MAT 137: Calculus!
Slides from Francisco's lectures (L0401)

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
    Mon, 10 Sep Introduction --- --- slides
    Wed, 12 Sep Sets and quantifiers 1.1, 1.2, 1.3, 1.4, 1.5, 1.6 1.1, 1.2, 1.3 slides
    Mon, 17 Sep Conditionals 1.7, 1.8, 1.9 1.3 slides
    Wed, 19 Sep Definitions, proofs and induction 1.10, 1.11, 1.12, 1.13, 1.14, 1.15 1.4 slides




  2. Limits and continuity

    Date Topics Required videos Supplementary videos Textbook sections Lecture slides
    Mon, 24 Sep Absolute value, distance and inequalities 2.4 --- 1.2, 1.8 slides
    Wed, 26 Sep Limits 2.1, 2.2, 2.3, 2.5, 2.6 --- 2.1, 2.2 slides
    Mon, 1 Oct Proofs from the definition of limit 2.7, 2.8 2.9 2.2 slides
    Wed, 3 Oct Limit laws and squeeze theorem 2.10, 2.11, 2.12, 2.13 --- 2.3 slides
    Wed, 10 Oct Continuity 2.14, 2.15, 2.16, 2.17 2.18 2.4 slides
    Mon, 15 Oct Computations 2.19,2.20 --- 2.1, 2.3,2.4 slides
    Wed, 17 Oct (1st part) IVT and EVT 2.21, 2.22 --- 2.5 slides




  3. Derivatives

    Date Topics Required videos Supplementary videos Textbook sections Lecture slides
    Wed, Oct 17 (2nd part) Definition of a derivative 3.1, 3.2, 3.3 --- 3.1 slides
    Mon, Oct 22 Differentiation rules 3.4, 3.5, 3.8 --- 3.2, 3.3 slides
    Wed, Oct 24 Proof of the differentiation rules and the chain rule 3.6, 3.7, 3.9, 3.10 --- 3.1, 3.3, 3.5 slides
    Mon, Oct 29 Trigonometric derivatives and implicit differentiation 3.11, 3.12 --- 3.4, 3.7 slides
    Wed, Oct 31 Derivatives of exponentials and logarithms, and related rates 3.13, 3.15, 3.16, 3.17, 3.18, 3.19, 3.20 3.14 3.4, 3.6, 3.7, 4.7 slides


  4. Inverse functions and inverse trigonometric functions

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


  5. The Mean Value Theorem and applications

    Date Topics Required videos Supplementary videos Textbook sections Lecture slides
    Mon, Nov 19 Local extrema 5.2, 5.3, 5.4 5.1 4.1 slides
    Wed, Nov 21 Rolle's Theorem and MVT 5.5, 5.6, 5.7, 5.8, 5.9 --- 4.2 slides
    Mon, Nov 26 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
    Wed, Nov 28 Applied optimization, Indeterminate forms and L'Hopital's Rule 6.1, 6.2, 6.4, 6.5, 6.7 6.3, 6.6 4.4, 4.5, 4.6, 4.8 slides
    Mon, Dec 3 Indeterminate forms and L'Hopital's Rule 6.8, 6.10 6.9 4.4, 4.5, 4.6 slides
    Wed, Dec 5 Concavity and Asymptotes 6.11, 6.12, 6.13, 6.14, 6.15 6.16 2.1, 4.9, slides
    Thu, Dec 6 Curve sketching --- --- 4.9 slides


  7. The definition of integral

    Date Topics Required videos Lecture slides
    Mon, Jan 7 Sums and sigmas 7.1, 7.2 Posted after lecture
    Wed, Jan 9 Suprema and infima, and integrable functions 7.3, 7.4, 7.5, 7.6, 7.7, 7.8, 7.9 Posted after lecture
    Mon, Jan 14 More integrable functions 7.5, 7.6, 7.7, 7.8, 7.9 Posted after lecture
    Wed, Jan 16 Riemann sums + second half (see next topic) 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
    Wed, Jan 16 First half + antiderivatives, indefinite integrals 8.1, 8.2 --- 5.5, 5.6 Posted after lecture
    Mon, Jan 21 FTC Part 1 8.3, 8.4 --- 5.6 Posted after lecture
    Wed, Jan 23 FTC Part 2 + second half (TBD) 8.5, 8.6 8.7 5.6 Posted after lecture