# MAT 137: Calculus! Slides from Zicheng's lectures (LEC 0201)

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 or after lecture.
1. Introduction to logic, sets, notation, definitions, and proofs

Date Topics Required videos Supplementary videos Lecture slides
Thu, 10 Sep Introduction --- --- To be posted
Fri, 11 Sep Sets 1.1, 1.2, 1.3 --- slide
Mon, 14 Sep Quantifiers 1.4, 1.5, 1.6 --- slide
Thu, 17 Sep Conditionals 1.7, 1.8 1.9 slide
Fri, 18 Sep Definitions and proofs 1.10, 1.11, 1.12, 1.13 --- slide
Mon, 21 Sep Induction 1.14, 1.15 --- slide

2. Limits and continuity

Date Topics Required videos Supplementary videos Lecture slides
Thu, 24 Sep Distance and absolute value 2.4 --- slide
Fri, 25 Sep Limits geometrically 2.1, 2.2, 2.3 --- slide
Mon, 28 Sep The definition of limit 2.5, 2.6 --- slide
Thu, 1 Oct Proofs from the definition of limit 2.7, 2.8 2.9 slide
Fri, 2 Oct Limit laws 2.10, 2.11 --- slide
Mon, 5 Oct Squeeze theorem and more proofs with limits 2.12, 2.13 --- slide
Thu, 9 Oct Continuity 2.14, 2.15 --- slide
Fri, 10 Oct More on continuity 2.16, 2.17 2.18 slide
Thu, 15 Oct Computations 2.19, 2.20 --- slide
Fri, 16 Oct IVT and EVT 2.21, 2.22 --- slide

3. Derivatives

Date Topics Required videos Supplementary videos Lecture slides
Mon, 19 Oct Definition of derivative 3.1, 3.2, 3.3 --- slide
Thu, 22 Oct Differentiation rules 3.4, 3.5, 3.8 --- slide
Fri, 23 Oct Proof of the differentiation rules 3.6, 3.7, 3.9 --- slide
Mon, 26 Oct The chain rule 3.10, 3.11 --- slide
Thu, 29 Oct Trig derivatives and implicit differentiation 3.12, 3.13 --- slide

4. Trascendental functions

Date Topics Required videos Supplementary videos Lecture slides
Fri, 30 Oct Inverse functions 4.1, 4.2 --- slide
Mon, 2 Nov Inverse functions 4.3, 4.4 --- slide
Thu, 5 Nov Exponentials and logarithms 4.5, 4.7, 4.8, 4.9 4.6, 4.10, 4.11 slide
Fri, 6 Nov Inverse trig functions 4.12, 4.13, 4.14 --- slide

5. The Mean Value Theorem and applications

Date Topics Required videos Supplementary videos Lecture slides
Mon, 16 Nov Local extrema 5.2, 5.3, 5.4 5.1 slide
Thu, 19 Nov Rolle's Theorem 5.5, 5.6 --- slide
Fri, 20 Nov MVT 5.7, 5.8, 5.9 --- slide
Mon, 23 Nov Monotonocity 5.10, 5.11 5.12 slide

6. Applications of derivatives and limits

Date Topics Required videos Supplementary videos Lecture slides
Thu, 26 Nov Related rates 6.1, 6.2 --- slide
Fri, 27 Nov Applied optimization 6.3, 6.4 --- slide
Mon, 30 Nov Indeterminate forms and L'Hôpital's Rule 6.6, 6.7, 6.9 6.5, 6.8 slide
Thu, 3 Dec Indeterminate forms and L'Hôpital's Rule 6.10, 6.12 6.11 slide
Fri, 4 Dec Concavity 6.13, 6.14 -- slide
Mon, 7 Dec Asymptotes 6.15, 6.16, 6.17 6.18 slide
Thu, 10 Dec Curve sketching --- --- slide

7. The definition of integral

Date Topics Required videos Supplementary videos Lecture slides
Mon, 11 Jan Sums and sigmas 7.1, 7.2 --- slide
Thu, 14 Jan Suprema and infima 7.3, 7.4 --- slide
Fri, 15 Jan The definition of integral 7.5, 7.6 --- slide
Mon, 18 Jan Examples and properties of the integral 7.7, 7.8, 7.11 --- slide
Thu, 21 Jan Integrals as limits 7.9, 7.10 -- slide

8. The Fundamental Theorem of Calculus

Date Topics Required videos Supplementary videos Lecture slides
Fri, 22 Jan Antiderivatives and indefinite integrals 8.1, 8.2 --- slide
Mon, 25 Jan FTC - Part 1 8.3, 8.4 --- slide
Thu, 28 Jan FTC - Part 2 8.5, 8.6 8.7 slide

9. Integration methods

Date Topics Required videos Supplementary videos Lecture slides
Fri, 29 Jan Integration by substitution 9.1, 9.3 9.2 slide
Mon, 1 Feb Integration by parts 9.4 9.5, 9.6 slide
Thu, 4 Feb Integration of products of trigonometric functions 9.7 9.8, 9.9 slide
Fri, 5 Feb Integration of rational functions 9.10 9.11, 9.12 slide

10. Applications of the integral

Date Topics Required videos Supplementary videos Lecture slides
Mon, 8 Feb Volumes 10.1 --- slide
Thu, 11 Feb Volumes 10.2 --- slide

11. Sequences

Date Topics Required videos Supplementary videos Lecture slides
Fri, 12 Feb Sequences 11.1, 11.2 --- slide
Mon, 22 Feb Properties of sequences 11.3, 11.4 --- slide
Thu, 25 Feb Theorems about sequences 11.5, 11.6 --- slide
Fri, 26 Feb The Big Theorem 11.7, 11.8 --- slide

12. Improper integrals

Date Topics Required videos Supplementary videos Lecture slides
Mon, 1 Mar Improper integrals 12.1, 12.4, 12.5 12.2, 12.3, 12.6 slide
Thu, 4 Mar The Basic Comparison Test 12.7, 12.8 --- slide
Fri, 5 Mar The Limit Comparison Test 12.9, 12.10 --- slide

13. Series

Date Topics Required videos Supplementary videos Lecture slides
Mon, 8 Mar Definition of series 13,2, 13.3, 13.4 13.1 slide
Thu, 11 Mar Properties of series 13.5, 13.6, 13.7 --- slide
Fri, 12 Mar Properties of series 13.8, 13.9 --- slide
Mon, 15 Mar Integral test and comparison tests 13.10, 13.12 13.11 slide
Thu, 18 Mar Alternating series 13.13 13.14 slide
Fri, 19 Mar Absolute and conditional convergence 13.15 13.16, 13.17 slide
Mon, 22 Mar Ratio test 13.18, 13.19 --- slide

14. Power series and Taylor series

Date Topics Required videos Supplementary videos Lecture slides
Thu, 25 Mar Power series 14.1, 14.2 --- slide
Fri, 26 Mar Taylor polynomials 14.3, 14.4 --- slide
Mon, 29 Mar Taylor series 14.5, 14.6 --- slide
Thu, 1 Apr Analytic functions 14.7, 14.8 --- slide
Fri, 2 Apr GOOD FRIDAY (no class) --- --- (no class)
Mon, 5 Apr Constructing new Taylor series 14.9, 14.10 --- slide
Thu, 8 Apr Applications 14.12, 14.14 --- slide
Fri, 9 Apr Applications 14.11, 14.13 14.15 slide
Mon, 12 Apr Outroduction --- --- slide