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 Videos to watch before lecture Slides used in lecture
    Fri, 8 Sep Introduction --- slides
    Mon, 11 Sep Sets 1.1, 1.2, 1.3 slides
    Wed, 13 Sep Quantifiers 1.4, 1.5, 1.6 slides
    Fri, 15 Sep Conditionals 1.7, 1.8, 1.9 slides
    Mon, 18 Sep Definitions and proofs 1.10, 1.11, 1.12, 1.13 slides
    Wed, 20 Sep Induction 1.14, 1.15 slides


  2. Limits and continuity

    Date Topics Videos to watch before lecture Slides used in lecture Textbook sections this corresponds to
    Fri, 22 Sep Inequalities and absolute values 2.4 slides 1.3
    Mon, 25 Sep The intuitive idea of limit 2.1, 2.2, 2.3 slides 2.1
    Wed, 27 Sep The definitions of limit 2.5, 2.6 slides 2.2
    Fri, 29 Sep More on the definitions of limit 2.7, 2.8 slides 2.2
    Mon, 2 Oct The limit laws 2.9, 2.10 slides 2.3
    Wed, 4 Oct More proof with limits, continuity 2.11, 2.12, 2.13 slides 2.5, 2.4
    Fri, 6 Oct More continuity 2.14, 2.15, 2.16 slides 2.4
    Wed, 11 Oct Trig limits and computations 2.17, 2.18 slides 2.5
    Fri, 13 Oct IVT and EVT 2.19, 2.20 slides 2.6


  3. Derivatives

    Date Topics Videos to watch before lecture Slides used in lecture Textbook sections this corresponds to
    Mon, 16 Oct Definition of derivative 3.1, 3.2, 3.3 slides 3.1, 3.3, 3.4
    Wed, 18 Oct Differentiation rules 3.4, 3.5, 3.8 slides 3.2, 3.3
    Fri, 20 Oct Proof of differentiation rules 3.6, 3.7, 3.9 slides 3.2, 3.3
    Mon, 23 Oct Chain rule 3.10 slides 3.5
    Wed, 25 Oct Trig derivatives and implicit differentiation 3.11, 3.12 slides 3.6, 3.7
    Fri, 27 Oct Exponentials and logarithms 3.13 to 3.18 slides ---


  4. Inverse functions and inverse trigonometric functions

    Date Topics Videos to watch before lecture Slides used in lecture Textbook sections this corresponds to
    Mon, 30 Oct Inverse functions 4.1, 4.2 slides 7.1 (partially)
    Wed, 1 Nov One-to-one functions 4.3, 4.4, 4.5 slides 7.1 (partially)
    Fri, 3 Nov Inverse trigonometric functions 4.6, 4.7, 4.8 slides 7.7


  5. The Mean Value Theorem and applications

    Date Topics Videos to watch before lecture Slides used in lecture Textbook sections this corresponds to
    Mon, 13 Nov Related rates --- slides 4.10
    Wed, 15 Nov Local extrema 5.1, 5.2, 5.3, 5.4 slides 4.3, 4.4
    Fri, 17 Nov Rolle's Theorem 5.5, 5.6 slides 4.1
    Mon, 20 Nov MVT 5.7, 5.8, 5.9 slides 4.1
    Wed, 22 Nov Increasing and decreasing functions 5.10, 5.11, 5.12 slides 4.2, 4.4
    Fri, 24 Nov Applied optimization problems --- slides 4.5


  6. Applications of the derivative. (From Mon 27 Nov to Thu 7 Dec)

    There won't be videos for this part.

    These two weeks will be taught by Qin Deng, who also teaches LEC 0501. Follow details of his lectures on his section website.

  7. The definition of integral

    Date Topics Videos to watch before lecture Slides used in lecture Textbook sections this corresponds to
    Fri, 5 Jan Sums and sigmas 7.1, 7.2 slides 12.1
    Mon, 8 Jan Suprema and infima 7.3, 7.4 slides 11.1
    Wed, 10 Jan Integrable functions 7.5, 7.6, 7.7, 7.8, 7.9 slides ---
    Fri, 12 Jan More integrable functions 7.5, 7.6, 7.7, 7.8, 7.9 slides ---
    Mon, 15 Jan Riemann sums 7.10, 7.11, 7.12 slides 5.2, 5.8


  8. The Fundamental Theorem of Calculus

    Date Topics Videos to watch before lecture Slides used in lecture Textbook sections this corresponds to
    Wed, 17 Jan Antiderivatives, indefinite integrals 8.1, 8.2 slides 5.3, 5.4
    Fri, 19 Jan FTC Part 1 8.3, 8.4 slides 5.3, 5.6, 5.8
    Mon, 22 Jan FTC Part 2 8.5, 8.6, 8.7 slides 5.4, 5.5, 6.1


  9. Integration Methods

    In this section, there are lots of videos with additional examples. The main theory for each topic is normally contained in one single video, and that is all I ask you to watch before each class. However, you will find the rest of the examples useful, so I recommend you watch them as well (before or after).

    Date Topics Required videos Recommended videos Slides used in lecture Textbook sections
    Wed, 24 Jan Integration by substitution 9.1 9.1 -- 9.4 slides 5.7
    Fri, 26 Jan Integration by parts 9.6 9.5 -- 9.9 slides 8.2
    Mon, 29 Jan Integration of trig functions 9.10, 9.11 9.10 -- 9.12 slides 8.3
    Wed, 31 Jan Trig substitution 9.13 9.13 -- 9.14 slides 8.4
    Fri, 2 Feb Integration of rational functions 9.15 9.15 -- 9.17 slides 8.5


  10. Volumes


    These two classes will be taught by instructors-in-training Mihai Alboui (9-10) and Matt Olechnowicz (10-11), as part of the math department training for future instructors. These two days will be "traditional lecture" and there won't be any videos.

  11. Sequences

    Date Topics Videos to watch before lecture Slides used in lecture Textbook sections this corresponds to
    Fri, 9 Feb Convergence of sequences 11.1, 11.2, 11.3 slides 11.2, 11.3
    Mon, 12 Feb Bounded and monotonic sequences 11.4, 11.5 slides 11.2, 11.3
    Wed, 14 Feb The big theorem for sequences 11.6, 11.7, 11.8 slides 11.3, 11.4


  12. Improper integrals

    In this section, there are additional videos again We want you to watch all of them, but there are only some that you need to watch before class. You may watch the rest before or after.

    Date Topics Required videos Recommended videos Slides used in lecture Textbook sections
    Fri, 16 Feb Definition of improper integral 12.1, 12.4 12.1--12.6 slides 11.7
    Mon, 26 Feb The Basic Comparison Test 12.7, 12.8 slides 11.7
    Wed, 28 Jan The Limit-Comparison Test 12.9, 12.10 slides 11.7


  13. Series

    Date Topics Required videos Recommended videos Slides used in lecture Textbook sections
    Fri, 2 Mar Definition of series 13.2, 13.3, 13.4 13.1 slides 12.2
    Mon, 5 Mar Properties of series 13.5, 13.6, 13.7 slides 12.2
    Wed, 7 Mar More properties of series 13.8, 13.9 slides 12.2
    Fri, 9 Mar Integral test and comparison tests 13.10, 13.11, 13.12 slides 12.3
    Mon, 12 Mar Alternating series 13.13, 13.14 slides 12.5
    Wed, 14 Mar Absolute and conditional convergence 13.15 13.16, 13.17 slides 12.5
    Fri, 16 Mar Ratio test 13.18, 13.19 slides 12.4


  14. Power series and Taylor series

    Date Topics Required videos Slides used in lecture Textbook sections
    Mon, 19 Mar Power series 14.1, 14.2 slides 12.8, 12.9
    Wed, 21 Mar Taylor polynomials 14.3, 14.4 slides 12.6, 12.7
    Fri, 23 Mar Taylor series 14.5, 14.6 slides 12.6, 12.7
    Mon, 26 Mar Analytic functions 14.7, 14.8 slides 12.6, 12.7
    Wed, 28 Mar New power series 14.9, 14.10 slides 12.6--12.9
    Mon, 2 Apr Applications 14.12, 14.14 slides 12.8--12.9
    Wed, 4 Apr Applications 14.11, 14.13 slides 12.6--12.7
    Thu, 5 Apr Applications 14.15 slides ---