MAT 137: Calculus!
Slides from Alfonso's lectures (L0101 and L0201)

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. Intro to logic, quantifers, definitions, and proofs

    Date Topics Required videos Textbook sections Lecture slides
    Fri, 7 Sep Introduction --- --- slides
    Mon, 10 Sep Sets 1.1, 1.2, 1.3 1.1, 1.2 slides
    Wed, 12 Sep Quantifiers 1.4, 1.5, 1.6 1.3 slides
    Fri, 14 Sep Conditionals 1.7, 1.8, 1.9 1.3 slides
    Mon, 17 Sep Definitions and proofs 1.10, 1.11, 1.12, 1.13 1.4 slides
    Wed, 19 Sep Induction 1.14, 1.15 1.4 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 slides
    Mon, 24 Sep The intuitive idea of limit 2.1, 2.2, 2.3 --- 2.1 slides
    Wed, 26 Sep The definition of limit 2.5, 2.6 --- 2.2 slides
    Fri, 28 Sep Proofs from the definition of limit 2.7, 2.8 2.9 2.2 slides
    Mon, 1 Oct Limit laws 2.10, 2.11 --- 2.3 slides
    Wed, 3 Oct Squeeze theorem and more proofs with limits 2.12, 2.13 --- 2.3 slides
    Fri, 5 Oct Continuity 2.14, 2.15 --- 2.4 slides
    Wed, 10 Oct More on continuity 2.16, 2.17 2.18 2.4 slides
    Fri, 12 Oct Computations 2.19, 2.20 --- 2.1, 2.3, 2.4 slides
    Mon, 15 Oct IVT and EVT 2.21, 2.22 --- 2.5 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 slides
    Fri, 19 Oct Differentiation rules 3.4, 3.5, 3.8 --- 3.2, 3.3 slides
    Mon, 22 Oct Proof of the differentiation rules 3.6, 3.7, 3.9 --- 3.1, 3.3 slides
    Wed, 24 Oct The chain rule 3.10 --- 3.5 slides
    Fri, 26 Oct Trig derivatives and implicit differentiation 3.11, 3.12 --- 3.4, 3.7 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 slides
    Wed, 31 Oct Related rates 3.19, 3.20 --- 4.7 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 slides
    Mon, 12 Nov One-to-one functions 4.3, 4.4, 4.5 1.7, 3.6 slides
    Wed, 14 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
    Fri, 16 Nov Local extrema 5.2, 5.3, 5.4 5.1 4.1 slides
    Mon, 19 Nov Rolle's Theorem 5.5, 5.6 --- 4.2 slides
    Wed, 21 Nov MVT 5.7, 5.8, 5.9 --- 4.2 slides
    Fri, 23 Nov Monotonocity 5.10, 5.11, 5.12 --- 4.3 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 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 slides
    Fri, 30 Nov Indeterminate forms and L'Hôpital's Rule 6.8, 6.10 6.9 4.4, 4.5, 4.6 slides
    Mon, 3 Dec Concavity 6.11, 6.12 --- 4.9 slides
    Wed, 5 Dec Asymptotes 6.13, 6.14, 6.15 6.16 2.1, 4.9 slides
    Thu, 6 Dec Curve sketching --- --- 4.9 slides


  7. The definition of integral

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


  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 posted after lecture
    Mon, 21 Jan FTC Part 1 8.3, 8.4 --- 5.6 posted after lecture
    Wed, 23 Jan FTC Part 2 8.5, 8.6 8.7 5.6 posted after lecture