Difference between revisions of "MAT1223"

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[https://openstax.org/details/books/calculus-volume-2 Calculus (Volume 2) by Gilbert Strang, Edwin Herman, et al.]
 
[https://openstax.org/details/books/calculus-volume-2 Calculus (Volume 2) by Gilbert Strang, Edwin Herman, et al.]
  
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A comprehensive list of all undergraduate math courses at UTSA can be found [https://catalog.utsa.edu/undergraduate/coursedescriptions/mat/  here].
 
  
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The Wikipedia summary of [https://en.wikipedia.org/wiki/Calculus  calculus and its history].
 
  
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==Topics List==
 
 
{| class="wikitable"
 
{| class="wikitable"
 
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
 
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes
 
|-
 
|-
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| Week 1 || <div style="text-align: center;">1.5</div> || [[Integration by Substitution]] || * [[Differentiation Rules]] < || -- 1214-3.3 -->
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| Week 1 || 1.5 || [[Integration by Substitution]] || * [[Differentiation Rules]] ||  
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* [[Linear Approximations and Differentials
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* [[Linear Approximations and Differentials]]
 
|-
 
|-
−
| Week 1 & 2 || <div style="text-align: center;">2.1</div> || [[Area between Curves]] || * [[Toolkit Functions || Graphing Elementary Functions]] <
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| Week 1 & 2 || 2.1 || [[Area between Curves]] || * [[Toolkit Functions]] || [[Graphing Elementary Functions]]  
 
|-
 
|-
−
| Week 2 || <div style="text-align: center;">2.2</div> || [[Determining Volumes by Slicing]] || * '''[[Areas of basic shapes]]''' < || -- Grades 6-12 -->
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| Week 2 || 2.2 || [[Determining Volumes by Slicing]] || * '''[[Areas of basic shapes]]''' ||  
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* '''[[Volume of a cylinder]]''' <
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* '''[[Volume of a cylinder]]'''  
 
|-
 
|-
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| Week 3 || <div style="text-align: center;">2.3</div> || [[Volumes of Revolution, Cylindrical Shells]] || * [[Toolkit Functions || Graphing elementary functions]] <
+
| Week 3 || 2.3 || [[Volumes of Revolution, Cylindrical Shells]] || * [[Toolkit Functions]] || [[Graphing elementary functions]]  
 
|-
 
|-
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| Week 3 || <div style="text-align: center;">2.4</div> || [[Arc Length and Surface Area]] || * [[Differentiation Rules]] < || -- 1214-3.3 -->
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| Week 3 || 2.4 || [[Arc Length and Surface Area]] || * [[Differentiation Rules]] ||  
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* [[The Fundamental Theorem of Calculus]] <
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* [[The Fundamental Theorem of Calculus]]  
 
|-
 
|-
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| Week 4 || <div style="text-align: center;">2.5</div> || [[Physical Applications]] || * '''[[Areas of basic shapes]]''' < || -- Grades 6-12 -->
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| Week 4 || 2.5 || [[Physical Applications]] || * '''[[Areas of basic shapes]]''' ||  
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* '''[[Volume of a cylinder]]''' <
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* '''[[Volume of a cylinder]]'''  
 
|-
 
|-
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| Week 4 & 5 || <div style="text-align: center;">2.6</div> || [[Moments and Center of Mass]] || * [[Toolkit Functions || Graphing elementary functions]] <
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| Week 4 & 5 || 2.6 || [[Moments and Center of Mass]] || * [[Toolkit Functions]] || [[Graphing elementary functions]]  
 
|-
 
|-
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| Week 5 || <div style="text-align: center;">3.1</div> || [[Integration by Parts]] || * [[Differentiation Rules]] < || -- 1214-3.3 -->
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| Week 5 || 3.1 || [[Integration by Parts]] || * [[Differentiation Rules]] ||  
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* [[Linear Approximations and Differentials
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* [[Linear Approximations and Differentials]]
 
|-
 
|-
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| Week 6 || <div style="text-align: center;">3.2</div> || [[Trigonometric Integrals]] || * [[Trigonometric Functions]] < || -- 1093-2.2 -->
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| Week 6 || 3.2 || [[Trigonometric Integrals]] || * [[Trigonometric Functions]] ||  
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* [[Properties of the Trigonometric Functions
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* [[Properties of the Trigonometric Functions]]
 
|-
 
|-
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| Week 6 & 7 || <div style="text-align: center;">3.3</div> || [[Trigonometric Substitution]] || * [[Completing the Square]] < || -- 1073-Mod 3.2-->
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| Week 6 & 7 || 3.3 || [[Trigonometric Substitution]] || * [[Completing the Square]] ||  
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* [[Trigonometric Functions]] <
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* [[Trigonometric Functions]]  
 
|-
 
|-
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| Week 7 || <div style="text-align: center;">3.4</div> || [[Partial Fractions]] || * [[Factoring Polynomials]] < || -- 1073-Mod 0.2 -->
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| Week 7 || 3.4 || [[Partial Fractions]] || * [[Factoring Polynomials]] ||  
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* [[Completing the Square]] <
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* [[Completing the Square]]  
 
|-
 
|-
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| Week 8  || <div style="text-align: center;">3.7</div> || [[Improper Integrals]] || * [[The Fundamental Theorem of Calculus]] < || -- 1214-5.3 -->
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| Week 8  || 3.7 || [[Improper Integrals]] || * [[The Fundamental Theorem of Calculus]] ||  
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* [[Integration by Substitution]] <
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* [[Integration by Substitution]]  
 
|-
 
|-
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| Week 9 || <div style="text-align: center;">5.1</div> || [[Sequences]] || * [[The Limit Laws || The Limit Laws and Squeeze Theorem]] <
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| Week 9 || 5.1 || [[Sequences]] || * [[The Limit Laws]] || [[The Limit Laws and Squeeze Theorem]]  
 
|-
 
|-
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| Week 10 || <div style="text-align: center;">5.2</div> || [[Infinite Series]] || * '''[[Sigma notation]]''' < || -- DNE (recommend 1093) -->
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| Week 10 || 5.2 || [[Infinite Series]] || * '''[[Sigma notation]]''' ||  
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* [[Sequences]] <
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* [[Sequences]]  
 
|-
 
|-
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| Week 11 || <div style="text-align: center;">5.3</div> || [[The Divergence and Integral Tests]] || * [[The Limit Laws]] < || -- 1214-2.3 -->
+
| Week 11 || 5.3 || [[The Divergence and Integral Tests]] || * [[The Limit Laws]] ||  
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* [[Limits at Infinity and Asymptotes
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* [[Limits at Infinity and Asymptotes]]
 
|-
 
|-
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| Week 11 || <div style="text-align: center;">5.4</div> || [[Comparison Tests]] || * [[Limits at Infinity and Asymptotes || Limits at Infinity]] <
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| Week 11 || 5.4 || [[Comparison Tests]] || * [[Limits at Infinity and Asymptotes]] || [[Limits at Infinity]]  
 
|-
 
|-
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| Week 12 || <div style="text-align: center;">5.5</div> || [[Alternating Series]] || * [[Limits at Infinity and Asymptotes || Limits at Infinity]] <
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| Week 12 || 5.5 || [[Alternating Series]] || * [[Limits at Infinity and Asymptotes]] || [[Limits at Infinity]]  
 
|-
 
|-
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| Week 12 || <div style="text-align: center;">5.6</div> || [[Ratio and Root Tests]] || * '''[[Factorials]]''' < || -- Grades 6-12 -->
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| Week 12 || 5.6 || [[Ratio and Root Tests]] || * '''[[Factorials]]''' ||  
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* [[Limits at Infinity and Asymptotes
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* [[Limits at Infinity and Asymptotes]]
 
|-
 
|-
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| Week 13 || <div style="text-align: center;">6.1</div> || [[Power Series and Functions]] || * [[Infinite Series || The Geometric Series Test]] <
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| Week 13 || 6.1 || [[Power Series and Functions]] || * [[Infinite Series]] || [[The Geometric Series Test]]  
 
|-
 
|-
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| Week 14 || <div style="text-align: center;">6.2</div> || [[Properties of Power Series]] || * [[Differentiation Rules]] < || -- 1214-3.3 -->
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| Week 14 || 6.2 || [[Properties of Power Series]] || * [[Differentiation Rules]] ||  
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* [[Antiderivatives]]  <
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* [[Antiderivatives]]   
 
|-
 
|-
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| Week 15 || <div style="text-align: center;">6.3</div> || [[Taylor and Maclaurin Series]] || * [[The Derivative as a Function || Higher-Order Derivatives]] <
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| Week 15 || 6.3 || [[Taylor and Maclaurin Series]] || * [[The Derivative as a Function]] || [[Higher-Order Derivatives]]  
 
|}
 
|}

Latest revision as of 15:50, 31 March 2023

The textbook for this course is Calculus (Volume 2) by Gilbert Strang, Edwin Herman, et al.


Date Sections Topics Prerequisite Skills Student Learning Outcomes
Week 1 1.5 Integration by Substitution * Differentiation Rules
Week 1 & 2 2.1 Area between Curves * Toolkit Functions Graphing Elementary Functions
Week 2 2.2 Determining Volumes by Slicing * Areas of basic shapes
Week 3 2.3 Volumes of Revolution, Cylindrical Shells * Toolkit Functions Graphing elementary functions
Week 3 2.4 Arc Length and Surface Area * Differentiation Rules
Week 4 2.5 Physical Applications * Areas of basic shapes
Week 4 & 5 2.6 Moments and Center of Mass * Toolkit Functions Graphing elementary functions
Week 5 3.1 Integration by Parts * Differentiation Rules
Week 6 3.2 Trigonometric Integrals * Trigonometric Functions
Week 6 & 7 3.3 Trigonometric Substitution * Completing the Square
Week 7 3.4 Partial Fractions * Factoring Polynomials
Week 8 3.7 Improper Integrals * The Fundamental Theorem of Calculus
Week 9 5.1 Sequences * The Limit Laws The Limit Laws and Squeeze Theorem
Week 10 5.2 Infinite Series * Sigma notation
Week 11 5.3 The Divergence and Integral Tests * The Limit Laws
Week 11 5.4 Comparison Tests * Limits at Infinity and Asymptotes Limits at Infinity
Week 12 5.5 Alternating Series * Limits at Infinity and Asymptotes Limits at Infinity
Week 12 5.6 Ratio and Root Tests * Factorials
Week 13 6.1 Power Series and Functions * Infinite Series The Geometric Series Test
Week 14 6.2 Properties of Power Series * Differentiation Rules
Week 15 6.3 Taylor and Maclaurin Series * The Derivative as a Function Higher-Order Derivatives
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