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**

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**

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**

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**

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