# MAT 137: Calculus! Slides from Sourav Sarkar's lectures (L0501)

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.
• Required videos: watch before lecture. Otherwise, you won't get anything out of it.
• Supplementary videos: further related videos. Watch before lecture if you have time; otherwise, watch after lecture.
• Textbook sections: what to read if you want further detail, additional explanations, or more examples.
1. Introduction to logic, quantifiers, definitions, and proofs

Date Topics Required videos Textbook sections (optional) Lecture slides
Mon, 9 Sep Introduction, Sets 1.1, 1.2, 1.3 1.1, 1.2 slides
Wed, 11 Sep Quantifiers, Conditionals 1.4, 1.5, 1.6, 1.7, 1.8, 1.9 1.3 slides
Mon, 16 Sep Definitions and proofs 1.10, 1.11, 1.12, 1.13 1.4 slides
Wed, 18 Sep Definitions and proofs continued, induction 1.14, 1.15 1.4, 1,2, 1.8 slides

2. Limits and continuity

Date Topics Required videos Supplementary videos Textbook sections Lecture slides
Mon, 23 Sep Distance and absolute value, intuitive idea of limit 2.4, 2.1, 2.2, 2.3 --- 1.2, 1.8 slides
Wed, 25 Sep The definition of limit, proofs from the definition of limit 2.5, 2.6, 2.7, 2.8 2.9 2.2 slides
Mon, 30 Sep Limit laws 2.10, 2.11 --- 2.3 slides
Wed, 2 Oct Squeeze theorem and more proofs with limits, continuity 2.12, 2.13, 2.14, 2.15 --- 2.3, 2.4 slides
Mon, 7 Oct More on continuity 2.16, 2.17 2.18 2.4 slides
Wed, 9 Oct Computations, IVT and EVT 2.19, 2.20, 2.21, 2.22 --- 2.1, 2.3, 2.4, 2.5 slides

3. Derivatives

Date Topics Required videos Supplementary videos Textbook sections Lecture slides
Mon, 14 Oct No Class --- --- ---
Wed, 16 Oct Definition of derivative, differentiation rules 3.1, 3.2, 3.3, 3.4, 3.5, 3.8 --- 3.1, 3.2, 3.3 slides
Mon, 21 Oct Proof of the differentiation rules 3.6, 3.7, 3.9 --- 3.1, 3.3 slides
Wed, 23 Oct The chain rule, Trig derivatives and implicit differentiation 3.10, 3.11, 3.12 --- 3.5, 3.4, 3.7 slides
Mon, 28 Oct Derivatives of exponentials and logarithms 3.13, 3.15, 3.16, 3.17, 3.18 3.14 3.4, 3.6, 3.7 slides
Wed, 30 Oct Related rates, Inverse functions 3.19, 3.20, 4.1, 4.2 --- 4.7, 1.5, 1.7 slides

4. Inverse functions and inverse trigonometric functions

Date Topics Required videos Textbook sections Lecture slides
Wed, 30 Oct Inverse functions 4.1, 4.2 1.5, 1.7 slides
Mon, 11 Nov One-to-one functions 4.3, 4.4, 4.5 1.7, 3.6 slides
Wed, 13 Nov Inverse trig functions 4.6, 4.7, 4.8 3.5 slides

5. The Mean Value Theorem and applications

Date Topics Required videos Supplementary videos Textbook sections Lecture slides
Wed, 13 Nov Local extrema 5.2, 5.3, 5.4 5.1 4.1 slides
Mon, 18 Nov Rolle's Theorem 5.5, 5.6 --- 4.2 slides
Wed, 20 Nov MVT, Monotonicity 5.7, 5.8, 5.9, 5.10, 5.11, 5.12 --- 4.2, 4.3 slides

6. Applications of the derivative

Date Topics Required videos Supplementary videos Textbook sections Lecture slides
Mon, 25 Nov Applied optimization 6.1, 6.2 --- 4.8 slides
Wed, 27 Nov Indeterminate forms and L'Hôpital's Rule 6.4, 6.5, 6.7, 6.8, 6.10 6.3, 6.6, 6.9 4.4, 4.5, 4.6 slides
Mon, 2 Dec Concavity 6.11, 6.12 --- 4.9 slides
Wed, 4 Dec Asymptotes, Curve sketching 6.13, 6.14, 6.15 6.16 2.1, 4.9 slides

7. The definition of integral

Date Topics Required videos Lecture slides
Mon, 6 Jan Sums and sigmas 7.1, 7.2 slides
Wed, 8 Jan Suprema and infima, integrable functions 7.3, 7.4, 7.5, 7.6, 7.7, 7.8, 7.9 slides
Mon, 13 Jan More integrable functions 7.5, 7.6, 7.7, 7.8, 7.9 slides
Wed, 15 Jan Riemann sums 7.10, 7.11, 7.12 slides

8. The Fundamental Theorem of Calculus

Date Topics Required videos Supplementary videos Textbook sections Lecture slides
Wed, 13 Jan Antiderivatives, indefinite integrals 8.1, 8.2 --- 5.5, 5.6 slides
Mon, 20 Jan FTC Part 1 8.3, 8.4 --- 5.6 slides
Wed, 22 Jan FTC Part 2 8.5, 8.6 8.7 5.6 slides

9. Integration methods

Note: We are skipping Videos 9.13, 9.14.

Date Topics Required videos Supplementary videos Textbook sections Lecture slides
Wed, 22 Jan Integration by substitution 9.1 9.1--9.4 6.1 slides
Mon, 27 Jan Integration by parts 9.6 9.5--9.9 6.2 slides
Wed, 29 Jan Integration of trigonometric functions, integration of rational functions 9.10, 9.15 9.10--9.12, 9,15--9.17 6.3, 6.5 slides

10. Volumes

Date Topics Required videos Textbook sections Lecture slides
Mon, 3 Feb Volumes 10.1 7.4 slides
Wed, 5 Feb Volumes 10.2 7.5 slides

11. Sequences

Date Topics Required videos Textbook sections Lecture slides
Wed, 5 Feb Sequences 11.1, 11.2 8.1, 8.2 slides
Mon, 10 Feb Properties of sequences 11.3, 11.4 8.1, 8,2 slides
Wed, 12 Feb Theorems about sequences, the Big Theorem 11.5, 11.6, 11.7, 11.8 8.2 slides

12. Improper integrals

Date Topics Required videos Supplementary videos Textbook sections Lecture slides
Mon, 24 Feb Improper integrals 12.1, 12.4 12.1--12.6 7.8, 7.9 slides
Wed, 26 Feb BCT for integrals, LCT for integrals 12.7, 12.8, 12.9, 12.10 --- 7.8, 7.9 slides

13. Series

Date Topics Required videos Supplementary videos Textbook sections Lecture slides
Mon, 2 Mar Definition of series 13.2, 13.3, 13.4 13.1 8.3 slides
Wed, 4 Mar Properties of series, properties of series 13.5, 13.6, 13.7, 13.8, 13.9 --- 8.3, 8.4 slides
Mon, 9 Mar Integral and comparison tests 13.10, 13.11, 13.12 --- 8.5, 8.7 slides
Wed, 11 Mar Alternating series, conditional and absolute convergence 13.13, 13.14, 13.15 13.16, 13.17 8.6 slides
Mon, 16 Mar Ratio test 13.18, 13.19 --- 8.7 --

14. Power series and Taylor series

Date Topics Required videos Supplementary videos Textbook sections Lecture slides
Wed, 18 Mar Power series, Taylor polynomials 14.1, 14.2, 14.3, 14.4 --- 9.1, 9.2, 9.3 --
Mon, 23 Mar Taylor series 14.5, 14.6 --- 9.1, 9.2, 9.3 --
Wed, 25 Mar Analytic functions, New power series 14.7, 14.8, 14.9, 14.10 --- 9.1, 9.2, 9.3 --
Mon, 30 March Applications 14.12, 14.14 --- 9.1, 9.2, 9.3, 9.4 --
Wed, 1 Apr Applications and outroduction 14.11, 14.13 14.15 9.1, 9.2, 9.3, 9.4 --
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