MAT 137: "Calculus with proofs" 2022-2023
Slides from Boris Khesin's lectures (L0601)

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.

Office hours for this course:
TU and TH 3-3:30pm - near the lecture room SF1105(TU) and then continuing in BA6228;
WE 9-10:30am - online at the address https://utoronto.zoom.us/j/851358883710
Zoom Meeting ID: 851 3588 3710
No password

Syllabus for this course


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

    Date Topics Required videos Supplementary videos Lecture slides
    Thu, 8 Sep Introduction --- --- Sep. 8 slides
    Tue, 13 Sep Sets 1.1, 1.2, 1.3 --- Sep. 13 slides
    Wed, 14 Sep Quantifiers 1.4, 1.5, 1.6 --- Sep. 14 slides
    Thu, 15 Sep Conditionals 1.7, 1.8 1.9 Sep. 15 slides
    Tue, 20 Sep Definitions and proofs 1.10, 1.11, 1.12, 1.13 --- Sep. 20 slides
    Wed, 21 Sep Induction 1.14, 1.15 --- Sep. 21 slides


  2. Limits and continuity

    Date Topics Required videos Supplementary videos Lecture slides
    Thu, 22 Sep Distance and absolute value 2.4 --- Sep. 22 slides
    Tue, 27 Sep Limits geometrically 2.1, 2.2, 2.3 --- Sep. 27 slides
    Wed, 28 Sep The definition of limit 2.5, 2.6 --- Sep. 28 slides
    Thu, 29 Sep Proofs from the definition of limit 2.7, 2.8 2.9 Sep. 29 slides
    Tue, 4 Oct Limit laws 2.10, 2.11 --- Oct. 4 slides
    annotated
    Wed, 5 Oct Squeeze theorem and more proofs with limits 2.12, 2.13 --- Oct. 5 slides
    Thu, 6 Oct Continuity 2.14, 2.15 --- Oct. 6 slides
    Tue, 11 Oct More on continuity 2.16, 2.17 2.18 Oct. 11 slides
    annotated
    Wed, 12 Oct Computations 2.19, 2.20 --- Oct. 12 slides
    Thu, 13 Oct IVT and EVT 2.21, 2.22 --- Oct. 13 slides


  3. Derivatives

    Date Topics Required videos Supplementary videos Lecture slides
    Tue, 18 Oct Definition of derivative 3.1, 3.2, 3.3 --- Oct. 18 slides
    annotated
    Wed, 19 Oct Differentiation rules 3.4, 3.5, 3.8 --- Oct. 19 slides
    Thu, 20 Oct Proof of the differentiation rules 3.6, 3.7, 3.9 --- Oct. 20 slides
    Tue, 25 Oct The chain rule 3.10, 3.11 --- Oct. 25 slides
    Wed, 26 Oct Trig derivatives and implicit differentiation 3.12, 3.13 --- Oct. 26 slides


  4. Transcendental functions

    Date Topics Required videos Supplementary videos Lecture slides
    Thu, 27 Oct Inverse functions 4.1, 4.2 --- Oct. 27 slides
    Tue, 1 Nov Inverse functions 4.3, 4.4 --- Nov. 1 slides
    Wed, 2 Nov Exponentials and logarithms 4.5, 4.7, 4.8, 4.9 4.6, 4.10, 4.11 Nov. 2 slides
    Thu, 3 Nov Inverse trig functions 4.12, 4.13, 4.14 --- Nov. 3 slides


  5. The Mean Value Theorem and applications

    Date Topics Required videos Supplementary videos Lecture slides
    Tue, 15 Nov Local extrema 5.2, 5.3, 5.4 5.1 Nov. 15 slides
    Wed, 16 Nov Rolle's Theorem 5.5, 5.6 --- Nov. 16 slides
    Thu, 17 Nov MVT 5.7, 5.8, 5.9 --- Nov. 17 slides
    Tue, 22 Nov Monotonicity 5.10, 5.11 5.12 Nov. 22 slides


  6. Applications of the derivatives and limits

    Date Topics Required videos Supplementary videos Lecture slides
    Wed, 23 Nov Related rates 6.1, 6.2 --- Nov. 23 slides
    Thu, 24 Nov Applied optimization 6.3, 6.4 --- Nov. 24 slides
    Tue, 29 Nov Indeterminate forms and L'Hôpital's Rule 6.6, 6.7, 6.9 6.5, 6.8 Nov. 29 slides
    Wed, 30 Nov Indeterminate forms and L'Hôpital's Rule 6.10, 6.12 6.11 Nov. 30 slides
    Thu, 1 Dec Concavity 6.13, 6.14 --- Dec. 1 slides
    Tue, 6 Dec Asymptotes 6.15, 6.16, 6.17 6.18 Dec. 6 slides
    Wed, 7 Dec Curve sketching --- --- Dec. 7 slides


  7. The definition of integral

    Date Topics Required videos Supplementary videos Lecture slides
    Tue, 10 Jan Sums and sigmas 7.1, 7.2 --- Jan. 10 slides
    Wed, 11 Jan Suprema and infima 7.3, 7.4 --- Jan. 11 slides
    Thu, 12 Jan The definition of integral 7.5, 7.6 --- Jan. 12 slides
    annotated
    Tue, 17 Jan Examples and properties of the integral 7.7, 7.8, 7.11 --- Jan. 17 slides
    Wed, 18 Jan Integral as limits 7.9, 7.10 --- Jan. 18 slides
    annotated


  8. The Fundamental Theorem of Calculus

    Date Topics Required videos Supplementary videos Lecture slides
    Thu, 19 Jan Antiderivatives and indefinite integrals 8.1, 8.2 --- Jan. 19 slides
    annotated
    Tue, 24 Jan FTC -- Part 1 8.3, 8.4 --- Jan. 24 slides
    Wed, 25 Jan FTC -- Part 2 8.5, 8.6 8.7 Jan. 25 slides


  9. Integration methods
    Date Topics Required videos Supplementary videos Lecture slides
    Thu, 26 Jan Integration by substitution 9.1, 9.3 9.2 Jan. 26 slides
    Tue, 31 Jan Integration by parts 9.4 9.5, 9.6 Jan. 31 slides
    Wed, 1 Feb Integration of products of trig functions 9.7 9.8, 9.9 Feb. 1 slides
    annotated
    Thu, 2 Feb Integration of rational functions 9.10 9.11, 9.12 Feb. 2 slides
    annotated


  10. Application of Integral--Volumes

    Date Topics Required videos Supplementary videos Lecture slides
    Tue, 7 Feb Volumes 10.1 --- Feb. 7 slides
    Wed, 8 Feb Volumes 10.2 --- Feb. 8 slides


  11. Sequences

    Date Topics Required videos Supplementary videos Lecture slides
    Thu, 9 Feb Sequences 11.1, 11.2 --- Feb. 9 slides
    Tue, 14 Feb Properties of sequences 11.3, 11.4 --- Feb. 14 slides
    Wed, 15 Feb Theorems about sequences 11.5, 11.6 --- Feb. 15 slides
    Thu, 16 Feb The Big Theorem 11.7, 11.8 --- Feb. 16 slides


  12. Improper integrals

    Date Topics Required videos Supplementary videos Lecture slides
    Tue, 28 Feb Improper integrals 12.1, 12.4, 12.5 12.2, 12.3, 12.6 Feb. 28 slides
    Wed, 1 Mar The Basic Comparison Test 12.7, 12.8 --- Mar. 1 slides
    Thu, 2 Mar The Limit Comparison Test 12.9, 12.10 --- Mar. 2 slides


  13. Series

    Date Topics Required videos Supplementary videos Lecture slides
    Tue, 7 Mar Definition of series 13.2, 13.3, 13.4 13.1 Mar. 7 slides
    Wed, 8 Mar Properties of series 13.5, 13.6, 13.7 --- Mar. 8 slides
    Thu, 9 Mar Properties of series 13.8, 13.9 --- Mar. 9 slides
    Tue, 14 Mar Integral test and comparison tests 13.10, 13.12 13.11 Mar. 14 slides
    Wed, 15 Mar Alternating series 13.13 13.14 Mar. 15 slides
    Thu, 16 Mar Absolute and conditional convergence 13.15 13.16, 13.17 Mar. 16 slides
    Tue, 21 Mar Ratio test 13.18, 13.19 --- Mar. 21 slides


  14. Power series and Taylor series

    Date Topics Required videos Supplementary videos Lecture slides
    Wed, 22 Mar Power series 14.1, 14.2 --- Mar. 22 slides
    Thu, 23 Mar Taylor polynomials 14.3, 14.4 --- Mar. 23 slides
    Tue, 28 Mar Taylor series 14.5, 14.6 --- Mar. 28 slides
    Wed, 29 Mar Analytic functions 14.7, 14.8 --- Mar. 29 slides
    Thu, 30 Mar Constructing new Taylor series 14.9, 14.10 --- Mar. 30 slides
    Tue, 4 Apr Applications 14.12, 14.14 --- Mar. 4 slides
    Wed, 5 Apr Applications 14.11, 14.13 14.15 Mar. 5 slides
    Thu, 6 Apr Outroduction --- --- Mar. 6 slides