# 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
• 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 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

• Derivatives

 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

• 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 rates 4.5, 4.6, 4.7, 4.8 No videos Lecture 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 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