MATH 352 - Theory of Calculus - Online Lectures Back to Main Page Under Construction!
Monday, January 18 MLK Day
Wednesday, January 20 Introduction: I will send a Zoom invation to the class. 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 22 Section 2, The Rational Zeros Theorem. Notes Video Review, Finite and Infinite Sets. Notes Video
Monday, January 25 Section 2, Algebraic Numbers. Notes Video Section 3, Ordered Fields. Notes Video Section 3, Triangle Inequality. Notes Video Read Section 4 before the next lecture.
Wednesday, January 27 Section 4: Completeness Axion 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 29 Sections 7-9. Sequences: Notes (Covers four lectures.) Sequences Video 1.
Monday, February 1 Sequences continued. Sequences Video 2.
Wednesday, February 3 Sequences continued. Sequences Video 3. Supplimental Notes
Friday, February 5 Sequences continued. Sequences Video 4.
Monday, February 8 Section 10, Cauchy Sequences. Notes (Covers two lectures.) Video 1 Lim sup & lim inf examples.
Wednesday, February 10 Cauchy Sequences continued. Video 2
Friday, February 12 Section 11. Subsequences. Notes Video
Monday, February 15 Section 12. More on lim sup and lim inf. Notes Video We skip Section 13.
Wednesday, February 17 Sections 14 & 15. Series. Notes (Covers two lectures.) Series Video 1
Friday, February 19 Series continued. Series Video 2 Geometric Series Examples Koch Snowflake
Monday, February 22 Section 17, Continuous Functions. Notes. Video.
Wednesday, February 24 Section 18, Theorems about Continuous Functions. Notes Video 1 Video 2
Friday, February 26 Section 19, Uniform Continuity. Notes. (Covers two lectures.) Video 1.
Monday, March 1 Test 1, 7 pm - 9 pm. Review Sheet. (Sent)
Wednesday, March 3 Section 19, continued. Video 2.
Friday, March 5 Hwk Set 6 Due Date Delayed Until 3/5 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 8 Section 23, Power Series. Notes. Video. Example 6. Video.
Wednesday, March 10 Section 24, Uniform Convergence. Notes. Video. Video for Examples Plots for Examples.
Friday, March 12 Section 25, Weierstrass M-test. Notes. Video
Monday, March 15 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!)
Wednesday, March 17 Section 26 (Part 2, Proof of Abel's Theorem). Notes Video
Friday, March 19 Section 28, The Derivative Part 1: Notes 1 Video 1
Monday, March 22 Section 28 Part 2: Notes 2 Video 2
Wednesday, March 24 Section 29: The Mean Value Theorem. Part I. Notes Video
Friday, March 26 Section 29 Part II. Notes 1 Notes 2 Video Suppliment on Concavity: Notes Video
Monday, March 29 Section 30: L'Hospital's Rule. Notes Video 1 Video 2 Optional Reading: On L'Hôpital's Rule by Lorenzo Sudan Extra Examples.
Wednesday, March 31 Section 31: Taylor's Theorem. Notes Video
Friday, April 2 Section 31: Binomial Theorem. Notes Video Note: You can skip the subsections on Newton's Method and the Secant Method.
Monday, April 5 Test 2. 7 pm - 9 pm.
Wednesday, April 7 Chapter 6: Integration. Section 32. Riemann Integral: Notes Video Drawing Video
Friday, April 9 Section 32 continued. Notes Video
Monday, April 12 Section 32 continued. Notes Video Notes Video
Wednesday, April 14 Section 33. Properties of the Riemann Integral: Notes Video
Friday, April 16 Section 34. Fundamental Theorem of Calculus. Notes Video footnote
Monday, April 19 Section 34 continued. Notes Video Suppliment: Integration by Substitution Suppliment: Integration by Parts Optional reading: Trapiziodal Rule Error Estimate Formula
Wednesday, April 21 Section 36: Notes Video
Friday, April 23 Student Presentations
Monday, April 26 Student Presentations
Wednesday, April 28
Friday, April 30 Test 3, 7 pm - 9 pm.
Optional Final Exam, TBA.