MATH 352 - Theory of Calculus - Spring 2024 Back to Main Page
Monday, January 15 MLK Day: Read this.
Wednesday, January 17 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.) Some Experiments With AI Math Proofs (new)
Friday, January 19 Section 2, The Rational Zeros Theorem. Notes Video Review, Finite and Infinite Sets. Notes Video
Monday, January 22 Section 2, Algebraic Numbers. Notes Video Section 3, Ordered Fields. Notes Video Section 3, Triangle Inequality. Notes Video Read Section 4.
Wednesday, January 24 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 26 Sections 7-9. Sequences: Notes (Covers four lectures.) Sequences Video 1.
Monday, January 29 Sequences continued. Sequences Video 2.
Wednesday, January 31 Sequences continued. Sequences Video 3. Supplimental Notes
Friday, February 2 Sequences continued. Sequences Video 4.
Monday, February 5 Section 10, Cauchy Sequences. Notes (Covers two lectures.) Video 1 Lim sup & lim inf examples. Sheet 1 Sheet 1
Wednesday, February 7 Cauchy Sequences continued. Video 2
Friday, February 9 Section 11. Subsequences. Notes Video
Monday, February 12 Test 1, 7 - 9 pm, Covers up through Section 11.
Wednesday, February 14 Section 12. More on lim sup and lim inf. Notes Video We skip Section 13.
Friday, February 16 Sections 14 & 15. Series. Notes (Covers two lectures.) Series Video 1
Monday, February 19 Series continued. Summary of Test for Series (From one of the Stewart calculus textbooks.) Series Video 2 Geometric Series Examples Koch Snowflake (We skip Section 16.)
Wednesday, February 21 Section 17, Continuous Functions. Notes. Video.
Friday, February 23 Section 18, Theorems about Continuous Functions. Notes Video 1 Video 2
Monday, February 26 Section 19, Uniform Continuity. Notes. (Covers two lectures.) Video 1.
Wednesday, February 28 Section 19, continued. Video 2.
Friday, March 1 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 4 Section 23, Power Series. Notes. Video. Example 6. Video.
Wednesday, March 6 Section 24, Uniform Convergence. Notes. Video. Video for Examples Plots for Examples.
Friday, March 8 Section 25, Weierstrass M-test. Notes. Video
Monday, March 11 Spring Break!
Wednesday, March 13 Spring Break!
Wednesday, March 15 Spring Break!
Monday, March 18 Test 2, 7 - 9 pm, Neckers 156.
Wednesday, March 20 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 22 Section 26 (Part 2, Proof of Abel's Theorem). Notes Video
Monday, March 25 Section 28, The Derivative Part 1: Notes 1 Video 1
Wednesday, March 27 Section 28 Part 2: Notes 2 Video 2
Friday, March 29 Section 29: The Mean Value Theorem. Part I. Notes Video
Monday, April 1 Section 29. Part II. Notes 1 Notes 2 Video Figure for Theorem 10-3 Suppliment on Concavity: Notes Video
Wednesday, April 3 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 5 Section 31: Taylor's Theorem. Notes Video
Monday, April 8 Section 31: Binomial Theorem. Notes Video Note: You can skip the subsections on Newton's Method and the Secant Method.
Wednesday, April 10 Chapter 6: Integration. Section 32. Riemann Integral: Notes Video Drawing Video
Friday, April 12 Section 32 continued. Notes Video
Monday, April 15 Section 32 continued. Notes Video Notes Video
Wednesday, April 17 Section 33. Properties of the Riemann Integral: Notes Video More Term By Term
Friday, April 19 Section 34. Fundamental Theorem of Calculus. Notes Video footnote
Monday, April 22 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 24 Section 36. Improper Integrals: Notes Video . Improper Integrals: New improved notes Arc Length.
Friday, April 26 Test 3, 7 - 9 pm, Neckers 156.
Monday, April 29 Student Presentations
Wednesday, May 1 Student Presentations
Friday, May 3 Student Presentations
Final Exam date and time TBA.