Difference between revisions of "MAT3213"

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(Topics until end of Chapter 3.)
(Full semester topics list.)
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* [[Sequences:Subsequences|Subsequences]]
 
* [[Sequences:Subsequences|Subsequences]]
−
* [[Theorem:Monotone Subsequence]]
+
* [[Theorem:Monotone Sequence]]
 
* [[Theorem:Bolzano-Weierstrass]]
 
* [[Theorem:Bolzano-Weierstrass]]
 
* [[Sequences: Limit Superior]]
 
* [[Sequences: Limit Superior]]
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|-
 
|-
  
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| <!--Date--> Week 12  
+
| <!--Date--> Week 12
  
 
|| <!--Sections-->  
 
|| <!--Sections-->  
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4.1
 
4.1
  
−
|| <!--Topics-->  
+
|| <!--Topics-->  
  
−
* [[Cluster Points]]
+
* [[Neighborhoods in 𝐑]]
 +
* [[Cluster Points in 𝐑]]
 +
* [[RealFunctions:Limits|Limits of Real Functions]]
  
 
|| <!--Prerequisite Skills-->  
 
|| <!--Prerequisite Skills-->  
  
−
* [[Absolute Value and the Real Line|Epsilon neighborhoods]] <!--- 3213-2.2 --->
+
* [[Sequences:Convergence]] <!--- 3213-3.1 --->
−
* [[The Limit of a Sequence]] <!--- 3213-3.1 --->
+
* [[Sequences:Limits]] <!--- 3213-3.1 --->
−
 
+
* [[Sequences:Cauchy|The Cauchy Criterion]] <!--- 3213-3.5 --->
−
|| <!--Student Learning Outcomes-->
 
−
 
 
−
<!-- ------------------------------------------------------------ -->
 
−
 
 
−
|-
 
−
 
 
−
 
 
−
| <!--Date--> Week 12 
 
−
 
 
−
|| <!--Sections-->
 
−
 
 
−
4.1
 
−
 
 
−
|| <!--Topics--> 
 
−
 
 
−
* [[The Definition of the Limit of a Function]]
 
−
 
 
−
|| <!--Prerequisite Skills-->
 
−
 
 
−
* [[Cluster Point]] <!--- 3213-4.1 --->
 
−
* [[RealNumbers:Intervals|Intervals]] <!--- 3213-2.5 --->
 
  
 
|| <!--Student Learning Outcomes-->  
 
|| <!--Student Learning Outcomes-->  
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−
| <!--Date--> Week 12/13  
+
| <!--Date--> Week 13
−
 
 
−
|| <!--Sections-->
 
−
 
 
−
4.1
 
−
 
 
−
|| <!--Topics--> 
 
−
 
 
−
* [[The Sequential Criterion and Divergence Criteria]]
 
−
 
 
−
|| <!--Prerequisite Skills-->
 
−
 
 
−
* [[The Limit of a Sequence]] <!--- 3213-3.1 --->
 
−
* [[The Definition of the Limit of a Function]] <!--- 3213-4.1 --->
 
−
 
 
−
|| <!--Student Learning Outcomes-->
 
−
 
 
−
<!-- ------------------------------------------------------------ -->
 
−
 
 
−
|-
 
−
 
 
−
 
 
−
| <!--Date--> Week 13 
 
  
 
|| <!--Sections-->  
 
|| <!--Sections-->  
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|| <!--Topics-->   
 
|| <!--Topics-->   
  
−
* [[The Limit Theorems for Functions]]
+
* [[RealFunctionLimits:Sequential Criterion|The Sequential Criterion for Limits]]
 +
* [[RealFunctionLimits:Divergence Criteria|Divergence Criteria]]
  
 
|| <!--Prerequisite Skills-->  
 
|| <!--Prerequisite Skills-->  
  
−
* [[The Definition of the Limit of a Function]] <!--- 3213-4.1 --->
+
* [[Sequences:Convergence]] <!--- 3213-3.1 --->
−
* [[The Sequential Criterion and Divergence Criteria]]<!--- 3213-4.1 --->
+
* [[Sequences:Limits]] <!--- 3213-3.1 --->
  
 
|| <!--Student Learning Outcomes-->  
 
|| <!--Student Learning Outcomes-->  
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|-
 
|-
  
−
 
+
| <!--Date--> Week 14
−
| <!--Date--> Week 14  
 
  
 
|| <!--Sections-->  
 
|| <!--Sections-->  
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4.3
 
4.3
  
−
|| <!--Topics-->  
+
|| <!--Topics-->  
−
 
 
−
* [[One Sided Limits]]
 
−
 
 
−
|| <!--Prerequisite Skills-->
 
−
 
 
−
* [[The Definition of the Limit of a Function]] <!--- 3213-4.1 --->
 
−
* [[The Sequential Criterion and Divergence Criteria]]<!--- 3213-4.1 --->
 
−
 
 
−
|| <!--Student Learning Outcomes-->
 
−
 
 
−
<!-- ------------------------------------------------------------ -->
 
−
 
 
−
|-
 
−
 
 
−
| <!--Date--> Week 14/15
 
−
 
 
−
|| <!--Sections-->
 
−
 
 
−
4.3
 
−
 
 
−
|| <!--Topics--> 
 
  
−
* [[Infinite Limits and Limits at Infinity]]
+
* [[RealFunctionLimits:One-Sided|One-Sided Limits of Functions]]
 +
* [[RealFunctionLimits:Infinite|Infinite Limits of Functions]]
 +
* [[RealFunctionLimits:At Infinity|Limits of Functions at Infinity]]
  
 
|| <!--Prerequisite Skills-->  
 
|| <!--Prerequisite Skills-->  
  
−
* [[The Definition of the Limit of a Function]] <!--- 3213-4.1 --->
+
* [[RealFunctions:Limits|Limits of Real Functions]]
−
* [[The Sequential Criterion and Divergence Criteria]]<!--- 3213-4.1 --->
 
−
* [[One Sided Limits]] <!--- 3213-4.1 --->
 
  
 
|| <!--Student Learning Outcomes-->  
 
|| <!--Student Learning Outcomes-->  

Revision as of 18:30, 15 August 2020

The textbook for this course is Introduction to Real Analysis by Bartle and Sherbert

A comprehensive list of all undergraduate math courses at UTSA can be found here.

The Wikipedia summary of Real Analysis.

Topics List

Date Sections Topics Prerequisite Skills Student Learning Outcomes
Week 1

1.1


Week 2

1.2


Week 3

1.3



Week 3

2.1-2.2


Week 3

2.3-2.4


Week 4

2.5


Week 5

3.1


Week 6

3.2


Week 7
  • Review
  • Midterm exam


Week 8

3.3


Week 9

3.4


Week 10

3.5-3.6


Week 11

3.7


Week 12

4.1


Week 13

4.2


Week 14

4.3


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