(s) of inflection
* Understand the shape of the graph, given the signs of the first and second derivatives.

|-

|Week 10

||

<div style="text-align: center;">4.7</div>

||

[[Applied Optimization Problems]]

||

* [[Mathematical Modeling]] 
* '''Formulas pertaining to area and volume''' 
* [[Functions|Evaluating Functions]] 
* [[Trigonometric Equations]] 
* [[Maxima and Minima|Critical Points of a Function]] 

||

* Set up a function to be optimized and find the value(s) of the independent variable which provide the optimal solution.

|-

|Week 10

||

<div style="text-align: center;">4.8</div>

||

[[L’Hôpital’s Rule]]

||

* [[Rational Function| Re-expressing Rational Functions ]] 
* [[The Limit of a Function|When a Limit is Undefined]] 
* [[The Derivative as a Function]] 

||

* Identify indeterminate forms produced by quotients, products, subtractions, and powers, and apply L’Hôpital’s rule in each case.
* Recognize when to apply L’Hôpital’s rule.

|-

|Week 11

||

<div style="text-align: center;">4.10</div>

||

[[Antiderivatives]]

||

* [[Inverse Functions]] 
* [[The Derivative as a Function]] 
* [[Differentiation Rule]] 
* [[Derivatives of the Trigonometric Functions]] 

||

* Find the general antiderivative of a given function.
* Explain the terms and notation used for an indefinite integral.
* State the power rule for integrals.
* Use anti-differentiation to solve simple initial-value problems.

|-

|Week 11/12

||

<div style="text-align: center;">5.1</div>

||

[[Approximating Areas]]

||

* '''[[Sigma notation]]''' 
* '''[[Area of a rectangle]]''' 
* [[Continuity]] 
* [[Toolkit Function]] 

||

* Calculate sums and powers of integers.
* Use the sum of rectangular areas to approximate the area under a curve.
* Use Riemann sums to approximate area.

|-

|Week 12

||

<div style="text-align: center;">5.2</div>

||

[[The Definite Integral]]

||

* [[Solving Inequalities|Interval notation]] 
* [[Antiderivatives]] 
* [[The Limit of a Functions|Limits of Riemann Sums]] 
* [[Continuity]] 

||

* State the definition of the definite integral.
* Explain the terms integrand, limits of integration, and variable of integration.
* Explain when a function is integrable.
* Rules for the Definite Integral.
* Describe the relationship between the definite integral and net area.
* Use geometry and the properties of definite integrals to evaluate them.
* Calculate the average value of a function.

|-

|Week 12/13

||

<div style="text-align: center;">5.3</div>

||

[[The Fundamental Theorem of Calculus]]

||

* [[The Derivative of a Function]] 
* [[Antiderivatives]] 
* [[Mean Value Theorem]] 
* [[Inverse Functions]] 

||

* Describe the meaning of the Mean Value Theorem for Integrals.
* State the meaning of the Fundamental Theorem of Calculus, Part 1.
* Use the Fundamental Theorem of Calculus, Part 1, to evaluate derivatives of integrals.
* State the meaning of the Fundamental Theorem of Calculus, Part 2.
* Use the Fundamental Theorem of Calculus, Part 2, to evaluate definite integrals.
* Explain the relationship between differentiation and integration.

|-

|Week 13

||

<div style="text-align: center;">5.4</div>

||

[[Integration Formulas and the Net Change Theorem]]

||

* [[Antiderivatives|Indefinite integrals]] 
* [[The Fundamental Theorem of Calculus|The Fundamental Theorem (part 2)]] 
* [[Toolkit Functions|Displacment vs. distance traveled]] 

||

* Apply the basic integration formulas.
* Explain the significance of the net change theorem.
* Use the net change theorem to solve applied problems.
* Apply the integrals of odd and even functions.

|-

|Week 14

||

<div style="text-align: center;">5.5</div>

||

[[Integration by Substitution]]

||

* [[The Definite Integral|Solving Basic Integrals]] 
* [[The Derivative of a Function]] 
* '''[[Change of Variables]]''' 

||

* Use substitution to evaluate indefinite integrals.
* Use substitution to evaluate definite integrals.

|-

|Week 14/15

||

<div style="text-align: center;">5.6</div>

||

[[Integrals Involving Exponential and Logarithmic Functions]]

||

* [[Exponential Functions]] 
* [[Logarithmic Functions]] 
* [[Differentiation Rules]] 
* [[Antiderivatives]] 

||

* Integrate functions involving exponential functions.
* Integrate functions involving logarithmic functions.

|-

|Week 15

||

<div style="text-align: center;">5.7</div>

||

[[Integrals Resulting in Inverse Trigonometric Functions]]

||

* [[The inverse sine, cosine and tangent functions|Trigonometric functions and their inverses]] 
* [[Inverse Functions|Injective Functions]] 
* [[The Definite Integral|Rules for Integration]] 

||

* Integrate functions resulting in inverse trigonometric functions.

||

Integration Formulas and the Net Change Theorem

2020-08-20T23:39:13Z

James.kercheville: Added video link

[https://youtu.be/df1Qr8pepx0 Net Change Theorem, Definite Integral & Rates of Change Word Problems, Calculus] by the Organic Chemistry Tutor

Arc Length and Surface Area

2020-08-20T23:37:14Z

James.kercheville: Added video links (surface areas by revolution)

[https://youtu.be/seoFxrNL85c Arc Length - Part 1 of 2] lecture video by James Sousa

[https://youtu.be/yfJB4n-IzBE Deriving the Arc Length Formula in Calculus] by patrickJMT

[https://youtu.be/PwmCZAWeRNE Arc Length] by patrickJMT

[https://youtu.be/Mz3ELMAhMxk Arc length x=g(y)] by Krista King

[https://youtu.be/tfn4cpkPHUI Arc Length] by Krista King

[https://youtu.be/DNDAwWIL5FY Arc Length Calculus Problems] by The Organic Chemistry Tutor

[https://youtu.be/4XLq-BWK5NY Surface Area of Revolution - Part 1 of 2] lecture video by James Sousa

[https://youtu.be/u-kEdDCno44 Surface Area of Revolution - Part 2 of 2 (about y-axis)] lecture video by James Sousa

[https://youtu.be/-j2eKo84Ef8 Finding Surface Area - Part 1] by patrickJMT

[https://youtu.be/Jxf_XeKsiyY Finding Surface Area - Part 2] by patrickJMT

[https://youtu.be/WlaFF-OgwJM Surface Area of Revolution] by Krista King

[https://youtu.be/VdDitAOifsY Surface Area of Revolution Example 2] by Krista King

[https://youtu.be/lQM-0Nqs9Pg Surface Area of Revolution By Integration Explained, Calculus Problems, Integral Formula, Examples] by The Organic Chemistry Tutor

Arc Length and Surface Area

2020-08-20T16:41:55Z

James.kercheville: Added video links

Volumes of Revolution, Cylindrical Shells

2020-08-20T16:11:34Z

James.kercheville: Added video links

[https://youtu.be/3B2YQbEzshg Ex 2: Volume of Revolution - The Shell Method about the y-axis] by James Sousa

[https://youtu.be/pCMkHkprN0I Volume of Revolution - The Shell Method about the x-axis] by James Sousa

[https://youtu.be/ZyFaaKhNPXo Volume of Revolution - Comparing the Washer and Shell Method] by James Sousa

[https://youtu.be/CiXME1u-oyU Volumes of Revolution using Cylindrical Shells] by patrickJMT

[https://youtu.be/V6nTsxumjgU Volumes of Revolution - Cylindrical Shells] by patrickJMT

[https://youtu.be/DQihcRym9Ew Volume of rotation: cylindrical shells about the y-axis or x] by Krista King

[https://youtu.be/Sa2FDL3hmJo Volume of rotation: cylindrical shells about the x-axis or y] by Krista King

[https://youtu.be/fE6vmorV-rA Shell Method - Volume of Revolution] by The Organic Chemistry Tutor

Determining Volumes by Slicing

2020-08-20T02:31:45Z

James.kercheville: Added video links

[https://youtu.be/ODNdwqJ7TAg Ex 2: Volume of a Solid with Known Cross Section Using Integration - Volume by Slices] by James Sousa

[https://youtu.be/LvBZ0jnAMbo Ex 3: Volume of a Solid with Known Cross Section Using Integration - Volume by Slices] by James Sousa

[https://youtu.be/BQ5sg21w-lA Ex 4: Volume of a Solid with Known Cross Section Using Integration - Volume by Slices] by James Sousa

[https://youtu.be/puSlVA6mwNQ Volumes Using Cross Sectional Slices, Ex 1] by patrickJMT

[https://youtu.be/XasIRTb5WH4 Volumes Using Cross Sections Calculus, Square, Semicircles, Rectangles, Equilateral Triangles] by The Organic Chemistry Tutor

The Limit Laws

2020-08-20T02:23:57Z

James.kercheville: Added video links

* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/The%20Limit%20Laws/MAT1214-2.3TheLimitLawsPwPt.pptx The Limit Laws] PowerPoint file created by Dr. Sara Shirinkam, UTSA.

* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/The%20Limit%20Laws/MAT1214_2.3TheLimitLawsWS1.pdf The Limit Laws Worksheet]

* [https://youtu.be/mQpU2nYG3Jw The Limit Laws Part 1] Video Lecture by Instructor Sharon, UTSA.

* [https://youtu.be/hquujjjX-3A The Limit Laws Part 2] Video Lecture by Instructor Sharon, UTSA.

* [https://youtu.be/DvND8hoNtHE The Limit Laws Part 3] Video Lecture by Instructor Sharon, UTSA.

* [https://youtu.be/KoxjCjrTrik The Limit Laws Part 4] Video Lecture by Instructor Sharon, UTSA.

* [https://youtu.be/jJsQxqU50Lw The Limit Laws Part 5] Video Lecture by Instructor Sharon, UTSA.

Area between Curves

2020-08-19T19:49:10Z

James.kercheville: Added video links

[https://youtu.be/DRFyNHdVgUA Finding Areas Between Curves] by patrickJMT

[https://youtu.be/1yxSA-FZ0gk Areas Between Curves - 2 Regions] by patrickJMT

[https://youtu.be/70NQ3ISYihw Area Between Curves - Integrating with Respect to y] by patrickJMT

[https://youtu.be/iAvF1Rn7How Finding Area by Integrating with Respect to Y] by patrickJMT

[https://youtu.be/Xne6Hv9useE Area Between Curves - Integrating with Respect to y - Part 2] by patrickJMT

[https://youtu.be/8w9l99W8ucY Area of a Region Bounded by 3 Curves (Calculus)] by patrickJMT

[https://youtu.be/AeInlCa-1Q8 Area between curves - dx] by Krista King

[https://youtu.be/fGvSy6U209Y Area between curves - dy] by Krista King

[https://youtu.be/7lrn-8FiTW0 Area between curves - sketching] by Krista King

[https://youtu.be/ltxdcegn8xc Area Between Two Curves] by The Organic Chemistry Tutor

[https://youtu.be/wXMr2YYDMiM Area Between Two Curves & Under Curve - Respect to Y & X - Calculus & Integration] by The Organic Chemistry Tutor

MAT4273

2020-08-19T19:36:18Z

James.kercheville: Completed first version of the table

The textbook(s) for this course is
[1] Undergraduate Topology, by R. H. Kasriel; topics from [2] Introduction
to Analysis by W. R. Wade (Stone-Weierstrass Theorem).

A comprehensive list of all undergraduate math courses at UTSA can be found [https://catalog.utsa.edu/undergraduate/coursedescriptions/mat/ here].

The Wikipedia summary of [https://en.wikipedia.org/wiki/Topology topology and its history].

==Topics List==
{| class="wikitable sortable"
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes

|-

|Week 1

||

<div style="text-align: center;">30-31</div>

||

[[Algebraic Structure of the Real Numbers]]

||

* [[Order of Operations]] 

||

* Review of algebraic properties of the Real Numbers

|-

|Week 1

||

<div style="text-align: center;">30-31</div>

||

[[Distance Between Two Points in the Real Numbers]]

||

* [[Absolute Value Functions| Absolute Value]] 
* [[Algebraic Structure of the Real Numbers]] 

||

* The distance between two point on the real line

|-

|Week 1

||

<div style="text-align: center;">30-31</div>

||

[[Limit of a sequence in the Real Numbers]]

||

* [[Distance Between Two Points in the Real Numbers]] 
* [[Suprema, Infima, and the Completeness Property]] 

||

* The definition of a limit of a sequence

|-

|Week 1

||

<div style="text-align: center;">30-31</div>

||

[[The Nested Interval Theorem for the Real Numbers]]

||

* [[Limit of a sequence in the Real Numbers]] 
* [[Intervals ]] 
* [[Suprema, Infima, and the Completeness Property]] 
* [[Mathematical Induction]] 

||

* The nested intervals property in the real numbers

||

|-

|Week 2

||

<div style="text-align: center;">34-38</div>

||

[[Cauchy-Schwarz Formula]]

||

* [[Absolute Value Functions| Absolute Value]] 
* [[Inequalities ]] 

||

* The Cauchy-Schwarz Formula

||

|-

|Week 2

||

<div style="text-align: center;">34-38</div>

||

[[Distance Between Two Points in Higher Dimensions]]

||

* [[Distance Between Two Points in the Real Numbers]] 

||

* Distance formula for higher dimensions

||

|-

|Week 2

||

<div style="text-align: center;">34-38</div>

||

[[Open Subsets in Higher Dimensions]]

||

* [[Sets:Operations]] 
* [[Intervals|Open Intervals ]] 
* [[Suprema, Infima, and the Completeness Property]] 

||

* Definition of an open set
* Definition of an interior point

||

|-

|Week 2

||

<div style="text-align: center;">34-38</div>

||

[[Limit Points (or Cluster Points) in Higher Dimensions]]

||

* [[Open Subsets in Higher Dimensions]] 
* [[Limit of a sequence in the Real Numbers]] 
* [[Mathematical Induction]] 

||

* Definition of a limit point (or cluster point)
* The limit point as the limit of a sequence

||

|-

|Week 3

||

<div style="text-align: center;">39-40</div>

||

[[Closed Subsets in Higher Dimensions]]

||

* [[Sets:Operations]] 
* [[Limit Points (or Cluster Points) in Higher Dimensions]]
* [[Open Subsets in Higher Dimensions]]

||

* Definition of a closed set
* Properties of a closed set

||

|-

|Week 3

||

<div style="text-align: center;">39-40</div>

||

[[Bounded sets in Higher Dimensions]]

||

* [[Closed Subsets in Higher Dimensions]]
* [[Limit Points (or Cluster Points) in Higher Dimensions]]
* [[Open Subsets in Higher Dimensions]]

||

* Definition of a bounded set
* Properties of a bounded set

||

|-

|Week 3

||

<div style="text-align: center;">39-40</div>

||

[[The Nested Interval Theorem in Higher Dimensions]]

||

* [[The Nested Interval Theorem for the Real Numbers]]
* [[Bounded sets in Higher Dimensions]]

||

* The nested intervals theorem in higher dimensions

||

|-

|Week 3

||

<div style="text-align: center;">39-40</div>

||

[[The Bolzano-Weierstrass Theorem in Higher Dimensions]]

||

* [[The Bolzano Weierstrass Theorem ]] 
* [[Bounded sets in Higher Dimensions]]

||

* The Bolzano Weierstrass Theorem in higher dimensions

||

|-

|Week 4

||

<div style="text-align: center;">41-43</div>

||

[[Convergent Sequences and the Cauchy Criterion in Higher Dimension]]

||

* [[Open Subsets in Higher Dimensions]]
* [[Limit of a sequence in the Real Numbers]]
* [[The Cauchy Criterion for Convergence]] 

||

* Definition of a convergent sequence in higher dimensions
* The Cauchy criterion for convergence of sequences in higher dimensions

||

|-

|Week 4

||

<div style="text-align: center;">41-43</div>

||

[[Heine-Borel Theorem]]

||

* [[Open Subsets in Higher Dimensions]]
* [[Intervals| Closed and Bounded sets]] 

||

* Definition of an open cover for a set
* Definition of compactness
* The Heine-Borel Theorem

||

|-

|Week 4

||

<div style="text-align: center;">41-43</div>

||

[[Lindeloff Theorem]]

||

* [[Heine-Borel Theorem]]
* [[Intervals]] 
* [[Unions and Intersections of Sets]] 

||

* The Lindeloff Theorem

||

|-

|Week 5

||

<div style="text-align: center;">45 and 75-76</div>

||

[[Topological Spaces]]

||

* [[Unions and Intersections of Sets]] 
* [[Open Subsets in Higher Dimensions]]
* [[Closed Subsets in Higher Dimensions]]

||

* Definition of a Topological space
* Examples of Topological spaces
* Basic theorems concerning topological spaces

||

|-

|Week 5

||

<div style="text-align: center;">45 and 75-76</div>

||

[[Distance Functions, Metrics]]

||

* [[Functions]] 
* [[Triangle Inequality]] 
* [[Bounded sets in Higher Dimensions]]

||

* Criteria for a function to be a distance function
* Common distance functions

||

|-

|Week 5

||

<div style="text-align: center;">45 and 75-76</div>

||

[[Metric Spaces]]

||

* [[Distance Functions, Metrics]]

||

* The definition of a metric space
* Basic examples of metric spaces

||

|-

|Week 6

||

<div style="text-align: center;">46-47</div>

||

[[Open Sets and Closed Sets in Metric Spaces]]

||

* [[Sets:Operations]] 
* [[Metric Spaces]]
* [[Open Subsets in Higher Dimensions]]
* [[Closed Subsets in Higher Dimensions]]

||

* Definition of an open set in a metric space
* Definition of a closed set in a metric space
* Basic examples of open and closed sets in metric spaces

||

|-

|Week 7

||

<div style="text-align: center;">48-49</div>

||

[[A Topology Given By A Metric]]

||

* [[Distance Functions, Metrics]]
* [[Open Sets and Closed Sets in Metric Spaces]]

||

* Typologies given by metrics

||

|-

|Week 7

||

<div style="text-align: center;">48-49</div>

||

[[Subspaces of Metric Spaces]]

||

* [[Open Sets and Closed Sets in Metric Spaces]]
* [[Metric Spaces]]

||

* Subspace topologies in metric spaces

||

|-

|Week 8

||

<div style="text-align: center;">50-52</div>

||

[[Convergent Sequences in Metric Spaces]]

||

* [[Limit of a Sequence in the Real Numbers|Sequences]] 
* [[Metric Spaces]]

||

* The Definition and basic properties of convergent sequences in a metric space

||

|-

|Week 8

||

<div style="text-align: center;">50-52</div>

||

[[Cartesian Products of Metric Spaces]]

||

* [[The Cartiesian Product]] 
* [[Bases of Open Sets|Open Sets and Closed Sets in Metric Spaces]]

||

* Product topologies

||

|-

|Week 8 and 9

||

<div style="text-align: center;">50-52</div>

||

[[Continuous Mappings Between Metric Spaces]]

||

* [[Open Subsets in Higher Dimensions]]
* [[Closed Subsets in Higher Dimensions]]
* [[Continuous Functions]] 

||

* Definition and basic properties of continuous mapping between metric spaces

||

|-

|Week 9

||

<div style="text-align: center;">53-55</div>

||

[[Separation Properties]]

||

* [[Topological Spaces]]
* [[Open/Closed sets in metric spaces]]

||

* Definition and basic examples of separations of a set

||

|-

|Week 9 and 10

||

<div style="text-align: center;">53-55</div>

||

[[Connectedness]]

||

* [[Open/Closed sets in metric spaces]]
* [[Continuous Mappings Between Metric Spaces]]

||

* Definition and basic properties of connected sets
* Invariance of connectedness under continuous mappings
* Path/polygonal connectedness

||

|-

|Week 10

||

<div style="text-align: center;">56-59</div>

||

[[Separable Metric Spaces]]

||

* [[Separation Properties]]
* [[Metric Spaces]]
* [[Convergent Sequences in Metric Spaces]]

||

* Definition and basic properties of continuous mapping between metric spaces

||

|-

|Week 10

||

<div style="text-align: center;">56-59</div>

||

[[Totally Bounded Metric Spaces]]

||

* [[Metric Spaces]]
* [[Open/Closed sets in metric spaces]]
* [[Bounded sets in Higher Dimensions]]

||

* Definition and basic properties of separable and totally bounded metric spaces

||

|-

|Week 10

||

<div style="text-align: center;">56-59</div>

||

[[Bounded Sets and Bounded Functions in a Metric Space]]

||

* [[Totally Bounded Metric Spaces]]
* [[Functions:Range]] 

||

* Basic properties of bounded sets and bounded functions in metric spaces

||

|-

|Week 11

||

<div style="text-align: center;">60-62</div>

||

[[Compactness in Metric Spaces]]

||

* [[Continuous Mappings Between Metric Spaces]]
* [[Open/Closed sets in metric spaces]]
* [[Bounded Sets and Bounded Functions in a Metric Space]]

||

* Definition and basic properties of compact sets in metric spaces
* Invariance of compactness under continuous mappings

||

|-

|Week 12

||

<div style="text-align: center;"></div>

||

[[Review]]

||

||

||

|-

|Week 13

||

<div style="text-align: center;">63-65</div>

||

[[Complete Metric Spaces]]

||

* [[The Cauchy Criterion]] 
* [[Convergent Sequences in Metric Spaces]]
* [[Bounded Sets and Bounded Functions in a Metric Space]]

||

* Definition and basic properties of complete metric spaces

||

|-

|Week 13

||

<div style="text-align: center;">63-65</div>

||

[[Baire's Theorem and Applications]]

||

* [[Open/Closed sets in metric spaces]]
* [[Separation Properties]]
* [[The Derivative]] 
* [[The Riemann Integral]] 
* [[Monotone Functions]] 

||

* Baire's Theorem for metric spaces
* Applications of Baire's Theorem for metric spaces

||

|-

|Week 14

||

<div style="text-align: center;">Edit</div>

||

[[Stone-Weierstrass Theorem]]

||

* [[Taylor and Maclaurin Series]] 
* [[Compactness in Metric Spaces]]
* [[Continuous Mappings Between Metric Spaces]]

||

* The Stone-Weierstrass Theorem

||

|-

|Week 15

||

<div style="text-align: center;">70-71</div>

||

[[The Hilbert Space L2 and the Hilbert Cube]]

||

* [[Compactness in Metric Spaces]]
* [[Open/Closed sets in metric spaces]]
* [[Infinite Series]] 

||

* Basic Topological Properties of l<sup>2</sup>.

||

|-

Integration by Substitution

2020-08-19T15:34:53Z

James.kercheville: minor edit

U-Substitution Example:
* [https://www.youtube.com/watch?v=uoCW8S-I9Es Example 1]. Produced by Professor Zachary Sharon, UTSA
* [https://www.youtube.com/watch?v=zqMxMtjbaBE Example 2]. Produced by TA Catherine Sporer, UTSA

[https://youtu.be/NFndmzYqbVA Integration by Substitution] lecture video by James Sousa

[https://youtu.be/VfvJ5C9FjcA Integration by Substitution Part 1] lecture video by James Sousa

[https://youtu.be/pmekyFVIorE Integration by Substitution Part 2] lecture video by James Sousa

[https://youtu.be/qclrs-1rpKI Integration using U-Substitution] by patrickJMT

[https://youtu.be/x06V9xuLdqg U-Substitution - More Complicated Examples] by patrickJMT

[https://youtu.be/3XOzg2-DdTA Integration by U-Substitution, Definite Integral] by patrickJMT

[https://youtu.be/FJoyIAIC1Ag U-Substitution : When Do I Have to Change the Limits of Integration?] by patrickJMT

[https://youtu.be/HHSepCzP56M U-Substitution] by Krista King

[https://youtu.be/iRIhO-w46L0 U-Substitution Example 2] by Krista King

[https://youtu.be/w1FHS-XV64Q U-Substitution Example 3] by Krista King

[https://youtu.be/gIj3objG09Q U-Substitution Example 5] by Krista King

[https://youtu.be/TlUW6ZenNXY U-Substitution Example 6] by Krista King

[https://youtu.be/W1WVFJ8iMqQ U-Substitution Example 7] by Krista King

[https://youtu.be/IAh00vU3FSY How To Integrate Using U-Substitution] by The Organic Chemistry Tutor

[https://youtu.be/0A2RlnutO8U U-Substitution Integration, Indefinite & Definite Integral - Fractions & Trig Functions Calculus] by The Organic Chemistry Tutor

Integration by Substitution

2020-08-19T15:34:24Z

James.kercheville: Added videos

U-Substitution Example:
* [https://www.youtube.com/watch?v=uoCW8S-I9Es Example 1]. Produced by Professor Zachary Sharon, UTSA
* [https://www.youtube.com/watch?v=zqMxMtjbaBE Example 2]. Produced by TA Catherine Sporer, UTSA

[https://youtu.be/NFndmzYqbVA Integration by Substitution] lecture video by James Sousa

[https://youtu.be/VfvJ5C9FjcA Integration by Substitution Part 1] lecture video by James Sousa

[https://youtu.be/pmekyFVIorE Integration by Substitution Part 2] lecture video by James Sousa

[https://youtu.be/qclrs-1rpKI Integration using U-Substitution] by patrickJMT

[https://youtu.be/x06V9xuLdqg U-Substitution - More Complicated Examples] by patrickJMT

[https://youtu.be/3XOzg2-DdTA Integration by U-Substitution, Definite Integral] by patrickJMT

[https://youtu.be/FJoyIAIC1Ag U-Substitution : When Do I Have to Change the Limits of Integration?] by patrickJMT

[https://youtu.be/HHSepCzP56M U-Substitution U-Substitution] by Krista King

[https://youtu.be/iRIhO-w46L0 U-Substitution Example 2] by Krista King

[https://youtu.be/w1FHS-XV64Q U-Substitution Example 3] by Krista King

[https://youtu.be/gIj3objG09Q U-Substitution Example 5] by Krista King

[https://youtu.be/TlUW6ZenNXY U-Substitution Example 6] by Krista King

[https://youtu.be/W1WVFJ8iMqQ U-Substitution Example 7] by Krista King

[https://youtu.be/IAh00vU3FSY How To Integrate Using U-Substitution] by The Organic Chemistry Tutor

[https://youtu.be/0A2RlnutO8U U-Substitution Integration, Indefinite & Definite Integral - Fractions & Trig Functions Calculus] by The Organic Chemistry Tutor