# MAT 137: "Calculus with proofs" 2021-2022 Slides from Boris Khesin's lectures (L0601)

I will post here any slides that I use in class, soon after each class. Notice that this only contains the slides, not a summary of the lectures.

My online office hours are on Wed 10am - 12pm at the address
https://utoronto.zoom.us/j/85135883710
Zoom Meeting ID: 851 3588 3710

There will be no office hours by B.Khesin on Wed Nov. 3! Please, use the in-person office hours of other instructors.

1. Intro to logic, quantifers, definitions, and proofs

Date Topics Required videos Supplementary videos Lecture slides
Thu, 9 Sep Introduction --- --- Sep. 9 slides
Tue, 14 Sep Sets 1.1, 1.2, 1.3 --- Sep. 14 slides
Wed, 15 Sep Quantifiers 1.4, 1.5, 1.6 --- Sep. 15 slides
Thu, 16 Sep Conditionals 1.7, 1.8 1.9 Sep. 16 slides
Tue, 21 Sep Definitions and proofs 1.10, 1.11, 1.12, 1.13 --- Sep. 21 slides
Wed, 22 Sep Induction 1.14, 1.15 --- Sep. 22 slides

2. Limits and continuity

Date Topics Required videos Supplementary videos Lecture slides
Thu, 23 Sep Distance and absolute value 2.4 --- Sep. 23 slides
Tue, 28 Sep Limits geometrically 2.1, 2.2, 2.3 --- Sep. 28 slides
Wed, 29 Sep The definition of limit 2.5, 2.6 --- Sep. 29 slides
Thu, 30 Sep Proofs from the definition of limit 2.7, 2.8 2.9 Sep. 30 slides
Tue, 5 Oct Limit laws 2.10, 2.11 --- Oct. 5 slides
Wed, 6 Oct Squeeze theorem and more proofs with limits 2.12, 2.13 --- Oct. 6 slides
Thu, 7 Oct Continuity 2.14, 2.15 --- Oct. 7 slides
Tue, 12 Oct More on continuity 2.16, 2.17 2.18 Oct. 12 slides
Wed, 13 Oct Computations 2.19, 2.20 --- Oct. 13 slides
Thu, 14 Oct IVT and EVT 2.21, 2.22 --- Oct. 14 slides

3. Derivatives

Date Topics Required videos Supplementary videos Lecture slides
Tue, 19 Oct Definition of derivative 3.1, 3.2, 3.3 --- Oct. 19 slides
Wed, 20 Oct Differentiation rules 3.4, 3.5, 3.8 --- Oct. 20 slides
Thu, 21 Oct Proof of the differentiation rules 3.6, 3.7, 3.9 --- Oct. 21 slides
Tue, 26 Oct The chain rule 3.10, 3.11 --- Oct. 26 slides
Wed, 27 Oct Trig derivatives and implicit differentiation 3.12, 3.13 --- Oct. 27 slides

4. Transcendental functions

Date Topics Required videos Supplementary videos Lecture slides
Thu, 28 Oct Inverse functions 4.1, 4.2 --- Oct. 28 slides
Tue, 2 Nov Inverse functions 4.3, 4.4 --- Nov. 2 slides
Wed, 3 Nov Exponentials and logarithms 4.5, 4.7, 4.8, 4.9 4.6, 4.10, 4.11 Nov. 3 slides
Thu, 4 Nov Inverse trig functions 4.12, 4.13, 4.14 --- Nov. 4 slides

5. The Mean Value Theorem and applications

Date Topics Required videos Supplementary videos Lecture slides
Tue, 16 Nov Local extrema 5.2, 5.3, 5.4 5.1 Nov. 16 slides
Wed, 17 Nov Rolle's Theorem 5.5, 5.6 --- Nov. 17 slides
Thu, 18 Nov MVT 5.7, 5.8, 5.9 --- Nov. 18 slides
Tue, 23 Nov Monotonicity 5.10, 5.11 5.12 Nov. 23 slides

6. Applications of the derivatives and limits

Date Topics Required videos Supplementary videos Lecture slides
Wed, 24 Nov Related rates 6.1, 6.2 --- Nov. 24 slides
Thu, 25 Nov Applied optimization 6.3, 6.4 --- Nov. 25 slides
Tue, 30 Nov Indeterminate forms and L'Hôpital's Rule 6.6, 6.7, 6.9 6.5, 6.8 Nov. 30 slides
Wed, 1 Dec Indeterminate forms and L'Hôpital's Rule 6.10, 6.12 6.11 Dec. 1 slides
Thu, 2 Dec Concavity 6.13, 6.14 --- Dec. 2 slides
Tue, 7 Dec Asymptotes 6.15, 6.16, 6.17 6.18 Dec. 7 slides
Wed, 8 Dec Curve sketching --- ---

7. The definition of integral

Date Topics Required videos Supplementary videos Lecture slides
Tue, 11 Jan Sums and sigmas 7.1, 7.2 ---
Wed, 12 Jan Suprema and infima 7.3, 7.4 ---
Thu, 13 Jan The definition of integral 7.5, 7.6 ---
Tue, 18 Jan Examples and properties of the integral 7.7, 7.8, 7.11 ---
Wed, 19 Jan Integral as limits 7.9, 7.10 ---

8. The Fundamental Theorem of Calculus

Date Topics Required videos Supplementary videos Lecture slides
Thu, 20 Jan Antiderivatives and indefinite integrals 8.1, 8.2 ---
Tue, 25 Jan FTC -- Part 1 8.3, 8.4 ---
Wed, 26 Jan FTC -- Part 2 8.5, 8.6 8.7

9. Integration methods
Date Topics Required videos Supplementary videos Lecture slides
Thu, 27 Jan Integration by substitution 9.1, 9.3 9.2
Tue, 1 Feb Integration by parts 9.4 9.5, 9.6
Wed, 2 Feb Integration of products of trig functions 9.7 9.8, 9.9
Thu, 3 Feb Integration of rational functions 9.10 9.11, 9.12

10. Application of Integral--Volumes

Date Topics Required videos Supplementary videos Lecture slides
Tue, 8 Feb Volumes 10.1 ---
Wed, 9 Feb Volumes 10.2 ---

11. Sequences

Date Topics Required videos Supplementary videos Lecture slides
Thu, 10 Feb Sequences 11.1, 11.2 ---
Tue, 15 Feb Properties of sequences 11.3, 11.4 ---
Wed, 16 Feb Theorems about sequences 11.5, 11.6 ---
Thu, 17 Feb The Big Theorem 11.7, 11.8 ---

12. Improper integrals

Date Topics Required videos Supplementary videos Lecture slides
Tue, 1 Mar Improper integrals 12.1, 12.4, 12.5 12.2, 12.3, 12.6
Wed, 2 Mar The Basic Comparison Test 12.7, 12.8 ---
Thu, 3 Mar The Limit Comparison Test 12.9, 12.10 ---

13. Series

Date Topics Required videos Supplementary videos Lecture slides
Tue, 8 Mar Definition of series 13.2, 13.3, 13.4 13.1
Wed, 9 Mar Properties of series 13.5, 13.6, 13.7 ---
Thu, 10 Mar Properties of series 13.8, 13.9 ---
Tue, 15 Mar Integral test and comparison tests 13.10, 13.12 13.11
Wed, 16 Mar Alternating series 13.13 13.14
Thu, 17 Mar Absolute and conditional convergence 13.15 13.16, 13.17
Tue, 22 Mar Ratio test 13.18, 13.19 ---

14. Power series and Taylor series

Date Topics Required videos Supplementary videos Lecture slides
Wed, 23 Mar Power series 14.1, 14.2 ---
Thu, 24 Mar Taylor polynomials 14.3, 14.4 ---
Tue, 29 Mar Taylor series 14.5, 14.6 ---
Wed, 30 Mar Analytic functions 14.7, 14.8 ---
Thu, 31 Mar Constructing new Taylor series 14.9, 14.10 ---
Tue, 5 Apr Applications 14.12, 14.14 ---
Wed, 6 Apr Applications 14.11, 14.13 14.15
Thu, 7 Apr Outroduction --- ---