Slides from Joel's lectures (L0301)

**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