MATH 352 - Theory of Calculus - Spring 2023 Back to Main Page
Monday, January 16 MLK Day: Read this.
Wednesday, January 18 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.)
Friday, January 20 Section 2, The Rational Zeros Theorem. Notes Video Review, Finite and Infinite Sets. Notes Video
Monday, January 23 Section 2, Algebraic Numbers. Notes Video Section 3, Ordered Fields. Notes Video Section 3, Triangle Inequality. Notes Video Read Section 4.
Wednesday, January 25 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 27 Sections 7-9. Sequences: Notes (Covers four lectures.) Sequences Video 1.
Monday, January 30 Sequences continued. Sequences Video 2.
Wednesday, February 1 Sequences continued. Sequences Video 3. Supplimental Notes
Friday, February 3 Sequences continued. Sequences Video 4.
Monday, February 6 Section 10, Cauchy Sequences. Notes (Covers two lectures.) Video 1 Lim sup & lim inf examples. Sheet 1 Sheet 1
Wednesday, February 8 Cauchy Sequences continued. Video 2
Friday, February 10 Section 11. Subsequences. Notes Video
Monday, February 13 Test 1, 7 - 9 pm, Covers up through Section 11.
Wednesday, February 15 Section 12. More on lim sup and lim inf. Notes Video We skip Section 13.
Friday, February 17 Sections 14 & 15. Series. Notes (Covers two lectures.) Series Video 1
Monday, February 20 Series continued. Series Video 2 Geometric Series Examples Koch Snowflake
Wednesday, February 22 Section 17, Continuous Functions. Notes. Video.
Friday, February 24 Section 18, Theorems about Continuous Functions. Notes Video 1 Video 2
Monday, February 27 Section 19, Uniform Continuity. Notes. (Covers two lectures.) Video 1.
Wednesday, March 1 Section 19, continued. Video 2.
Friday, March 3 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, March 6 Section 23, Power Series. Notes. Video. Example 6. Video.
Wednesday, March 8 Section 24, Uniform Convergence. Notes. Video. Video for Examples Plots for Examples.
Friday, March 10 Section 25, Weierstrass M-test. Notes. Video
Monday, March 13 Spring Break!
Wednesday, March 15 Spring Break!
Wednesday, March 17 Spring Break!
Monday, March 20 Test 2, 7 - 9 pm, Neckers 156.
Wednesday, March 22 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 24 Section 26 (Part 2, Proof of Abel's Theorem). Notes Video
Monday, March 27 Section 28, The Derivative Part 1: Notes 1 Video 1
Wednesday, March 29 Section 28 Part 2: Notes 2 Video 2
Friday, March 31 Section 29: The Mean Value Theorem. Part I. Notes Video
Monday, April 3 Section 29. Part II. Notes 1 Notes 2 Video Suppliment on Concavity: Notes Video
Wednesday, April 5 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 7 Section 31: Taylor's Theorem. Notes Video
Monday, April 10 Section 31: Binomial Theorem. Notes Video Note: You can skip the subsections on Newton's Method and the Secant Method.
Wednesday, April 12 Chapter 6: Integration. Section 32. Riemann Integral: Notes Video Drawing Video
Friday, April 14 Section 32 continued. Notes Video
Monday, April 17 Section 32 continued. Notes Video Notes Video
Wednesday, April 19 Section 33. Properties of the Riemann Integral: Notes Video More Term By Term
Friday, April 21 Section 34. Fundamental Theorem of Calculus. Notes Video footnote
Monday, April 24 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 26 Section 36. Improper Integrals: Notes Video Arc Length.
Friday, April 28 Test 3, 7 - 9 pm, Neckers 156.
Monday, May 1 Student Presentations
Wednesday, May 3 Student Presentations
Friday, May 5 Student Presentations
Final Exam date and time TBA.