MATH 352 - Theory of Calculus - Spring 2022
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Monday, January 10
You should read Sections 1-3 in the Ross textbook.
Lecture Notes (Why this course?)
Optional Reading (someday!): The Analyst: A Discourse Addressed to an Infidel Mathematician, by George Berkeley, 1734. 
Lecture Notes (Starting Assumptions, Rational Numbers, Real Numbers.)

Wednesday, January 12
Section 2, The Rational Zeros Theorem. Notes Video
Review, Finite and Infinite Sets. Notes Video

Friday, January 14
Section 2, Algebraic Numbers. Notes Video 
Section 3, Ordered Fields. Notes Video 
Section 3, Triangle Inequality. Notes Video
Read Section 4 for next week.

Monday, January 17
MLK Day

Wednesday, January 19
Section 4: Completeness Axiom Notes Video
Optional: Proof that e is Irrational Notes Video
Read Section 5 on your own.
Section 6 is optional reading.
Start reading Section 7. This is the start of Chapter 2.

Friday, January 21
Sections 7-9. Sequences: Notes (Covers four lectures.)
Sequences Video 1.

Monday,January 24 
Sequences continued. Sequences Video 2.

Wednesday, January 26
Sequences continued.  Sequences Video 3.
Supplimental Notes

Friday, January 28
Sequences continued.  Sequences Video 4.

Monday, January 31
Section 10, Cauchy Sequences. Notes (Covers two lectures.)
Video 1
Lim sup & lim inf examples.
Sheet 1 Sheet 1 

Wednesday, February 2
Cauchy Sequences continued. Video 2

Friday, February 4
Section 11. Subsequences. Notes Video

Monday, February 7
Test 1, 7 - 9 pm, Covers up through Section 11.

Wednesday, February 9
Section 12. More on lim sup and lim inf.
Notes
Video
We skip Section 13. 

Friday, February 11
Sections 14 & 15. Series. Notes (Covers two lectures.)
Series Video 1

Monday, February 14
Series continued.
Series Video 2
Geometric Series Examples
Koch Snowflake

Wednesday, February 16
Section 17, Continuous Functions. Notes. Video. 

Friday, February 18
Section 18, Theorems about Continuous Functions. Notes Video 1  Video 2

Monday, February 21
Section 19, Uniform Continuity. Notes. (Covers two lectures.) 
Video 1.

Wednesday, February 23
Section 19, continued.
Video 2.

Friday, February 25
Section 20: Limits of Functions. Notes.  Video. 
Handout: All 15 Limit Definitions - ε-δ form
Handout: All 15 Limit Definitions - sequence form
Handout: Limit Rules Summary 
We skip Sections 21 & 22.

Monday, February 28
Section 23, Power Series. Notes. Video.
Example 6. Video.

Wednesday, March 2
Section 24, Uniform Convergence. Notes. Video.
Video for Examples Plots for Examples.

Friday, March 4
Section 25, Weierstrass M-test. Notes. Video

Monday, March 7
Spring Break!

Wednesday, March 9
Spring Break!

Wednesday, March 11
Spring Break!

Monday, March 14
Test 2, 7 - 9 pm
 
Wednesday, March 16
Section 26, Term-By-Term (part 1). Notes  Video 
Suppliment: Youtube video on arctan series
Suppliment: Video with arctan Taylor series plots (Stop after two minutes!)

Friday, March 18
Section 26 (Part 2, Proof of Abel's Theorem). Notes Video
 
Monday, March 21
Section 28, The Derivative
Part 1: Notes 1 Video 1

Wednesday, March 23
Section 28
Part 2: Notes 2 Video 2

Friday, March 25
Section 29: The Mean Value Theorem.
Part I. Notes Video

Monday, March 28
Section 29.
Part II. Notes 1  Notes 2  Video
Suppliment on Concavity: Notes Video

Wednesday, March 30
Section 30: L'Hospital's Rule.
Notes Video 1 Video 2 
Optional Reading: On L'Hôpital's Rule by Lorenzo Sudan
Extra Examples.

Friday, April 1
Section 31: Taylor's Theorem. Notes Video

Monday, April 4
Section 31: Binomial Theorem. Notes Video
Note: You can skip the subsections on Newton's Method and the Secant Method.

Wednesday, April 6
Chapter 6: Integration.
Section 32. Riemann Integral: Notes Video
                              Drawing Video 

Friday, April 8
Section 32 continued. Notes Video

Monday, April 11
Section 32 continued. Notes Video
                      Notes Video

Wednesday, April 13
Section 33. Properties of the Riemann Integral: Notes Video
More Term By Term

Friday, April 15
Section 34. Fundamental Theorem of Calculus. Notes Video footnote

Monday, April 18
Section 34 continued. Notes Video
Suppliment: Integration by Substitution
Suppliment: Integration by Parts
Optional reading: Trapiziodal Rule Error Estimate Formula
We skip Section 35.

Wednesday, April 20
Section 36. Improper Integrals: Notes Video

Friday, April 22
Arc Length.

Monday, April 25
Test 3, 7 - 9 pm

Wednesday, April 27
Student Presentations

Friday, April 29
Student Presentations

Final Exam date and time TBA.