MAT 137: Calculus with proofs
Slides from Alfonso's lectures (LEC 0101 and LEC 0401)

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.
  1. Introduction to logic, sets, notation, definitions, and proofs

    Date Topics Required videos Supplementary videos Lecture slides
    Fri, 11 Sep Introduction --- --- Slides
    Mon, 14 Sep Sets 1.1, 1.2, 1.3 --- Slides
    Wed, 16 Sep Quantifiers 1.4, 1.5, 1.6 --- Slides
    Fri, 18 Sep Conditionals 1.7, 1.8 1.9 Slides
    Mon, 21 Sep Definitions and proofs 1.10, 1.11, 1.12, 1.13 --- Slides
    Wed, 23 Sep Induction 1.14, 1.15 --- Slides


  2. Limits and continuity

    Date Topics Required videos Supplementary videos Lecture slides
    Fri, 25 Sep Distance and absolute value 2.4 --- Slides
    Mon, 28 Sep Limits geometrically 2.1, 2.2, 2.3 --- Slides
    Wed, 30 Sep The definition of limit 2.5, 2.6 --- Slides
    Fri, 2 Oct Proofs from the definition of limit 2.7, 2.8 2.9 Slides
    Mon, 5 Oct Limit laws 2.10, 2.11 --- Slides
    Wed, 7 Oct Squeeze theorem and more proofs with limits 2.12, 2.13 --- Slides
    Fri, 9 Oct Continuity 2.14, 2.15 --- Slides
    Mon, 12 Oct THANKSGIVING (no class) --- --- (no class)
    Wed, 14 Oct More on continuity 2.16, 2.17 2.18 Slides
    Fri, 16 Oct Computations 2.19, 2.20 --- Slides
    Mon, 19 Oct IVT and EVT 2.21, 2.22 --- Sllides


  3. Derivatives

    Date Topics Required videos Supplementary videos Lecture slides
    Wed, 21 Oct Definition of derivative 3.1, 3.2, 3.3 --- Slides
    Fri, 23 Oct Differentiation rules 3.4, 3.5, 3.8 --- Slides
    Mon, 26 Oct Proof of the differentiation rules 3.6, 3.7, 3.9 --- Slides
    Wed, 28 Oct The chain rule 3.10, 3.11 --- Slides
    Fri, 30 Oct Trig derivatives and implicit differentiation 3.12, 3.13 --- Slides


  4. Trascendental functions

    Date Topics Required videos Supplementary videos Lecture slides
    Mon, 2 Nov Inverse functions 4.1, 4.2 --- Slides
    Wed, 4 Nov Inverse functions 4.3, 4.4 --- Slides
    Fri, 6 Nov Exponentials and logarithms 4.5, 4.7, 4.8, 4.9 4.6, 4.10, 4.11 Slides
    Mon, 16 Nov Inverse trig functions 4.12, 4.13, 4.14 --- Slides


  5. The Mean Value Theorem and applications

    Date Topics Required videos Supplementary videos Lecture slides
    Wed, 18 Nov Local extrema 5.2, 5.3, 5.4 5.1 Slides
    Fri, 20 Nov Rolle's Theorem 5.5, 5.6 --- Slides
    Mon, 23 Nov MVT 5.7, 5.8, 5.9 --- Slides
    Wed, 25 Nov Monotonicity 5.10, 5.11 5.12 Slides


  6. Applications of derivatives and limits

    Date Topics Required videos Supplementary videos Lecture slides
    Fri, 27 Nov Related rates 6.1, 6.2 --- Slides
    Mon, 30 Nov Applied optimization 6.3, 6.4 --- Slides
    Wed, 2 Dec Indeterminate forms and L'Hôpital's Rule 6.6, 6.7, 6.9 6.5, 6.8 Slides
    Fri, 4 Dec Indeterminate forms and L'Hôpital's Rule 6.10, 6.12 6.11 Slides
    Mon, 7 Dec Concavity 6.13, 6.14 -- Slides
    Wed, 9 Dec Asymptotes 6.15, 6.16, 6.17 6.18 Slides
    Thu, 10 Dec Curve sketching --- --- Slides


  7. The definition of integral

    Date Topics Required videos Supplementary videos Lecture slides
    Mon, 11 Jan Sums and sigmas 7.1, 7.2 --- Slides
    Wed, 13 Jan Suprema and infima 7.3, 7.4 --- Slides
    Fri, 15 Jan The definition of integral 7.5, 7.6 --- Slides
    Mon, 18 Jan Examples and properties of the integral 7.7, 7.8, 7.11 --- Slides
    Wed, 20 Jan Integrals as limits 7.9, 7.10 -- Slides


  8. The Fundamental Theorem of Calculus

    Date Topics Required videos Supplementary videos Lecture slides
    Fri, 22 Jan Antiderivatives and indefinite integrals 8.1, 8.2 --- Slides
    Mon, 25 Jan FTC - Part 1 8.3, 8.4 --- Slides
    Wed, 27 Jan FTC - Part 2 8.5, 8.6 8.7 Slides


  9. Integration methods

    Date Topics Required videos Supplementary videos Lecture slides
    Fri, 29 Jan Integration by substitution 9.1, 9.3 9.2 Slides
    Mon, 1 Feb Integration by parts 9.4 9.5, 9.6 Slides
    Wed, 3 Feb Integration of products of trigonometric functions 9.7 9.8, 9.9 Slides
    Fri, 5 Feb Integration of rational functions 9.10 9.11, 9.12 Slides


  10. Applications of the integral

    Date Topics Required videos Supplementary videos Lecture slides
    Mon, 8 Feb Volumes 10.1 --- Slides
    Wed, 10 Feb Volumes 10.2 --- Slides


  11. Sequences

    Date Topics Required videos Supplementary videos Lecture slides
    Fri, 12 Feb Sequences 11.1, 11.2 --- Slides
    Mon, 22 Feb Properties of sequences 11.3, 11.4 --- Slides
    Wed, 24 Feb Theorems about sequences 11.5, 11.6 --- Slides
    Fri, 26 Feb The Big Theorem 11.7, 11.8 --- Slides


  12. Improper integrals

    Date Topics Required videos Supplementary videos Lecture slides
    Mon, 1 Mar Improper integrals 12.1, 12.4, 12.5 12.2, 12.3, 12.6 Slides
    Wed, 3 Mar The Basic Comparison Test 12.7, 12.8 --- Slides
    Fri, 5 Mar The Limit Comparison Test 12.9, 12.10 --- Slides


  13. Series

    Date Topics Required videos Supplementary videos Lecture slides
    Mon, 8 Mar Definition of series 13,2, 13.3, 13.4 13.1 Slides
    Wed, 10 Mar Properties of series 13.5, 13.6, 13.7 --- Slides
    Fri, 12 Mar Properties of series 13.8, 13.9 --- Slides
    Mon, 15 Mar Integral test and comparison tests 13.10, 13.12 13.11 Slides
    Wed, 17 Mar Alternating series 13.13 13.14 Slides
    Fri, 19 Mar Absolute and conditional convergence 13.15 13.16, 13.17 Slides
    Mon, 22 Mar Ratio test 13.18, 13.19 --- Slides


  14. Power series and Taylor series

    Date Topics Required videos Supplementary videos Lecture slides
    Wed, 24 Mar Power series 14.1, 14.2 --- Slides
    Fri, 26 Mar Taylor polynomials 14.3, 14.4 --- Slides
    Mon, 29 Mar Taylor series 14.5, 14.6 --- Slides
    Wed, 31 Mar Analytic functions 14.7, 14.8 --- Slides
    Fri, 2 Apr GOOD FRIDAY (no class) --- --- (no class)
    Mon, 5 Apr Constructing new Taylor series 14.9, 14.10 --- Slides
    Wed, 7 Apr Applications 14.12, 14.14 --- Slides
    Fri, 9 Apr Applications 14.11, 14.13 14.15 Slides
    Mon, 12 Apr Outroduction --- --- Slides