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 slides
    Wed, Jan 9 Suprema and infima, and integrable functions 7.3, 7.4, 7.5, 7.6, 7.7, 7.8, 7.9 slides
    Mon, Jan 14 More integrable functions 7.5, 7.6, 7.7, 7.8, 7.9 slides
    Wed, Jan 16 Riemann sums + second half (see next topic) 7.10, 7.11, 7.12 slides


  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 slides
    Mon, Jan 21 FTC Part 1 8.3, 8.4 --- 5.6 slides
    Wed, Jan 23 FTC Part 2 + second half (see next topic) 8.5, 8.6 8.7 5.6 slides


  9. Integration methods

    Date Topics Required videos Supplementary videos Textbook sections Lecture slides
    Wed, Jan 23 First half (see previous topic) + Integration by substitution 9.1 9.2-9.4 6.1 slides
    Mon, Jan 28 Integration by parts 9.6 9.5-9.9 6.2 slides
    Wed, Jan 30 Integration of trigonometric and rational functions 9.10,9.15 9.11-9.12 and 9.16-9.17 6.3, 6.5 slides


  10. Volumes

    Date Topics Required videos Supplementary videos Textbook sections Lecture slides Special announcement
    Mon, Feb 4 Volumes 10.1 --- 7.4 slides ---
    Fri, Feb 8 Volumes + second half (see next topic) 10.2, 11.1,11.2 --- 7.5 slides Make up lecture at MP 102, 4-6pm


  11. Sequences

    Date Topics Required videos Supplementary videos Textbook sections Lecture slides Special announcement
    Fri, Feb 8 Sequences + first half (see previous topic) 10.2, 11.1,11.2 --- 8.1,8.2 slides Make up lecture at MP 102, 4-6pm
    Mon, Feb 11 Properties of sequences 11.3,11.4 --- 8.1,8.2 slides ---
    Wed, Feb 13 Theorems about sequences 11.5-11.8 --- 8.2 slides ---


  12. Improper integrals

    Date Topics Required videos Supplementary videos Textbook sections Lecture slides
    Mon, Feb 25 Improper integrals 12.1, 12.4 12.1--12.6 7.8, 7.9 Posted after lecture ---
    Wed, Feb 27 BCT and LCT for integrals 12.7--12.10 --- 7.8,7.9 Posted after lecture ---


  13. Series

    Date Topics Required videos Supplementary videos Textbook sections Lecture slides
    Mon, March 4 Definition of series 13.2--13.4 13.1 8.3 Posted after lecture
    Wed, March 6 Properties of series 13.5--13.9 --- 8.3,8.4 Posted after lecture
    Mon, March 11 Integral and comparison tests 13.10--13.12 --- 8.5,8.7 Posted after lecture
    Wed, March 13 Alternating series and conditional and absolute convergence 13.13--13.15 13.16,13.17 8.6 Posted after lecture
    Mon, March 18 Ratio test 13.18--13.19 --- 8.7 Posted after lecture