# MAT 137: Calculus! Slides from Sourav Sarkar's lectures (LEC5101)

This is the course I am teaching in Summer 2020. I will post here any slides that I use in class. Notice that this only contains the slides, not a summary of the lectures.
• Required videos: watch before lecture. Otherwise, you won't get anything out of it.
• Supplementary videos: further related videos. Watch before lecture if you have time; otherwise, watch after lecture.
1. Introduction to logic, quantifiers, definitions, and proofs

Date Topics Required videos Supplementary videos Lecture slides
Tue. May 5 Introduction, Sets, Quantifiers 1.1-1.6 None Slides
Thur. May 7 Conditionals, Definitions, Proofs, Induction 1.7-1.15 None Slides

2. Limits and continuity

Date Topics Required videos Supplementary videos Lecture slides
Tue. May 12 Absolute Values, Inequalities, Limits and Their Formal Definition 2.1-2.6 None Slides
Thur. May 14 Formal Proofs With Limits, Limit Laws, The Squeeze Theorem, and More 2.7, 2.8, 2.10-2.13 2.9 Slides
Tue. May 19 Continuity and Limit Computations 2.14-2.17, 2.19, 2.20 2.18 Slides
Thur. May 21 IVT, EVT, Definition of Derivative, Differentiation Rules 2.21, 2.22, 3.1-3.5, 3.8 None Slides

3. Derivatives

Date Topics Required videos Supplementary videos Lecture slides
Tue. May 26 Proof of Differentiation Rules, Chain Rule, Trig. Derivatives, Implicit Differentiation 3.6, 3.7, 3.9-3.12 None Slides
Thur. May 28 Derivatives of Exponentials and Logarithms, Related Rates, Inverse Functions 3.13, 3.15-3.20, 4.1, 4.2 3.14 Slides

4. Inverse functions and inverse trigonometric functions

Date Topics Required videos Supplementary videos Lecture slides
Tue. June 2 One-to-One Functions, Inverse Trig. Functions, Local Extrema 4.3-4.8, 5.2-5.4 5.1 Slides

5. The Mean Value Theorem and applications

Date Topics Required videos Supplementary videos Lecture slides
Thur. June 4 Rolle's Theorem, Mean Value Theorem, Monotonicity 5.5 - 5.12 None Slides

6. Applications of the derivative

Date Topics Required videos Supplementary videos Lecture slides
Tue. June 9 Optimization, Indeterminate Forms, L'Hopital's Rule 6.1, 6.2, 6.4, 6.5, 6.7, 6.8, 6.10 6.3, 6.6, 6.9 Slides
Thur. June 11 Concavity, Asymptotes, Curve Sketching 6.11-6.15 6.16 Slides