Associate Professor and
Distinguished Teaching Professor
Department of Mathematics
The University of Texas at Arlington

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 Syllabus

 Schedule

January 2016
Tuesday Thursday

 

List of Study Problems not from the textbook 

 

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First day of class

 

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To prepare for today:

Review and study Definitions 4.2.1 (limit),
4.3.1(continuity), 4.4.4 (uniform continuity),
4.4.9 (Lipschitz functions), and 5.2.1(differentiability).

Study p. 145 -- 149.
Prepare Problems 4.3.6, 4.3.8(a), 4.4.9, 5.2.2

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For today:
Study p. 145 -- 150.
Prepare Problems 5.2.3, 5.2.5

28 
Study p. 136--139 and 151--152.
Prepare Problem 5.2.9, and SP1 (in the link above)

February 2016 
Tuesday Thursday


Review the concepts, definitions, problems, examples, 
questions, and theorems that we have studied in the
course so far. Be able to state the definitions and
theorems and prove your answers to the problems
and questions.


Review p. 151--152 carefully. 
Prove the Interior Extremum Theorem (5.2.6)
Work out Problem 5.2.11 (a lemma for Darboux's Thm)
Use the results above to prove Darboux's Theorem

9
Study p. 155--158.
Prepare Problems 5.3.1(a), 5.3.2, 5.3.3, 5.3.7

11
Study p. 155--160.
Prepare Problems 5.3.5, 5.3.9, 5.3.10, 5.3.11
Find the typo in Problem 5.3.10! And do the corrected problem.

16 
Review the problems/material that we studied so far.
Read and think about the main points in Sec. 5.4 and 5.5.
Make a summary/list of the key points in those sections.
Read and think about the main points in Sec. 6.1.
Explain what the key points are in those sections.

18
Study p. 169--178.
Work out Examples 6.2.2 and 6.2.4 on your own.
Prepare Problem 6.2.1.

23

Study Sec. 6.2.
Prepare Problems 6.2.2, 6.2.3, 6.2.6 

 

25
Review Sections 6.1 and 6.2.
Understand solidly the assigned problems from Section 6.2.

March 2016  
Tuesday Thursday

1
Study Sec. 6.3
Prepare Problems 6.3.1, 6.3.4, 6.3.6(a,b)


Study Sec. 6.4
Prepare Problems 6.4.1, 6.4.2(a,b), 6.4.5;
Prove the claim in the first sentence of 6.4.5(b).

8
Study Sections 6.1--6.4 carefully again.
Be ready for a quiz on 6.2 and 6.3. 

10 
Office Hour moved to 12:30-1:30 today
Study Section 6.5
Prepare Problems 6.5.1, 6.5.2, 6.5.3

15 

SPRING BREAK

17

SPRING BREAK

22
Study again Section 6.5
Prepare Problems 6.5.4, 6.5.6, 6.5.8

24 
Study Section 6.6 (Taylor Series)
Prepare Problems 6.6.1, 6.6.2, 6.6.3
Review Section 6.5 (Power Series)

29 
Study Section 6.6 (Taylor Series)
Prepare Problems 6.6.4, 6.6.5, 6.6.6

31 
Read and think about the main points Sec. 6.7 and 6.8.
Make a summary/list of the key points in these sections.
Review Chapter 6 and be ready for a quiz on this chapter.
April 2016 
Tuesday Thursday 
5
Study Sections 7.1 and 7.2.
Prepare Problems 7.2.1, 7.2.2, 7.2.4



Study Section 7.2.
Prepare Problems 7.2.3, 7.2.5

12 
Study Sections 7.2 and 7.3.
Prepare Problems 7.2.3, 7.2.5, 7.3.1, 7.3.3

14
Review Sections 7.1--7.3.
and review the Study Problems from April 5--April 12.
Think about Problems 7.3.5 and 7.3.9
and have some good ideas on them to discuss in class.

19
Review Sections 7.1--7.3.
Have good proofs written up for Problems 7.3.5 and 7.3.9.

21 
Study Section 7.4.
Be able to prove Theorem 7.4.4.
Show how the conclusion of 7.4.4 can fail if the
convergence is not uniform but f is still integrable.
Prepare Problem 7.4.3.
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Review Sections 7.1--7.4 (including the study problems, examples, definitions, theorems, and class notes). 

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Study Section 7.5 and be able to state and prove
the famous Fundamental Theorem of Calculus (all parts).
Prepare Problems 7.5.1, 7.5.2, 7.5.4.

May 2016  
Tuesday Thursday 

3
Be ready to present Problems 7.5.1, 7.5.2, and 7.5.4.
Read through and think about the main ideas in Sections
7.6 (measure zero and Lebesgue's Theorem) and 7.7.

5

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FINAL EXAM 11 -- 1:30 PM

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