| Math 352 | Theory of Calculus | Spring 2020 |
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You are responsible for all the material in Chapters 1-6 in Elementary Analysis: The Theory of Calculus, 2nd, by Kenneth A. Ross, Springer-Verlag except for sections 6, 13, 21, 22, and 35.
There will be three regular exams and an optional final exam. Each of the regular exams will be in the evening and you will have two hours. Exam 1 will cover Chapters 1 & 2, Exam 2 will cover Chapters 3 & 4, and Exam 3 will cover chapters 5 & 6. No books, notes or electronic devices are premitted.
Homework will be collected weekly. You will be asked to give short presentations to the class.
Each of the three regular exams will count as 25% of your course grade. Homework will count as the remaining 25%. If you take the optional final it will count as 20% of your grade with the other exams and homework counting as 20% each.
Solutions to many textbook problems can be found on the internet. I know how to find them. If you turn in work that is not your own I will lower your course grade by one letter grade. Cheating on an exam will result in a grade of F in the course.
Homework Assignments
Hwk Set 1
Hwk Set 2
Hwk Set 3
Hwk Set 4
Hwk Set 5
Hwk Set 6
Hwk Set 7 (Due Monday 3/2.)
Hwk Set 8 (Due Friday 3/6.)
Hwk Set 9 (Due Monday 3/23.)
Hwk Set 10 (Due Friday 4/3.)
Hwk Set 11 (Due Wednesday 4/8.)
Hwk Set 12 (Due Monday 4/13.)
Hwk Set 13 (Due Monday 4/20.)
Hwk Set 14 (Due Firday 5/1.)
Handouts
Finite and Infinite Sets
Algebraic and Transcendental Numbers
Summary of Calculus
Ordered Fields
Triangle Inequality
Completeness Axiom
Sequences and Finite Limits
Sequences and Infinite Limits
Experimental Field Axioms Worksheet
Cauchy Sequences (Section 10)
Subsequences (Section 11)
Series (Sections 14 & 15)
Chapter 3
Continuous Functions (Section 17)
Extreme Theorems (Section 18)
Uniform Continuity (Section 19)
Limits of Functions (Section 20) [In Progress]
*Limit Definitions (Section 20)
*Limit Rules (Section 20)
Chapter 4
Power Series (Section 23)
Uniform Convergence (Section 24)
*Plots for 24.3-5
*Example from class
Weierstrass M-Test (Section 25)
Begin Online Here
Monday, March 23: Section 26 (part 1): notes video webm Suppliment: Youtube video on arctan series Suppliment: Video with arctan plot (short) in webm format
Wednesday, March 25, (Proof of Abel's Theorem): Section 26 (part 2): notes video: mp4 webm
Friday, March 27. Section 28, Part 1: notes video: mp4 webm Section 28, Part 2: notes video: mp4 webm
Monday, March 30. Test 2. 7 pm - 10 pm.
Wednesday, April 1. Section 29: The Mean Value Theorem. Part I. notes video: mp4 webm Section 29: The Mean Value Theorem. Part II. notes 1 notes 2 webm Suppliment on Concavity: notes webm
Friday, April 3. Section 30: L'Hospital's Rule. notes webm 1 webm 2 Optional Reading: On L'Hôpital's Rule by Lorenzo Sudan Examples: here
Monday, April 6. Section 31: Taylor's Theorem. notes webm
Wednesday, April 8. Section 31: Binomial Theorem. notes webm Note: You can skip the subsections on Newton's Method and the Secant Method.
Friday, April 10. Chapter 6: Integration. Section 32. notes webm drawing webm
Monday, April 13. Section 32. notes webm
Wednesday, April 15. Section 32. notes webm notes webm
Friday, April 17. Section 33. notes webm
Monday, April 20. Section 34. notes webm footnote
Wednesday, April 22. Section 34. notes webm Suppliment: Substitution Suppliment: Integration by Parts Optional reading: Trapiziodal Rule Error Estimate Formula
Friday, April 24. Section 36: notes webm
Monday, April 27. Test 3????
Wednesday, April 29.
Friday, May 1.
Final Exam: To be arranged.
Books You Should Read Some Day
The History of the Calculus and Its Conceptual Development by Carl Boyer, 1949.
Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World by Amir Alexander, 2014.
Proofs and Refutations: The Logic of Mathematical Discovery by Imre Lakatos, 1976.
The Analyst: A Discourse Addressed to an Infidel Mathematician by George Berkeley, 1734.
