# MAT 137: Calculus! Slides from Boris Khesin's lectures (L0301)

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.

Here is the link to the main website of MAT 137 Y.

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

Date Topics Required videos Textbook sections Lecture slides
Fri, 7 Sep Introduction --- --- Sep. 7 slides
Mon, 10 Sep Sets 1.1, 1.2, 1.3 1.1, 1.2 Sep. 10 slides
Wed, 12 Sep Quantifiers 1.4, 1.5, 1.6 1.3 Sep. 12 slides
Fri, 14 Sep Conditionals 1.7, 1.8, 1.9 1.3 Sep. 14 slides
Mon, 17 Sep Definitions and proofs 1.10, 1.11, 1.12, 1.13 1.4 Sep. 17 slides
Wed, 19 Sep Induction 1.14, 1.15 1.4 Sep. 19 slides

2. Limits and continuity

Date Topics Required videos Supplementary videos Textbook sections Lecture slides
Fri, 21 Sep Distance and absolute value 2.4 --- 1.2, 1.8 Sep. 21 slides
Mon, 24 Sep The intuitive idea of limit 2.1, 2.2, 2.3 --- 2.1 Sep. 24 slides
Wed, 26 Sep The definition of limit 2.5, 2.6 --- 2.2 Sep. 26 slides
Fri, 28 Sep Proofs from the definition of limit 2.7, 2.8 2.9 2.2 Sep. 28 slides
Mon, 1 Oct Limit laws 2.10, 2.11 --- 2.3 Oct. 1 slides
Wed, 3 Oct Squeeze theorem and more proofs with limits 2.12, 2.13 --- 2.3 Oct. 3 slides
Fri, 5 Oct Continuity 2.14, 2.15 --- 2.4 Oct. 5 slides
Wed, 10 Oct More on continuity 2.16, 2.17 2.18 2.4 Oct. 10 slides
Fri, 12 Oct Computations 2.19, 2.20 --- 2.1, 2.3, 2.4 Oct. 12 slides
Mon, 15 Oct IVT and EVT 2.21, 2.22 --- 2.5 Oct. 15 slides

3. Derivatives

Date Topics Required videos Supplementary videos Textbook sections Lecture slides
Wed, 17 Oct Definition of derivative 3.1, 3.2, 3.3 --- 3.1 Oct. 17 slides
Fri, 19 Oct Differentiation rules 3.4, 3.5, 3.8 --- 3.2, 3.3 Oct. 19 slides
Mon, 22 Oct Proof of the differentiation rules 3.6, 3.7, 3.9 --- 3.1, 3.3 Oct. 22 slides
Wed, 24 Oct The chain rule 3.10 --- 3.5 Oct. 24 slides
Fri, 26 Oct Trig derivatives and implicit differentiation 3.11, 3.12 --- 3.4, 3.7 Oct. 26 slides
Mon, 29 Oct Derivatives of exponentials and logarithms 3.13, 3.15, 3.16, 3.17, 3.18 3.14 3.4, 3.6, 3.7 Oct. 29 slides
Wed, 31 Oct Related rates 3.19, 3.20 --- 4.7 Oct. 31 slides

4. Inverse functions and inverse trigonometric functions

Date Topics Required videos Textbook sections Lecture slides
Fri, 2 Nov Inverse functions 4.1, 4.2 1.5, 1.7 Nov. 2 slides
Mon, 12 Nov One-to-one functions 4.3, 4.4, 4.5 1.7, 3.6 Nov. 12 slides
Wed, 14 Nov Inverse trig functions 4.6, 4.7, 4.8 3.5 Nov. 14 slides

5. The Mean Value Theorem and applications

Date Topics Required videos Supplementary videos Textbook sections Lecture slides
Fri, 16 Nov Local extrema 5.2, 5.3, 5.4 5.1 4.1 Nov. 16 slides
Mon, 19 Nov Rolle's Theorem 5.5, 5.6 --- 4.2 Nov. 19 slides
Wed, 21 Nov MVT 5.7, 5.8, 5.9 --- 4.2 Nov. 21 slides
Fri, 23 Nov Monotonicity 5.10, 5.11, 5.12 --- 4.3 Nov. 23 slides

6. Applications of the derivative

Date Topics Required videos Supplementary videos Textbook sections Lecture slides
Mon, 26 Nov Applied optimization 6.1, 6.2 --- 4.8 Nov. 26 slides
Wed, 28 Nov Indeterminate forms and L'Hôpital's Rule 6.4, 6.5, 6.7 6.3, 6.6 4.4, 4.5, 4.6 Nov. 28 slides
Fri, 30 Nov Indeterminate forms and L'Hôpital's Rule 6.8, 6.10 6.9 4.4, 4.5, 4.6 Nov. 30 slides
Mon, 3 Dec Concavity and asymptotes 6.11, 6.12, 6.13, 6.14, 6.15 6.16 2.1, 4.9 Dec. 3 slides
Wed, 5 Dec Curve sketching --- --- 4.9 Dec. 5 slides

7. The definition of integral

Date Topics Required videos Lecture slides
Mon, 7 Jan Sums and sigmas 7.1, 7.2 Jan. 7 slides
Wed, 9 Jan Suprema and infima 7.3, 7.4 Jan. 9 slides
Fri, 11 Jan Integrable functions 7.5, 7.6, 7.7, 7.8, 7.9 Jan. 11 slides
Mon, 14 Jan More integrable functions 7.5, 7.6, 7.7, 7.8, 7.9 Jan. 14 slides
Wed, 16 Jan Riemann sums 7.10, 7.11, 7.12 Jan. 16 slides

8. The Fundamental Theorem of Calculus

Date Topics Required videos Supplementary videos Textbook sections Lecture slides
Fri, 18 Jan Antiderivatives, indefinite integrals 8.1, 8.2 --- 5.5, 5.6 Jan. 18 slides
Mon, 21 Jan FTC Part 1 8.3, 8.4 --- 5.6 Jan. 21 slides
Wed, 23 Jan FTC Part 2 8.5, 8.6 8.7 5.6 Jan. 23 slides

9. Integration methods

Note: We are skipping Videos 9.13, 9.14.

Date Topics Required videos Supplementary videos Textbook sections Lecture slides
Fri, 25 Jan Integration by substitution 9.1 9.1--9.4 6.1 Jan. 25 slides
Mon, 28 Jan Integration by parts 9.6 9.5--9.9 6.2 Jan. 28 slides
Wed, 30 Jan Integration of trigonometric functions 9.10 9.10--9.12 6.3 Jan. 30 slides
Fri, 1 Feb Integration of rational functions 9.15 9.15--9.17 6.5 Feb.1 slides

10. Volumes

Date Topics Required videos Supplementary videos Textbook sections Lecture slides
Mon, 4 Feb Volumes 10.1 --- 7.4 Feb.4 slides
Wed, 6 Feb Volumes 10.2 --- 7.5 Feb.6 slides

11. Sequences

Date Topics Required videos Supplementary videos Textbook sections Lecture slides
Fri, 8 Feb Sequences 11.1, 11.2 --- 8.1, 8.2 Feb.8 slides
Mon, 11 Feb Properties of sequences 11.3, 11.4 --- 8.1, 8,2 Feb.11 slides
Wed, 13 Feb Theorems about sequences 11.5, 11.6 --- 8.2 Feb.13 slides
Fri, 15 Feb The Big Theorem 11.7, 11.8 --- --- Feb.15 slides

12. Improper integrals

Date Topics Required videos Supplementary videos Textbook sections Lecture slides
Mon, 25 Feb Improper integrals 12.1, 12.4 12.1--12.6 7.8, 7.9 Feb.25 slides
Wed, 27 Feb BCT for integrals 12.7, 12.8 --- 7.8, 7.9 Feb.27 slides
Fri, 1 Mar LCT for integrals 12.9, 12.10 --- 7.8, 7.9 Mar.1 slides

13. Series

Date Topics Required videos Supplementary videos Textbook sections Lecture slides
Mon, 4 Mar Definition of series 13.2, 13.3, 13.4 13.1 8.3 Mar.4 slides
Wed, 6 Mar Properties of series 13.5, 13.6, 13.7 --- 8.3, 8.4 Mar.6 slides
Fri, 8 Mar Properties of series 13.8, 13.9 --- 8.4 Mar.8 slides
Mon, 11 Mar Integral and comparison tests 13.10, 13.11, 13.12 --- 8.5, 8.7 Mar.11 slides
Wed, 13 Mar Alternating series 13.13, 13.14 --- 8.6 Mar.13 slides
Fri, 15 Mar Conditional and absolute convergence 13.15 13.16, 13.17 8.6 Mar.15 slides
Mon, 18 Mar Ratio test 13.18, 13.19 --- 8.7 Mar.18 slides

14. Power series and Taylor series

Date Topics Required videos Textbook sections Lecture slides
Wed, 20 Mar Power series 14.1, 14.2 9.1 Mar.20 slides
Fri, 22 Mar Taylor polynomials 14.3, 14.4 9.1, 9.2, 9.3 Mar.22 slides
Mon, 25 Mar Taylor series 14.5, 14.6 9.1, 9.2, 9.3 Mar.25 slides
Wed, 27 Mar Analytic functions 14.7, 14.8 9.1, 9.2, 9.3 Mar.27 slides
Fri, 29 Mar New power series 14.9, 14.10 9.1, 9.2, 9.3 Mar.29 slides
Mon, 1 Apr Applications 14.12, 14.14 9.1, 9.2, 9.3, 9.4 Apr.1 slides
Wed, 3 Apr Applications 14.11, 14.13 9.1, 9.2, 9.3, 9.4 Apr.3 slides
Fri, 5 Apr Applications 14.15 9.4 Apr.5 slides