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

• 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