# MAT 137: Calculus! Slides from Francisco's lectures (L0401)

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.

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

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

2. Limits and continuity

Date Topics Required videos Supplementary videos Textbook sections Lecture slides
Mon, 24 Sep Absolute value, distance and inequalities 2.4 --- 1.2, 1.8 slides
Wed, 26 Sep Limits 2.1, 2.2, 2.3, 2.5, 2.6 --- 2.1, 2.2 slides
Mon, 1 Oct Proofs from the definition of limit 2.7, 2.8 2.9 2.2 slides
Wed, 3 Oct Limit laws and squeeze theorem 2.10, 2.11, 2.12, 2.13 --- 2.3 slides
Wed, 10 Oct Continuity 2.14, 2.15, 2.16, 2.17 2.18 2.4 slides
Mon, 15 Oct Computations 2.19,2.20 --- 2.1, 2.3,2.4 slides
Wed, 17 Oct (1st part) IVT and EVT 2.21, 2.22 --- 2.5 slides

3. Derivatives

Date Topics Required videos Supplementary videos Textbook sections Lecture slides
Wed, Oct 17 (2nd part) Definition of a derivative 3.1, 3.2, 3.3 --- 3.1 slides
Mon, Oct 22 Differentiation rules 3.4, 3.5, 3.8 --- 3.2, 3.3 slides
Wed, Oct 24 Proof of the differentiation rules and the chain rule 3.6, 3.7, 3.9, 3.10 --- 3.1, 3.3, 3.5 slides
Mon, Oct 29 Trigonometric derivatives and implicit differentiation 3.11, 3.12 --- 3.4, 3.7 slides
Wed, Oct 31 Derivatives of exponentials and logarithms, and related rates 3.13, 3.15, 3.16, 3.17, 3.18, 3.19, 3.20 3.14 3.4, 3.6, 3.7, 4.7 slides

4. Inverse functions and inverse trigonometric functions

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

5. The Mean Value Theorem and applications

Date Topics Required videos Supplementary videos Textbook sections Lecture slides
Mon, Nov 19 Local extrema 5.2, 5.3, 5.4 5.1 4.1 slides
Wed, Nov 21 Rolle's Theorem and MVT 5.5, 5.6, 5.7, 5.8, 5.9 --- 4.2 slides
Mon, Nov 26 Monotonocity 5.10, 5.11, 5.12 --- 4.3 slides

6. Applications of the derivative

Date Topics Required videos Supplementary videos Textbook sections Lecture slides
Wed, Nov 28 Applied optimization, Indeterminate forms and L'Hopital's Rule 6.1, 6.2, 6.4, 6.5, 6.7 6.3, 6.6 4.4, 4.5, 4.6, 4.8 slides
Mon, Dec 3 Indeterminate forms and L'Hopital's Rule 6.8, 6.10 6.9 4.4, 4.5, 4.6 slides
Wed, Dec 5 Concavity and Asymptotes 6.11, 6.12, 6.13, 6.14, 6.15 6.16 2.1, 4.9, slides
Thu, Dec 6 Curve sketching --- --- 4.9 slides

7. The definition of integral

Date Topics Required videos Lecture slides
Mon, Jan 7 Sums and sigmas 7.1, 7.2 slides
Wed, Jan 9 Suprema and infima, and integrable functions 7.3, 7.4, 7.5, 7.6, 7.7, 7.8, 7.9 slides
Mon, Jan 14 More integrable functions 7.5, 7.6, 7.7, 7.8, 7.9 slides
Wed, Jan 16 Riemann sums + second half (see next topic) 7.10, 7.11, 7.12 slides

8. The Fundamental Theorem of Calculus

Date Topics Required videos Supplementary videos Textbook sections Lecture slides
Wed, Jan 16 First half + antiderivatives, indefinite integrals 8.1, 8.2 --- 5.5, 5.6 slides
Mon, Jan 21 FTC Part 1 8.3, 8.4 --- 5.6 slides
Wed, Jan 23 FTC Part 2 + second half (see next topic) 8.5, 8.6 8.7 5.6 slides

9. Integration methods

Date Topics Required videos Supplementary videos Textbook sections Lecture slides
Wed, Jan 23 First half (see previous topic) + Integration by substitution 9.1 9.2-9.4 6.1 slides
Mon, Jan 28 Integration by parts 9.6 9.5-9.9 6.2 slides
Wed, Jan 30 Integration of trigonometric and rational functions 9.10,9.15 9.11-9.12 and 9.16-9.17 6.3, 6.5 slides

10. Volumes

Date Topics Required videos Supplementary videos Textbook sections Lecture slides Special announcement
Mon, Feb 4 Volumes 10.1 --- 7.4 slides ---
Fri, Feb 8 Volumes + second half (see next topic) 10.2, 11.1,11.2 --- 7.5 slides Make up lecture at MP 102, 4-6pm

11. Sequences

Date Topics Required videos Supplementary videos Textbook sections Lecture slides Special announcement
Fri, Feb 8 Sequences + first half (see previous topic) 10.2, 11.1,11.2 --- 8.1,8.2 slides Make up lecture at MP 102, 4-6pm
Mon, Feb 11 Properties of sequences 11.3,11.4 --- 8.1,8.2 slides ---
Wed, Feb 13 Theorems about sequences 11.5-11.8 --- 8.2 slides ---

12. Improper integrals

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

13. Series

Date Topics Required videos Supplementary videos Textbook sections Lecture slides
Mon, March 4 Definition of series 13.2--13.4 13.1 8.3 slides
Wed, March 6 Properties of series 13.5--13.9 --- 8.3,8.4 slides
Mon, March 11 Integral and comparison tests 13.10--13.12 --- 8.5,8.7 slides
Wed, March 13 Alternating series and conditional and absolute convergence 13.13--13.15 13.16,13.17 8.6 slides
Mon, March 18 Ratio test 13.18--13.19 --- 8.7 slides

14. Power series and Taylor series

Date Topics Required videos Supplementary videos Textbook sections Lecture slides
Wed, March 20 Power series and Taylor polynomials 14.1--14.4 --- 9.1, 9.2, 9.3 slides
Mon, March 25 Taylor series 14.5, 14.6 --- 9.1, 9.2, 9.3 slides
Wed, March 27 Analytic functions and new power series 14.7--14.10 --- 9.1, 9.2, 9.3 slides
Mon, April 1 Applications 14.12, 14.14 --- 9.1, 9.2, 9.3, 9.4 slides
Wed, April 3 Applications 14.11, 14.13, 14.15 --- 9.1, 9.2, 9.3, 9.4 slides