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

**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

**Limits and continuity**

Date Topics Videos to watch before lecture Slides used in lecture Thu, Sep 21 Inequalities and absolute values

Intuitive definition of limit2.4, 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 theorem2.8, 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

**Derivatives**

Date Topics Videos to watch before lecture Slides used in lecture Mon, Oct 16 Differentiability implies continuity

Proofs of differentiation rules3.5, 3.6, 3.7 Lecture 11 slides Thu, Oct 19 Higher-order derivatives

The chain rule

Derivatives of trigonometric functions3.8, 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

**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 rates4.5, 4.6, 4.7, 4.8

No videosLecture 16 slides

Related rates

**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

**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 InfinityMon, Nov 27 Limit at $\infty$ (continued)

L'Hopital's RuleNo videos Limits at Infinity (Cont.) Thu, Nov 30 L'Hopital's Rule

Curve sketchingNo videos L'Hopital's Rule Mon, Dec 4 Concavity, Curve sketching No videos Curve Sketching Thu, Dec 7 (makeup) Curve sketching (continued) No videos

**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

**The Fundamental Theorem of Calculus**

Date Topics Videos to watch before lecture Slides used in lecture Mon, Jan 15 Antiderivatives, indefinite integrals

FTC Part 18.1, 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

**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 parts9.4, 9.5, 9.6, 9.7, 9.8, 9.9 Lecture 26 slides Mon, Jan 29 Integration of trigonometric functions

Integration by trigonometric substitution9.10, 9.11, 9.12, 9.13, 9.14 Lecture 27 slides Thu, Feb 1 Trig substitution (continued)

Volumes: washer method9.15, 9.16, 9.17

No videosLecture 28 slides

Volume1Mon, Feb 5 Volumes: shell method No videos Volume2

**Sequences**

Date Topics Videos to watch before lecture Slides used in lecture Thu, Feb 8 Convergence of sequences

Bounded and monotonic sequences11.1, 11.2, 11.3, 11.4, 11.5 Lecture 29 slides Mon, Feb 12 The monotone convergence theorem for sequences

The big theorem for sequences11.6, 11.7, 11.8 Lecture 30 slides

**Improper integrals**

Date Topics Required videos Recommended videos Slides used in lecture Thu, Feb 15 Definition of improper integrals

The basic comparison test12.1, 12.4

12.7, 12.812.1--12.6

Lecture 31 slides Mon, Feb 26 The limit comparison test 12.9, 12.10 Lecture 32 slides

**Series**

Date Topics Required videos Recommended videos Slides used in lecture Thu, March 1 Definition of series

Properties of series13.2, 13.3, 13.4

13.5, 13.613.1 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 series13.10, 13.11, 13.12

13.13, 13.14Lecture 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 series13.18, 13.19

14.1, 14.2Lecture 37 slides

**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 Will be posted after lecture Thu, March 22 Taylor series

Analytic functions14.5, 14.6

14.7, 14.8Will be posted after lecture