MAT 137: "Calculus with proofs" 2021-2022
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.

My online office hours are on Wed 10am - 12pm at the address
https://utoronto.zoom.us/j/85135883710
Zoom Meeting ID: 851 3588 3710
No password

There will be no office hours by B.Khesin on Wed Nov. 3! Please, use the in-person office hours of other instructors.

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

    Date Topics Required videos Supplementary videos Lecture slides
    Thu, 9 Sep Introduction --- --- Sep. 9 slides
    Tue, 14 Sep Sets 1.1, 1.2, 1.3 --- Sep. 14 slides
    Wed, 15 Sep Quantifiers 1.4, 1.5, 1.6 --- Sep. 15 slides
    Thu, 16 Sep Conditionals 1.7, 1.8 1.9 Sep. 16 slides
    Tue, 21 Sep Definitions and proofs 1.10, 1.11, 1.12, 1.13 --- Sep. 21 slides
    Wed, 22 Sep Induction 1.14, 1.15 --- Sep. 22 slides


  2. Limits and continuity

    Date Topics Required videos Supplementary videos Lecture slides
    Thu, 23 Sep Distance and absolute value 2.4 --- Sep. 23 slides
    Tue, 28 Sep Limits geometrically 2.1, 2.2, 2.3 --- Sep. 28 slides
    Wed, 29 Sep The definition of limit 2.5, 2.6 --- Sep. 29 slides
    Thu, 30 Sep Proofs from the definition of limit 2.7, 2.8 2.9 Sep. 30 slides
    Tue, 5 Oct Limit laws 2.10, 2.11 --- Oct. 5 slides
    Wed, 6 Oct Squeeze theorem and more proofs with limits 2.12, 2.13 --- Oct. 6 slides
    Thu, 7 Oct Continuity 2.14, 2.15 --- Oct. 7 slides
    Tue, 12 Oct More on continuity 2.16, 2.17 2.18 Oct. 12 slides
    Wed, 13 Oct Computations 2.19, 2.20 --- Oct. 13 slides
    Thu, 14 Oct IVT and EVT 2.21, 2.22 --- Oct. 14 slides


  3. Derivatives

    Date Topics Required videos Supplementary videos Lecture slides
    Tue, 19 Oct Definition of derivative 3.1, 3.2, 3.3 --- Oct. 19 slides
    Wed, 20 Oct Differentiation rules 3.4, 3.5, 3.8 --- Oct. 20 slides
    Thu, 21 Oct Proof of the differentiation rules 3.6, 3.7, 3.9 --- Oct. 21 slides
    Tue, 26 Oct The chain rule 3.10, 3.11 --- Oct. 26 slides
    Wed, 27 Oct Trig derivatives and implicit differentiation 3.12, 3.13 --- Oct. 27 slides


  4. Transcendental functions

    Date Topics Required videos Supplementary videos Lecture slides
    Thu, 28 Oct Inverse functions 4.1, 4.2 --- Oct. 28 slides
    Tue, 2 Nov Inverse functions 4.3, 4.4 --- Nov. 2 slides
    Wed, 3 Nov Exponentials and logarithms 4.5, 4.7, 4.8, 4.9 4.6, 4.10, 4.11 Nov. 3 slides
    Thu, 4 Nov Inverse trig functions 4.12, 4.13, 4.14 --- Nov. 4 slides


  5. The Mean Value Theorem and applications

    Date Topics Required videos Supplementary videos Lecture slides
    Tue, 16 Nov Local extrema 5.2, 5.3, 5.4 5.1 Nov. 16 slides
    Wed, 17 Nov Rolle's Theorem 5.5, 5.6 --- Nov. 17 slides
    Thu, 18 Nov MVT 5.7, 5.8, 5.9 --- Nov. 18 slides
    Tue, 23 Nov Monotonicity 5.10, 5.11 5.12 Nov. 23 slides


  6. Applications of the derivatives and limits

    Date Topics Required videos Supplementary videos Lecture slides
    Wed, 24 Nov Related rates 6.1, 6.2 --- Nov. 24 slides
    Thu, 25 Nov Applied optimization 6.3, 6.4 --- Nov. 25 slides
    Tue, 30 Nov Indeterminate forms and L'Hôpital's Rule 6.6, 6.7, 6.9 6.5, 6.8 Nov. 30 slides
    Wed, 1 Dec Indeterminate forms and L'Hôpital's Rule 6.10, 6.12 6.11 Dec. 1 slides
    Thu, 2 Dec Concavity 6.13, 6.14 --- Dec. 2 slides
    Tue, 7 Dec Asymptotes 6.15, 6.16, 6.17 6.18 Dec. 7 slides
    Wed, 8 Dec Curve sketching --- ---


  7. The definition of integral

    Date Topics Required videos Supplementary videos Lecture slides
    Tue, 11 Jan Sums and sigmas 7.1, 7.2 ---
    Wed, 12 Jan Suprema and infima 7.3, 7.4 ---
    Thu, 13 Jan The definition of integral 7.5, 7.6 ---
    Tue, 18 Jan Examples and properties of the integral 7.7, 7.8, 7.11 ---
    Wed, 19 Jan Integral as limits 7.9, 7.10 ---


  8. The Fundamental Theorem of Calculus

    Date Topics Required videos Supplementary videos Lecture slides
    Thu, 20 Jan Antiderivatives and indefinite integrals 8.1, 8.2 ---
    Tue, 25 Jan FTC -- Part 1 8.3, 8.4 ---
    Wed, 26 Jan FTC -- Part 2 8.5, 8.6 8.7


  9. Integration methods
    Date Topics Required videos Supplementary videos Lecture slides
    Thu, 27 Jan Integration by substitution 9.1, 9.3 9.2
    Tue, 1 Feb Integration by parts 9.4 9.5, 9.6
    Wed, 2 Feb Integration of products of trig functions 9.7 9.8, 9.9
    Thu, 3 Feb Integration of rational functions 9.10 9.11, 9.12


  10. Application of Integral--Volumes

    Date Topics Required videos Supplementary videos Lecture slides
    Tue, 8 Feb Volumes 10.1 ---
    Wed, 9 Feb Volumes 10.2 ---


  11. Sequences

    Date Topics Required videos Supplementary videos Lecture slides
    Thu, 10 Feb Sequences 11.1, 11.2 ---
    Tue, 15 Feb Properties of sequences 11.3, 11.4 ---
    Wed, 16 Feb Theorems about sequences 11.5, 11.6 ---
    Thu, 17 Feb The Big Theorem 11.7, 11.8 ---


  12. Improper integrals

    Date Topics Required videos Supplementary videos Lecture slides
    Tue, 1 Mar Improper integrals 12.1, 12.4, 12.5 12.2, 12.3, 12.6
    Wed, 2 Mar The Basic Comparison Test 12.7, 12.8 ---
    Thu, 3 Mar The Limit Comparison Test 12.9, 12.10 ---


  13. Series

    Date Topics Required videos Supplementary videos Lecture slides
    Tue, 8 Mar Definition of series 13.2, 13.3, 13.4 13.1
    Wed, 9 Mar Properties of series 13.5, 13.6, 13.7 ---
    Thu, 10 Mar Properties of series 13.8, 13.9 ---
    Tue, 15 Mar Integral test and comparison tests 13.10, 13.12 13.11
    Wed, 16 Mar Alternating series 13.13 13.14
    Thu, 17 Mar Absolute and conditional convergence 13.15 13.16, 13.17
    Tue, 22 Mar Ratio test 13.18, 13.19 ---


  14. Power series and Taylor series

    Date Topics Required videos Supplementary videos Lecture slides
    Wed, 23 Mar Power series 14.1, 14.2 ---
    Thu, 24 Mar Taylor polynomials 14.3, 14.4 ---
    Tue, 29 Mar Taylor series 14.5, 14.6 ---
    Wed, 30 Mar Analytic functions 14.7, 14.8 ---
    Thu, 31 Mar Constructing new Taylor series 14.9, 14.10 ---
    Tue, 5 Apr Applications 14.12, 14.14 ---
    Wed, 6 Apr Applications 14.11, 14.13 14.15
    Thu, 7 Apr Outroduction --- ---