MAT 137: Calculus!
Slides from Sourav Sarkar's lectures (L0501)

• 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.
• Textbook sections: what to read if you want further detail, additional explanations, or more examples.

1. Introduction to logic, quantifiers, definitions, and proofs
   
   

   Date	Topics	Required videos	Textbook sections (optional)	Lecture slides
   Mon, 9 Sep	Introduction, Sets	1.1, 1.2, 1.3	1.1, 1.2	slides
   Wed, 11 Sep	Quantifiers, Conditionals	1.4, 1.5, 1.6, 1.7, 1.8, 1.9	1.3	slides
   Mon, 16 Sep	Definitions and proofs	1.10, 1.11, 1.12, 1.13	1.4	slides
   Wed, 18 Sep	Definitions and proofs continued, induction	1.14, 1.15	1.4, 1,2, 1.8	slides

   
   
   
2. Limits and continuity
   
   

   Date	Topics	Required videos	Supplementary videos	Textbook sections	Lecture slides
   Mon, 23 Sep	Distance and absolute value, intuitive idea of limit	2.4, 2.1, 2.2, 2.3	---	1.2, 1.8	slides
   Wed, 25 Sep	The definition of limit, proofs from the definition of limit	2.5, 2.6, 2.7, 2.8	2.9	2.2	slides
   Mon, 30 Sep	Limit laws	2.10, 2.11	---	2.3	slides
   Wed, 2 Oct	Squeeze theorem and more proofs with limits, continuity	2.12, 2.13, 2.14, 2.15	---	2.3, 2.4	slides
   Mon, 7 Oct	More on continuity	2.16, 2.17	2.18	2.4	slides
   Wed, 9 Oct	Computations, IVT and EVT	2.19, 2.20, 2.21, 2.22	---	2.1, 2.3, 2.4, 2.5	slides

   
   
   
3. Derivatives
   
   

   Date	Topics	Required videos	Supplementary videos	Textbook sections	Lecture slides
   Mon, 14 Oct	No Class	---	---	---
   Wed, 16 Oct	Definition of derivative, differentiation rules	3.1, 3.2, 3.3, 3.4, 3.5, 3.8	---	3.1, 3.2, 3.3	slides
   Mon, 21 Oct	Proof of the differentiation rules	3.6, 3.7, 3.9	---	3.1, 3.3	slides
   Wed, 23 Oct	The chain rule, Trig derivatives and implicit differentiation	3.10, 3.11, 3.12	---	3.5, 3.4, 3.7	slides
   Mon, 28 Oct	Derivatives of exponentials and logarithms	3.13, 3.15, 3.16, 3.17, 3.18	3.14	3.4, 3.6, 3.7	slides
   Wed, 30 Oct	Related rates, Inverse functions	3.19, 3.20, 4.1, 4.2	---	4.7, 1.5, 1.7	slides

   
   
   
4. Inverse functions and inverse trigonometric functions
   
   

   Date	Topics	Required videos	Textbook sections	Lecture slides
   Wed, 30 Oct	Inverse functions	4.1, 4.2	1.5, 1.7	slides
   Mon, 11 Nov	One-to-one functions	4.3, 4.4, 4.5	1.7, 3.6	slides
   Wed, 13 Nov	Inverse trig functions	4.6, 4.7, 4.8	3.5	slides

   
   
   
5. The Mean Value Theorem and applications
   
   

   Date	Topics	Required videos	Supplementary videos	Textbook sections	Lecture slides
   Wed, 13 Nov	Local extrema	5.2, 5.3, 5.4	5.1	4.1	slides
   Mon, 18 Nov	Rolle's Theorem	5.5, 5.6	---	4.2	slides
   Wed, 20 Nov	MVT, Monotonicity	5.7, 5.8, 5.9, 5.10, 5.11, 5.12	---	4.2, 4.3	slides

   
   
   
6. Applications of the derivative
   
   

   Date	Topics	Required videos	Supplementary videos	Textbook sections	Lecture slides
   Mon, 25 Nov	Applied optimization	6.1, 6.2	---	4.8	slides
   Wed, 27 Nov	Indeterminate forms and L'Hôpital's Rule	6.4, 6.5, 6.7, 6.8, 6.10	6.3, 6.6, 6.9	4.4, 4.5, 4.6	slides
   Mon, 2 Dec	Concavity	6.11, 6.12	---	4.9	slides
   Wed, 4 Dec	Asymptotes, Curve sketching	6.13, 6.14, 6.15	6.16	2.1, 4.9	slides

   
   
   
7. The definition of integral
   
   

   Date	Topics	Required videos	Lecture slides
   Mon, 6 Jan	Sums and sigmas	7.1, 7.2	slides
   Wed, 8 Jan	Suprema and infima, integrable functions	7.3, 7.4, 7.5, 7.6, 7.7, 7.8, 7.9	slides
   Mon, 13 Jan	More integrable functions	7.5, 7.6, 7.7, 7.8, 7.9	slides
   Wed, 15 Jan	Riemann sums	7.10, 7.11, 7.12	slides

   
   
   
8. The Fundamental Theorem of Calculus
   
   

   Date	Topics	Required videos	Supplementary videos	Textbook sections	Lecture slides
   Wed, 13 Jan	Antiderivatives, indefinite integrals	8.1, 8.2	---	5.5, 5.6	slides
   Mon, 20 Jan	FTC Part 1	8.3, 8.4	---	5.6	slides
   Wed, 22 Jan	FTC Part 2	8.5, 8.6	8.7	5.6	slides

   
   
   
9. Integration methods

   Note: We are skipping Videos 9.13, 9.14.

   Date	Topics	Required videos	Supplementary videos	Textbook sections	Lecture slides
   Wed, 22 Jan	Integration by substitution	9.1	9.1--9.4	6.1	slides
   Mon, 27 Jan	Integration by parts	9.6	9.5--9.9	6.2	slides
   Wed, 29 Jan	Integration of trigonometric functions, integration of rational functions	9.10, 9.15	9.10--9.12, 9,15--9.17	6.3, 6.5	slides

   
   
   
10. Volumes
    
    

    Date	Topics	Required videos	Textbook sections	Lecture slides
    Mon, 3 Feb	Volumes	10.1	7.4	slides
    Wed, 5 Feb	Volumes	10.2	7.5	slides

    
    
    
11. Sequences
    
    

    Date	Topics	Required videos	Textbook sections	Lecture slides
    Wed, 5 Feb	Sequences	11.1, 11.2	8.1, 8.2	slides
    Mon, 10 Feb	Properties of sequences	11.3, 11.4	8.1, 8,2	slides
    Wed, 12 Feb	Theorems about sequences, the Big Theorem	11.5, 11.6, 11.7, 11.8	8.2	slides

    
    
    
12. Improper integrals
    
    

    Date	Topics	Required videos	Supplementary videos	Textbook sections	Lecture slides
    Mon, 24 Feb	Improper integrals	12.1, 12.4	12.1--12.6	7.8, 7.9	slides
    Wed, 26 Feb	BCT for integrals, LCT for integrals	12.7, 12.8, 12.9, 12.10	---	7.8, 7.9	slides

    
    
    
13. Series
    
    

    Date	Topics	Required videos	Supplementary videos	Textbook sections	Lecture slides
    Mon, 2 Mar	Definition of series	13.2, 13.3, 13.4	13.1	8.3	slides
    Wed, 4 Mar	Properties of series, properties of series	13.5, 13.6, 13.7, 13.8, 13.9	---	8.3, 8.4	slides
    Mon, 9 Mar	Integral and comparison tests	13.10, 13.11, 13.12	---	8.5, 8.7	slides
    Wed, 11 Mar	Alternating series, conditional and absolute convergence	13.13, 13.14, 13.15	13.16, 13.17	8.6	slides
    Mon, 16 Mar	Ratio test	13.18, 13.19	---	8.7	--

    
    
    
14. Power series and Taylor series
    
    

    Date	Topics	Required videos	Supplementary videos	Textbook sections	Lecture slides
    Wed, 18 Mar	Power series, Taylor polynomials	14.1, 14.2, 14.3, 14.4	---	9.1, 9.2, 9.3	--
    Mon, 23 Mar	Taylor series	14.5, 14.6	---	9.1, 9.2, 9.3	--
    Wed, 25 Mar	Analytic functions, New power series	14.7, 14.8, 14.9, 14.10	---	9.1, 9.2, 9.3	--
    Mon, 30 March	Applications	14.12, 14.14	---	9.1, 9.2, 9.3, 9.4	--
    Wed, 1 Apr	Applications and outroduction	14.11, 14.13	14.15	9.1, 9.2, 9.3, 9.4	--

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