# MAT 137: Calculus! Slides from Huan'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.

For those who are interested, I highly recommend the following playlist Essence of Calculus, which will tell you what calculus is all about.

MAT137 Homepage
1. Intro to logic, quantifers, definitions, and proofs

Date Topics Videos to watch before lecture Slides used in lecture
Thu, Sep 7 Introduction+Sets 1.1, 1.2, 1.3 Lecture 1 slides
Mon, Sep 11 Negation+Quantifiers 1.4, 1.5, 1.6 Lecture 2 slides
Thu, Sep 14 Conditionals+Definitions 1.7 to 1.13 Lecture 3 slides
Mon, Sep 18 Induction 1.14, 1.15 Lecture 4 slides

2. Limits and continuity

Date Topics Videos to watch before lecture Slides used in lecture
Thu, Sep 21 Inequalities and absolute values
Intuitive definition of limit
2.4, 2.1, 2.2, 2.3 Lecture 5 slides
Mon, Sep 25 The formal definition of limit 2.5, 2.6, 2.7 Lecture 6 slides
Thu, Sep 28 More on definitions of limit
Limit laws, squeeze theorem
2.8, 2.9, 2.10, 2.11, 2.12 Lecture 7 slides
Mon, Oct 2 Continuity 2.13, 2.14, 2.15 Lecture 8 slides
Thu, Oct 5 Discontinuities, Trigonometric Limits 2.16, 2.17, 2.18 Lecture 9 slides
Thu, Oct 12 IVT, EVT, Definition of Derivative 2.19, 2.20, 3.1, 3.2, 3.3, 3.4 Lecture 10 slides

3. Derivatives

Date Topics Videos to watch before lecture Slides used in lecture
Mon, Oct 16 Differentiability implies continuity
Proofs of differentiation rules
3.5, 3.6, 3.7 Lecture 11 slides
Thu, Oct 19 Higher-order derivatives
The chain rule
Derivatives of trigonometric functions
3.8, 3.9, 3.10, 3.11 Lecture 12 slides
Mon, Oct 23 Implicit Differentiation 3.12 Lecture 13 slides
Thu, Oct 26 Exponentials and Logarithms 3.13, 3.14, 3.15, 3.16, 3.17, 3.18 Lecture 14 slides

4. Inverse functions and inverse trigonometric functions

Date Topics Videos to watch before lecture Slides used in lecture
Mon, Oct 30 Inverse Functions 4.1, 4.2, 4.3, 4.4 Lecture 15 slides
Thu, Nov 2 Inverse trigonometric functions
Related rates
4.5, 4.6, 4.7, 4.8
No videos
Lecture 16 slides
Related rates

5. The Mean Value Theorem and applications

Date Topics Videos to watch before lecture Slides used in lecture
Mon, Nov 13 Local extrema 5.1, 5.2, 5.3, 5.4 Lecture 17 slides
Thu, Nov 16 Rolle's Theorem, MVT 5.5, 5.6, 5.7, 5.8, 5.9 Lecture 18 slides
Mon, Nov 20 Increasing and decreasing functions 5.10, 5.11, 5.12 Lecture 19 slides

6. Limit at $\infty$ and L'Hospital's Rule

Date Topics Videos to watch before lecture Slides used in lecture
Thu, Nov 23 Applied optimization problems
Limit at $\infty$
No videos Applied Optimization Problems
Limits at Infinity
Mon, Nov 27 Limit at $\infty$ (continued)
L'Hopital's Rule
No videos Limits at Infinity (Cont.)
Thu, Nov 30 L'Hopital's Rule
Curve sketching
No videos L'Hopital's Rule
Mon, Dec 4 Concavity, Curve sketching No videos Curve Sketching
Thu, Dec 7 (makeup) Curve sketching (continued) No videos

7. The Definition of Integral

Date Topics Videos to watch before lecture Slides used in lecture
Thu, Jan 4 Sums and sigmas, suprema, infima 7.1, 7.2, 7.3, 7.4 Lecture 20 slides
Mon, Jan 8 Integrable functions 7.5, 7.6, 7.7, 7.8, 7.9 Lecture 21 slides
Thu, Jan 11 Integrable functions, Riemann sums 7.5 to 7.12 Lecture 22 slides

8. The Fundamental Theorem of Calculus

Date Topics Videos to watch before lecture Slides used in lecture
Mon, Jan 15 Antiderivatives, indefinite integrals
FTC Part 1
8.1, 8.2, 8.3 Lecture 23 slides
Thu, Jan 18 FTC Part 1 + Part 2 8.3, 8.4, 8.5, 8.6, 8.7 Lecture 24 slides

9. Integration methods

Date Topics Videos to watch before lecture Slides used in lecture
Mon, Jan 22 Substitution rule 9.1, 9.2, 9.3 Lecture 25 slides
Thu, Jan 25 Substitution rule (continued)
Integration by parts
9.4, 9.5, 9.6, 9.7, 9.8, 9.9 Lecture 26 slides
Mon, Jan 29 Integration of trigonometric functions
Integration by trigonometric substitution
9.10, 9.11, 9.12, 9.13, 9.14 Lecture 27 slides
Thu, Feb 1 Trig substitution (continued)
Volumes: washer method
9.15, 9.16, 9.17
No videos
Lecture 28 slides
Volume1
Mon, Feb 5 Volumes: shell method No videos Volume2

10. Sequences

Date Topics Videos to watch before lecture Slides used in lecture
Thu, Feb 8 Convergence of sequences
Bounded and monotonic sequences
11.1, 11.2, 11.3, 11.4, 11.5 Lecture 29 slides
Mon, Feb 12 The monotone convergence theorem for sequences
The big theorem for sequences
11.6, 11.7, 11.8 Lecture 30 slides

11. Improper integrals

Date Topics Required videos Recommended videos Slides used in lecture
Thu, Feb 15 Definition of improper integrals
The basic comparison test
12.1, 12.4
12.7, 12.8
12.1--12.6
Lecture 31 slides
Mon, Feb 26 The limit comparison test 12.9, 12.10 Lecture 32 slides

12. Series

Date Topics Required videos Recommended videos Slides used in lecture
Thu, March 1 Definition of series
Properties of series
13.2, 13.3, 13.4
13.5, 13.6
13.1 Lecture 33 slides
Mon, March 5 The divergence test 13.7, 13.8, 13.9 Lecture 34 slides
Thu, March 8 Integral test and comparison test
Alternating series
13.10, 13.11, 13.12
13.13, 13.14
Lecture 35 slides
Mon, March 12 Absolute and conditional convergence 13.15 13.6, 13.7 Lecture 36 slides
Thu, March 15 The ratio test
Power series
13.18, 13.19
14.1, 14.2
Lecture 37 slides

13. Power series and Taylor series

Date Topics Required videos Recommended videos Slides used in lecture
Mon, March 19 Taylor polynomials 14.3, 14.4 Taylor Series Lecture 38 slides
Thu, March 22 Taylor series
Analytic functions
14.5, 14.6
14.7, 14.8
Lecture 39 slides
Mon, March 26 New power series 14.9, 14.10 Lecture 40 slides
Thu, March 29 Applications 14.11, 14.12, 14.13, 14.14 Lecture 41 slides
Mon, April 2 Applications 14.5 Lecture 42 slides