MAT 137: Calculus!
Slides from Boris Khesin's lectures (L0301)

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.

Here is the link to the main website of MAT 137 Y.


  1. Intro to logic, quantifers, definitions, and proofs

    Date Topics Required videos Textbook sections Lecture slides
    Fri, 7 Sep Introduction --- --- Sep. 7 slides
    Mon, 10 Sep Sets 1.1, 1.2, 1.3 1.1, 1.2 Sep. 10 slides
    Wed, 12 Sep Quantifiers 1.4, 1.5, 1.6 1.3 Sep. 12 slides
    Fri, 14 Sep Conditionals 1.7, 1.8, 1.9 1.3 Sep. 14 slides
    Mon, 17 Sep Definitions and proofs 1.10, 1.11, 1.12, 1.13 1.4 Sep. 17 slides
    Wed, 19 Sep Induction 1.14, 1.15 1.4 Sep. 19 slides


  2. Limits and continuity

    Date Topics Required videos Supplementary videos Textbook sections Lecture slides
    Fri, 21 Sep Distance and absolute value 2.4 --- 1.2, 1.8 Sep. 21 slides
    Mon, 24 Sep The intuitive idea of limit 2.1, 2.2, 2.3 --- 2.1 Sep. 24 slides
    Wed, 26 Sep The definition of limit 2.5, 2.6 --- 2.2 Sep. 26 slides
    Fri, 28 Sep Proofs from the definition of limit 2.7, 2.8 2.9 2.2 Sep. 28 slides
    Mon, 1 Oct Limit laws 2.10, 2.11 --- 2.3 Oct. 1 slides
    Wed, 3 Oct Squeeze theorem and more proofs with limits 2.12, 2.13 --- 2.3 Oct. 3 slides
    Fri, 5 Oct Continuity 2.14, 2.15 --- 2.4 Oct. 5 slides
    Wed, 10 Oct More on continuity 2.16, 2.17 2.18 2.4 Oct. 10 slides
    Fri, 12 Oct Computations 2.19, 2.20 --- 2.1, 2.3, 2.4 Oct. 12 slides
    Mon, 15 Oct IVT and EVT 2.21, 2.22 --- 2.5 Oct. 15 slides


  3. Derivatives

    Date Topics Required videos Supplementary videos Textbook sections Lecture slides
    Wed, 17 Oct Definition of derivative 3.1, 3.2, 3.3 --- 3.1 Oct. 17 slides
    Fri, 19 Oct Differentiation rules 3.4, 3.5, 3.8 --- 3.2, 3.3 Oct. 19 slides
    Mon, 22 Oct Proof of the differentiation rules 3.6, 3.7, 3.9 --- 3.1, 3.3 Oct. 22 slides
    Wed, 24 Oct The chain rule 3.10 --- 3.5 Oct. 24 slides
    Fri, 26 Oct Trig derivatives and implicit differentiation 3.11, 3.12 --- 3.4, 3.7 Oct. 26 slides
    Mon, 29 Oct Derivatives of exponentials and logarithms 3.13, 3.15, 3.16, 3.17, 3.18 3.14 3.4, 3.6, 3.7 Oct. 29 slides
    Wed, 31 Oct Related rates 3.19, 3.20 --- 4.7 Oct. 31 slides


  4. Inverse functions and inverse trigonometric functions

    Date Topics Required videos Textbook sections Lecture slides
    Fri, 2 Nov Inverse functions 4.1, 4.2 1.5, 1.7 Nov. 2 slides
    Mon, 12 Nov One-to-one functions 4.3, 4.4, 4.5 1.7, 3.6 Nov. 12 slides
    Wed, 14 Nov Inverse trig functions 4.6, 4.7, 4.8 3.5 Nov. 14 slides


  5. The Mean Value Theorem and applications

    Date Topics Required videos Supplementary videos Textbook sections Lecture slides
    Fri, 16 Nov Local extrema 5.2, 5.3, 5.4 5.1 4.1 Nov. 16 slides
    Mon, 19 Nov Rolle's Theorem 5.5, 5.6 --- 4.2 Nov. 19 slides
    Wed, 21 Nov MVT 5.7, 5.8, 5.9 --- 4.2 Nov. 21 slides
    Fri, 23 Nov Monotonicity 5.10, 5.11, 5.12 --- 4.3 Nov. 23 slides


  6. Applications of the derivative

    Date Topics Required videos Supplementary videos Textbook sections Lecture slides
    Mon, 26 Nov Applied optimization 6.1, 6.2 --- 4.8 Nov. 26 slides
    Wed, 28 Nov Indeterminate forms and L'Hôpital's Rule 6.4, 6.5, 6.7 6.3, 6.6 4.4, 4.5, 4.6 Nov. 28 slides
    Fri, 30 Nov Indeterminate forms and L'Hôpital's Rule 6.8, 6.10 6.9 4.4, 4.5, 4.6 Nov. 30 slides
    Mon, 3 Dec Concavity and asymptotes 6.11, 6.12, 6.13, 6.14, 6.15 6.16 2.1, 4.9 Dec. 3 slides
    Wed, 5 Dec Curve sketching --- --- 4.9 Dec. 5 slides


  7. The definition of integral

    Date Topics Required videos Lecture slides
    Mon, 7 Jan Sums and sigmas 7.1, 7.2 Jan. 7 slides
    Wed, 9 Jan Suprema and infima 7.3, 7.4 Jan. 9 slides
    Fri, 11 Jan Integrable functions 7.5, 7.6, 7.7, 7.8, 7.9 Jan. 11 slides
    Mon, 14 Jan More integrable functions 7.5, 7.6, 7.7, 7.8, 7.9 Jan. 14 slides
    Wed, 16 Jan Riemann sums 7.10, 7.11, 7.12 Jan. 16 slides


  8. The Fundamental Theorem of Calculus

    Date Topics Required videos Supplementary videos Textbook sections Lecture slides
    Fri, 18 Jan Antiderivatives, indefinite integrals 8.1, 8.2 --- 5.5, 5.6 Jan. 18 slides
    Mon, 21 Jan FTC Part 1 8.3, 8.4 --- 5.6 Jan. 21 slides
    Wed, 23 Jan FTC Part 2 8.5, 8.6 8.7 5.6 Jan. 23 slides


  9. Integration methods

    Note: We are skipping Videos 9.13, 9.14.

    Date Topics Required videos Supplementary videos Textbook sections Lecture slides
    Fri, 25 Jan Integration by substitution 9.1 9.1--9.4 6.1 Jan. 25 slides
    Mon, 28 Jan Integration by parts 9.6 9.5--9.9 6.2 Jan. 28 slides
    Wed, 30 Jan Integration of trigonometric functions 9.10 9.10--9.12 6.3 Jan. 30 slides
    Fri, 1 Feb Integration of rational functions 9.15 9.15--9.17 6.5 Feb.1 slides


  10. Volumes

    Date Topics Required videos Supplementary videos Textbook sections Lecture slides
    Mon, 4 Feb Volumes 10.1 --- 7.4 Feb.4 slides
    Wed, 6 Feb Volumes 10.2 --- 7.5 Feb.6 slides


  11. Sequences

    Date Topics Required videos Supplementary videos Textbook sections Lecture slides
    Fri, 8 Feb Sequences 11.1, 11.2 --- 8.1, 8.2 Feb.8 slides
    Mon, 11 Feb Properties of sequences 11.3, 11.4 --- 8.1, 8,2 Feb.11 slides
    Wed, 13 Feb Theorems about sequences 11.5, 11.6 --- 8.2 Feb.13 slides
    Fri, 15 Feb The Big Theorem 11.7, 11.8 --- --- Feb.15 slides


  12. Improper integrals

    Date Topics Required videos Supplementary videos Textbook sections Lecture slides
    Mon, 25 Feb Improper integrals 12.1, 12.4 12.1--12.6 7.8, 7.9 Feb.25 slides
    Wed, 27 Feb BCT for integrals 12.7, 12.8 --- 7.8, 7.9 Feb.27 slides
    Fri, 1 Mar LCT for integrals 12.9, 12.10 --- 7.8, 7.9 Mar.1 slides


  13. Series

    Date Topics Required videos Supplementary videos Textbook sections Lecture slides
    Mon, 4 Mar Definition of series 13.2, 13.3, 13.4 13.1 8.3 Mar.4 slides
    Wed, 6 Mar Properties of series 13.5, 13.6, 13.7 --- 8.3, 8.4 Mar.6 slides
    Fri, 8 Mar Properties of series 13.8, 13.9 --- 8.4 Mar.8 slides
    Mon, 11 Mar Integral and comparison tests 13.10, 13.11, 13.12 --- 8.5, 8.7 Mar.11 slides
    Wed, 13 Mar Alternating series 13.13, 13.14 --- 8.6 Mar.13 slides
    Fri, 15 Mar Conditional and absolute convergence 13.15 13.16, 13.17 8.6 Mar.15 slides
    Mon, 18 Mar Ratio test 13.18, 13.19 --- 8.7 Mar.18 slides


  14. Power series and Taylor series

    Date Topics Required videos Textbook sections Lecture slides
    Wed, 20 Mar Power series 14.1, 14.2 9.1 Mar.20 slides
    Fri, 22 Mar Taylor polynomials 14.3, 14.4 9.1, 9.2, 9.3 Mar.22 slides
    Mon, 25 Mar Taylor series 14.5, 14.6 9.1, 9.2, 9.3 Mar.25 slides
    Wed, 27 Mar Analytic functions 14.7, 14.8 9.1, 9.2, 9.3 Mar.27 slides
    Fri, 29 Mar New power series 14.9, 14.10 9.1, 9.2, 9.3 Mar.29 slides
    Mon, 1 Apr Applications 14.12, 14.14 9.1, 9.2, 9.3, 9.4 Apr.1 slides
    Wed, 3 Apr Applications 14.11, 14.13 9.1, 9.2, 9.3, 9.4 Apr.3 slides
    Fri, 5 Apr Applications 14.15 9.4 Apr.5 slides