# MAT 137: Calculus! Slides from Joel's lectures (LEC 0301)

I will post here the slides that I use in class, just before 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 --- --- slides
Mon, 14 Sep Sets 1.1, 1.2, 1.3 --- slides
Wed, 16 Sep Quantifiers 1.4, 1.5, 1.6 --- slides
Thu, 17 Sep Conditionals 1.7, 1.8 1.9 slides
Mon, 21 Sep Definitions and proofs 1.10, 1.11, 1.12, 1.13 --- slides
Wed, 23 Sep Induction 1.14, 1.15 --- slides

2. Limits and continuity

Date Topics Required videos Supplementary videos Lecture slides
Thu, 24 Sep Distance and absolute value 2.4 --- slides
Mon, 28 Sep Limits geometrically 2.1, 2.2, 2.3 --- slides
Wed, 30 Sep The definition of limit 2.5, 2.6 --- slides
Thu, 1 Oct Proofs from the definition of limit 2.7, 2.8 2.9 slides
Mon, 5 Oct Limit laws 2.10, 2.11 --- slides
Wed, 7 Oct Squeeze theorem and more proofs with limits 2.12, 2.13 --- slides
Thu, 8 Oct Continuity 2.14, 2.15 --- slides
Wed, 14 Oct More on continuity 2.16, 2.17 2.18 slides
Thu, 15 Oct Computations 2.19, 2.20 slides
Mon, 19 Oct IVT and EVT 2.21, 2.22 --- slides

3. Derivatives

Date Topics Required videos Supplementary videos Lecture slides
Wed, 21 Oct Definition of derivative 3.1, 3.2, 3.3 --- slides
Thu, 22 Oct Differentiation rules 3.4, 3.5, 3.8 --- slides
Mon, 26 Oct Proof of the differentiation rules 3.6, 3.7, 3.9 --- slides
Wed, 28 Oct The chain rule 3.10, 3.11 --- slides
Thu, 29 Oct Trig derivatives and implicit differentiation 3.12, 3.13 --- slides

4. Trascendental functions

Date Topics Required videos Supplementary videos Lecture slides
Mon, 2 Nov Inverse functions 4.1, 4.2 --- slides
Wed, 4 Nov Inverse functions 4.3, 4.4 --- slides
Thu, 5 Nov Exponentials and logarithms 4.5, 4.7, 4.8, 4.9 4.6, 4.10, 4.11 slides
Mon, 16 Nov Inverse trig functions 4.12, 4.13, 4.14 --- slides

5. The Mean Value Theorem and applications

Date Topics Required videos Supplementary videos Lecture slides
Wed, 18 Nov Local extrema 5.2, 5.3, 5.4 5.1 slides
Thu, 19 Nov Rolle's Theorem 5.5, 5.6 --- slides
Mon, 23 Nov MVT 5.7, 5.8, 5.9 --- slides
Wed, 25 Nov Monotonocity 5.10, 5.11 5.12 slides

6. Applications of derivatives and limits

Date Topics Required videos Supplementary videos Lecture slides
Thu, 26 Nov Related rates 6.1, 6.2 --- slides
Mon, 30 Nov Applied optimization 6.3, 6.4 --- slides
Wed, 2 Dec Indeterminate forms and L'Hôpital's Rule 6.6, 6.7, 6.9 6.5, 6.8 slides
Thu, 3 Dec Indeterminate forms and L'Hôpital's Rule 6.10, 6.12 6.11 slides
Mon, 7 Dec Concavity 6.13, 6.14 -- slides
Wed, 9 Dec Asymptotes 6.15, 6.16, 6.17 6.18 slides
Thu, 10 Dec Curve sketching --- --- slides

7. The definition of the integral

Date Topics Required videos Supplementary videos Lecture slides
Mon, 11 Jan Sums and sigmas 7.1, 7.2 --- slides
Wed, 13 Jan Suprema and infima 7.3, 7.4 --- slides
Thu, 14 Jan The definition of the integral 7.5, 7.6 --- slides
Mon, 18 Jan Examples and properties of the integral 7.7, 7.8, 7.11 --- slides
Wed, 20 Jan Integrals as limits 7.9, 7.10 --- slides

8. The Fundamental Theorem of Calculus

Date Topics Required videos Supplementary videos Lecture slides
Thu, 21 Jan Antiderivative and indefinite integrals 8.1, 8.2 --- slides
Mon, 25 Jan FTC part 1 8.3, 8.4 --- slides
Wed, 27 Jan FTC part 2 8.5, 8.6 8.7 slides

9. Integration methods

Date Topics Required videos Supplementary videos Lecture slides
Thu, 28 Jan Integration by substitution 9.1, 9.3 9.2 slides
Mon, 1 Feb Integration by parts 9.4 9.5, 9.6 slides
Wed, 3 Feb Integration of products of trigonometric functions 9.7 9.8, 9.9 slides
Thu, 4 Feb Integration of rational functions 9.10 9.11, 9.12 slides

10. Volumes

Date Topics Required videos Supplementary videos Lecture slides
Mon, 8 Feb Volume part 1 10.1 --- slides
Wed, 10 Feb Volume part 2 10.2 --- slides

11. Sequences

Date Topics Required videos Supplementary videos Lecture slides
Thu, 11 Feb Sequences 11.1, 11.2 --- slides
Mon, 22 Feb Properties of sequences 11.3, 11.4 --- slides
Wed, 24 Feb Theorems about sequences 11.5, 11.6 --- slides
Thu, 25 Feb The big theorem 11.7, 11.8 --- slides

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 slides
Wed, 3 Mar The Basic Comparison Test 12.7, 12.8 --- slides
Thus, 4 Mar The Limit Comparison Test 12.9, 12.10 --- slides

13. Series

Date Topics Required videos Supplementary videos Lecture slides
Mon, 8 Mar Definition of series 13,2, 13.3, 13.4 13.1 slides
Wed, 10 Mar Properties of series 13.5, 13.6, 13.7 --- slides
Thu, 12 Mar Properties of series 13.8, 13.9 --- slides
Mon, 15 Mar Integral test and comparison tests 13.10, 13.12 13.11 slides
Wed, 17 Mar Alternating series 13.13 13.14 slides
Thu, 19 Mar Absolute and conditional convergence 13.15 13.16, 13.17 slides
Mon, 22 Mar Ratio test 13.18, 13.19 --- slides

14. Power Series and Taylor Series

Date Topics Required videos Supplementary videos Lecture slides
Wed, 24 Mar Power series 14.1, 14.2 --- slides
Thu, 25 Mar Taylor polynomials 14.3, 14.4 --- slides
Mon, 29 Mar Taylor Series 14.5, 14.6 --- slides
Wed, 31 Mar Analytic functions 14.7, 14.8 --- slides
Thu, 1 Apr Constructing new Taylor series 14.9, 14.10 --- slides
Mon, 5 April Applications 14.12, 14.14 --- slides
Wed, 7 April Applications 14.11, 14.13 14.15 slides
Thu, 8 April Epilogue --- --- slides