MAT 137: Calculus! - 2019/20
Slides from Ahmed Ellithy's lectures (L5101)

Lecture Time : Mondays 5 pm - 7 pm in MP102 and Tuesdays 5 pm - 6 pm in MP202

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.

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  1. Intro to logic, quantifers, definitions, and proofs

    Date Topics Required videos Textbook sections (optional) Lecture slides
    Mon, 9 Sep Introduction, Sets & Quantifiers 1.1, 1.2, 1.3, 1.4, 1.5, 1.6 1.1, 1.2, 1.3 slides
    Tue, 10 Sep Conditionals 1.7, 1.8, 1.9 1.3 slides
    Mon, 16 Sep Conditionals, Definitions and Proofs 1.10, 1.11, 1.12, 1.13, 1.14, 1.15 1.3, 1.4 slides
    Tue, 17 Sep Induction 1.14, 1.15 1.4 slides


  2. Limits and continuity

    Date Topics Required videos Supplementary videos Textbook sections (optional) Lecture slides
    Mon, 23 Sep Distance and absolute value,
    The intuitive idea of limit     		2.1, 2.2, 2.3, 2.4 --- 1.2, 1.8, 2.1 slides
    Tue, 24 Sep The definition of limit 2.5, 2.6 --- 2.2 slides
    Mon, 30 Sep Proofs from the definition of limit,
    Limit laws     		2.7, 2.8, 2.10, 2.11 2.9 2.2, 2.3 slides
    Tue, 1 Oct Squeeze theorem and more proofs with limits 2.12, 2.13 --- 2.3 slides
    Mon, 7 Sep Continuity 2.14, 2.15, 2.16, 2.17 2.18 2.4 slides
    Tue, 8 Oct Computations 2.19, 2.20 --- 2.1, 2.3, 2.4 slides
    Mon, 14 Oct NO CLASS --- --- ---
    Tue, 15 Oct IVT and EVT 2.21,2.22 --- 2.5 slides




  3. Derivatives

    Date Topics Required videos Supplementary videos Textbook sections (optional) Lecture slides
    Mon, 21 Oct Definition of derivative,
    Differentiation Rules     		3.1, 3.2, 3.3, 3.4, 3.5, 3.8 --- 3.1, 3.2, 3.3 slides
    Tue, 22 Oct Proof of the differentiation rules 3.6, 3.7, 3.9 --- 3.1, 3.3 slides
    Mon, 28 Oct The Chain Rule,
    Trig derivatives and implicit differentiation     		3.10, 3.11, 3.12 --- 3.4, 3.5, 3.7 slides
    Tue, 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
    Mon, 11 Nov Related rates,
    Inverse functions
    		3.19, 3.20, 4.1, 4.2 --- 4.7, 1.5, 1.7 slides




  4. Inverse functions and inverse trigonometric functions

    Date Topics Required videos Textbook sections Lecture slides
    Mon, 11 Nov Related rates,
    Inverse functions
    		3.19, 3.20, 4.1, 4.2 4.7, 1.5, 1.7 slides
    Tue, 12 Nov One-to-one functions 4.3, 4.4, 4.5 1.7, 3.6 slides
    Mon, 18 Nov Inverse trig functions,
    Local extrema
    		 4.6, 4.7, 4.8, 5.1, 5.2, 5.3, 5.4 3.5, 4.1 slides


  5. The Mean Value Theorem and applications

    Date Topics Required videos Supplementary videos Textbook sections Lecture slides
    Mon, 18 Nov Inverse trig functions,
    Local extrema
    		 4.6, 4.7, 4.8, 5.1, 5.2, 5.3, 5.4 --- 3.5, 4.1 slides
    Tue, 19 Nov Rolle's Theorem 5.5, 5.6 --- 4.2 slides
    Mon, 25 Nov MVT,
    Monotonicity
    		5.7, 5.8, 5.9, 5.10, 5.11, 5.12 --- 4.2, 4.3 slides


  6. Applications of the derivative

    Date Topics Required videos Supplementary videos Textbook sections Lecture slides
    Tue, 26 Nov Applied optimization 6.1, 6.2 --- 4.8 slides
    Mon, 2 Dec Indeterminate forms and L'Hôpital's Rule 6.4, 6.5, 6.7, 6.8, 6.10 6.3, 6.6, 6.9 4.4, 4.5, 4.6 slides
    Tue, 3 Dec Concavity 6.11, 6.12 --- 4.9 slides
    Thu, 5 Dec Asymptotes,
    Curve Sketching
    		6.13, 6.14, 6.15 6.16 2.1, 4.9 slides


  7. The definition of integral

    Date Topics Required videos Lecture slides
    Mon, 6 Jan Sums and sigmas,
    Suprema and infima
    		7.1, 7.2, 7.3, 7.4 slides
    Tue, 7 Jan Integrable functions 7.5, 7.6, 7.7, 7.8, 7.9 slides
    Mon, 13 Jan More integrable functions,
    Riemann sums
    		 7.5, 7.6, 7.7, 7.8, 7.9, 7.10, 7.11, 7.12 slides


  8. The Fundamental Theorem of Calculus

    Date Topics Required videos Textbook sections Lecture slides
    Tue, 14 Jan Antiderivatives, indefinite integrals 8.1, 8.2 5.5, 5.6 slides
    Mon, 20 Jan FTC Part 1 and Part 2 8.3, 8.4, 8.5, 8.6, 8.7 5.6 slides


  9. Integration methods

    Note: We are skipping Videos 9.13, 9.14.

    Date Topics Required videos Supplementary videos Textbook sections Lecture slides
    Tue, 21 Jan Integration by substitution 9.1, 9.4 9.2, 9.3 6.1 slides
    Mon, 27 Jan Integration by parts,
    Integration of trigonometric functions
    		 9.5, 9.6, 9.10 9.7--9.9, 9.11, 9.12 6.2, 6.3 slides
    Tue, 28 Jan Integration of rational functions 9.15 9.16, 9.17 6.5 slides


  10. Volumes

    Date Topics Required videos Textbook sections Lecture slides
    Mon, 3 Feb Volumes 10.1, 10.2 7.4, 7.5 slides


  11. Sequences

    Date Topics Required videos Textbook sections Lecture slides
    Tue, 4 Feb Sequences 11.1, 11.2 8.1, 8.2 slides
    Mon, 10 Feb Properties of sequences,
    Theorems about sequences
    		11.3, 11.4, 11.5, 11.6 8.1, 8.2 slides
    Tue, 11 Feb The Big Theorem 11.7, 11.8 --- slides


  12. Improper integrals

    Date Topics Required videos Supplementary videos Textbook sections Lecture slides
    Mon, 24 Feb Improper integrals,
    BCT for integrals
    		 12.1, 12.4, 12.7, 12.8 12.2--12.6 7.8, 7.9 slides
    Tue, 25 Feb LCT for integrals 12.9, 12.10 --- 7.8, 7.9 slides


  13. Series

    Date Topics Required videos Supplementary videos Textbook sections Lecture slides
    Mon, 2 Mar Definition of series,
    Properties of series
    		 13.2, 13.3, 13.4, 13.5, 13.6, 13.7 13.1 8.3, 8.4 slides
    Tue, 3 Mar Properties of series 13.8, 13.9 --- 8.4 slides
    Mon, 9 Mar Integral and comparison tests,
    Alternating series
    		 13.10, 13.11, 13.12, 13.13, 13.14 --- 8.5, 8.6, 8.7 slides
    Tue, 10 Mar Conditional and absolute convergence 13.15 13.16, 13.17 8.6 slides
    Mon, 16 Mar Ratio test,
    Power series
    		 13.18, 13.19, 14.1, 14.2 --- 8.7, 9.1 slides,
    Notes


  14. Power series and Taylor series

    Date Topics Required videos Supplementary videos Textbook sections Lecture slides
    Mon, 16 Mar Ratio test,
    Power series
    		 13.18, 13.19, 14.1, 14.2 --- 8.7, 9.1 slides,
    Notes
    Tue, 17 Mar Taylor polynomials 14.3, 14.4 --- 9.1, 9.2, 9.3 slides,
    Notes
    Mon, 23 Mar Taylor series,
    Analytic functions
    		 14.5, 14.6, 14.7, 14.8 --- 9.1, 9.2, 9.3 slides ,
    Notes
    Tue, 24 Mar New power series 14.9, 14.10 --- 9.1, 9.2, 9.3 slides,
    Notes
    Mon, 30 Mar Applications 14.11, 14.12, 4.13 14.14 14.5 9.1, 9.2, 9.3, 9.4 slides,
    Notes
    Tue, 31 Mar Outroduction --- --- --- slides,
    Notes