# MAT 137: Calculus! Slides from Joel's lectures (L0301)

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.

• Intro to logic, quantifers, definitions, and proofs

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

• Limits and continuity

Date Topics Videos to watch before lecture Slides used in lecture
Fri, 22 Sep Inequalities and absolute values 2.4 Sept 22 slides
Mon, 25 Sep The intuitive idea of limit 2.1, 2.2, 2.3 Sept 25 slides
Wed, 27 Sep Formal definition of limit 2.5, 2.6 Sept 27 slides
Fri, 29 Sep Formal definition of limit 2.7, 2.8 Sept 29 slides
Mon, 2 Oct Limit laws 2.9, 2.10 Oct 2 slides
Wed, 4 Oct More proofs with limits 2.11, 2.12, 2.13 Oct 4 slides
Fri, 6 Oct Continuity 2.14, 2.15, 2.16 Oct 6 slides
Wed, 11 Oct Trigonometric limits 2.17, 2.18 Oct 11 slides
Fri, 13 Oct EVT and IVT 2.19, 2.20 Oct 13 slides

• Derivatives

Date Topics Videos to watch before lecture Slides used in lecture
Mon, 16 Oct Definition of Derivative 3.1, 3.2, 3.3 Oct 16 slides
Wed, 18 Oct Differentiation rules 3.4, 3.5, 3.8 Oct 18 slides
Fri, 20 Oct Differentiation rules 3.6, 3.7, 3.9 Oct 20 slides
Mon, 23 Oct Chain rule 3.10 Oct 23 slides
Wed, 25 Oct Trig derivative and implicit differentiation 3.11, 3.12 Oct 25 slides
Fri, 27 Oct Exponentials and Logarithms 3.13, 3.14, 3.15, 3.16, 3.17, 3.18 Oct 27 slides

• Inverse functions

Date Topics Videos to watch before lecture Slides used in lecture
Mon, 30 Oct Functions 4.1, 4.2 Oct 30 slides
Wed, 1 Nov Inverse functions and their derivatives 4.3, 4.4, 4.5 Nov 1 slides
Fri, 20 Oct Inverse trigonometric functions 4.6, 4.7, 4.8 Nov 3 slides

• Mean value theorem and applications

Date Topics Videos to watch before lecture Slides used in lecture
Mon, 13 Nov Related rates 5.1 Nov 13 slides
Wed, 15 Nov Local extrema 5.2, 5.3, 5.4 Nov 15 slides
Fri, 17 Nov Rolle's Theorem 5.5, 5.6 Nov 17 slides
Mon, 20 Nov Mean Value Theorem 5.7,5.8,5.9 Nov 20 slides
Wed, 22 Nov Increasing functions 5.10, 5.11, 5.12 Nov 22 slides
Fri, 24 Nov Applied Optimization none Nov 24 slides

• Limits at infinity, l'Hopital's rule, curve sketching

Date Topics Textbook sections to read before lecture Slides used in lecture
Mon, 27 Nov Limits at infinity Nov 27 slides
Wed, 29 Nov L'Hopital's rule 11.5 Nov 29 slides
Fri, 1 Dec L'Hopital's rule 11.6 Dec 1 slides
Mon, 4 Dec Concavity 4.6 Dec 4 slides
Wed, 6 Dec Asymptotes 4.7 Dec 6 slides
Thu, 7 Dec Curve sketching 4.8 Dec 7 slides

• Definition of the integral

Date Topics Videos to watch before lecture Slides used in lecture
Fri Jan 5 Introduction and summation notation 7.1, 7.2 Jan 5 slides
Mon Jan 8 Suprema and Infima 7.3, 7.4 Jan 8 slides
Wed Jan 10 Integrable functions 7.5-7.9 Jan 10 slides
Fri Jan 12 Integrable functions 7.5-7.9 Jan 12 slides
Mon Jan 15 Riemann sums 7.10-7.12 Jan 15 slides

• Fundamental Theorem of calculus

Date Topics Videos to watch before lecture Slides used in lecture
Wed Jan 17 More integration and indefinite integrals 8.1, 8.2 Jan 17 slides
Fri Jan 19 Fundamental Theorem of Calculus 8.3, 8.4 Jan 19 slides
Mon Jan 22 Fundamental Theorem of Calculus 8.5, 8.6, 8.7 Jan 22 slides

• Integration Methods

Date Topics Videos to watch before lecture Slides used in lecture
Wed Jan 24 Integration by substitution 9.1-9.4 Jan 24 slides
Fri Jan 26 Integration by parts 9.5-9.9 Jan 26 slides
Mon Jan 29 Integration of trig functions 9.10-9.12 Jan 29 slides
Wed Jan 31 Trig substitution 9.13, 9.14 Jan 31 slides
Fri Feb 2 Integration of rational functions 9.15 - 9.17 Feb 2 slides

• Volumes

Date Topics Textbook sections Slides used in lecture
Mon Feb 5 Volume by cross-sections 6.2 Feb 5 slides
Wed Feb 7 Volume by shells 6.3 Feb 7 slides

• Sequences

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

• Improper integrals

Date Topics Videos to watch before lecture Slides used in lecture
Fri Feb 16 Improper integrals 12.1 - 12.6 Feb 16 slides
Mon Feb 26 The basic comparison test 12.7, 12.8 Feb 26 slides
Wed Feb 26 The limit comparison test 12.9, 12.10 Feb 28 slides

• Series

Date Topics Videos to watch before lecture Slides used in lecture
Fri Mar 2 Introduction to Series 13.1 - 13.4 Mar 2 slides
Mon Mar 5 Properties of series 13.5 - 13.7 Mar 5 slides
Wed Mar 7 More properties of series 13.8, 13.9 Mar 7 slides
Fri Mar 9 Integral and comparison tests 13.10 - 13.12 Mar 9 slides
Mon Mar 12 Alernating series 13.13, 13.14 Mar 12 slides
Wed Mar 14 Absolute and conditional convergence 13.15 - 13.17 Mar 14 slides
Fri Mar 16 Ratio test 13.18, 13.19 Mar 16 slides

• Power series and Taylor series

Date Topics Videos to watch before lecture Slides used in lecture
Mon Mar 19 Power series 14.1, 14.2 Mar 19 slides
Wed Mar 21 Taylor polynomials 14.3, 14.4 Mar 21 slides
Fri Mar 23 Taylor series 14.5, 14.6 Mar 23 slides
Mon Mar 26 Analytic functions 14.7, 14.8 Mar 26 slides
Wed Mar 28 More Taylor series 14.9, 14.10 Mar 28 slides
Mon Apr 2 Estimating with Taylor series 14.11, 14.12 Apr 2 slides
Wed Apr 4 Taylor series applications 14.13 Apr 4 slides
Thu Apr 5 More Taylor series applications 14.14, 14.15 Apr 5 slides