MAT137 Calculus! 2019-2020 L0701

Lecturer: Qin Deng

E-mail: qin.deng@mail.utoronto.ca

Class Time: T3-5 @ES1050, W5-6 @MS3153

Office hours: T5-7 @ PG003




Unit 1: Set Theory and Logic

Date Topic Videos Slides Textbook section
T 10/09/19 Introduction, sets 1.1, 1.2, 1.3 Lec 1.1 slides 1.1, 1.2
W 11/09/19 Quantifiers 1.4, 1.5, 1.6 Lec 1.2 slides 1.3
T 17/09/19 Conditionals, definitions, proofs 1.7 - 1.13 Lec 1.3 slides 1.3, 1.4
W 18/09/19 Induction 1.14, 1.15 Lec 1.4 slides 1.4



Unit 2: Limit and Continuity

Date Topic Videos Slides Textbook section
T 24/09/19 Inequalties, absolute values, intuitive idea of a limit 2.1 - 2.4 Lec 2.1 slides 1.2, 1.8, 2.1
T 25/09/19 Definition of a limit 2.5, 2.6 Lec 2.2 slides 2.2
T 01/10/19 Proofs from the definition of limit, limit laws 2.7 - 2.11 Lec 2.3 slides 2.2, 2.3
W 02/10/19 Squeeze theorem and more proofs with limits 2.12, 2.13 Lec 2.4 slides 2.3
T 08/10/19 Continuity 2.14 - 2.18 Lec 2.5 slides 2.4
W 09/10/19 Computations 2.19, 2.20 Lec 2.6 slides 2.1, 2.3, 2.4



Unit 3: Derivatives

Date Topic Videos Slides Textbook section
T 15/10/19 IVT, EVT, definition of derivative 2.21, 2.22, 3.1 - 3.3 Lec 3.1 slides 2.5, 3.1
W 16/10/19 Differentiation rules 3.4, 3.5, 3.8 Lec 3.2 slides 3.2, 3.3
T 22/10/19 Proofs of differentiation rules, chain rule 3.6, 3.7, 3.9, 3.10 Lec 3.3 slides 3.1, 3.3, 3.5
W 23/10/19 Trig derivatives and implicit differentiation 3.11, 3.12 Lec 3.4 slides 3.4, 3.7
T 29/10/19 Derivative of exponentials and logarithms, related rates 3.13 - 3.20 Lec 3.5 slides 3.4, 3.6, 3.7, 4.7



Unit 4: Inverse functions and inverse trigonometric functions

Date Topic Videos Slides Textbook section
W 30/10/19 Inverse functions 4.1 - 4.2 Lec 4.1 slides 1.5, 1.7
T 12/11/19 One-to-one functions, inverse trig functions 4.3 - 4.8 Lec 4.2 slides 1.7, 3.5, 3.6



Unit 5: The mean value theorem and applications

Date Topic Videos Slides Textbook section
W 13/11/19 Local extrema 5.1 - 5.4 Lec 5.1 slides 4.1
T 19/11/19 Rolle's Theorem, MVT 5.5 - 5.9 Lec 5.2 slides 4.2
W 19/11/19 Monotonicity 5.10 - 5.12 Lec 5.3 slides 4.3



Unit 6: Applications of the derivative

Date Topic Videos Slides Textbook section
T 26/11/19 Indeterminate forms and L'Hôpital's Rule 6.3 - 6.10 Lec 6.1 slides 4.4 - 4.6
W 27/11/19 Applied optimization 6.1, 6.2 Lec 6.2 slides 4.8
T 03/12/19 Concavity, Asymptotes 6.11 - 6.16 Lec 6.3 slides 2.1, 4.9
W 04/12/19 Curve sketching - Lec 6.4 slides 4.9



Unit 7: Definition of integral

Date Topic Videos Slides Textbook section
T 07/01/20 Sums and sigmas, suprema and infima 7.1 - 7.4 Lec 7.1 slides -
W 08/01/20 Formal definition of integrals 7.5 - 7.7 Lec 7.2 slides -
T 14/01/20 Integrable functions, Riemann integrals, antiderivatives 7.8 - 7.12 Lec 7.3 slides -



Unit 8: The Fundamental Theorem of Calculus

Date Topic Videos Slides Textbook section
W 15/01/20 Antiderivatives, indefinite integrals 8.1, 8.2 Lec 8.1 slides 5.5, 5.6
T 21/01/20 FTC I and II 8.3 - 8.7 Lec 8.2 slides 5.6



Unit 9: Integration methods

Date Topic Videos Supplementary Videos Slides Textbook section
W 22/01/20 Integration by substitution 9.1 - 9.4 9.2, 9.3 Lec 9.1 slides 6.1
T 28/01/20 Integration by parts, of trig functions 9.5 - 9.12 9.7 - 9.9, 9.11, 9.12 Lec 9.2 slides 6.2, 6.3
W 29/01/20 Integration of rational functions 9.15 - 9.17 9.16, 9.17 Lec 9.3 slides 6.5



Unit 10: Volumes
Date Topic Videos Slides Textbook section
T 04/02/20 Volume 10.1, 10.2 Lec 10.1 slides 7.4, 7.5



Unit 11: Sequences
Date Topic Videos Slides Textbook section
W 05/02/20 Sequences 11.1, 11.2 Lec 11.1 slides 8.1, 8.2
T 11/02/20 Properties of sequences, Theorems about sequences 11.3 - 11.6 Lec 11.2 slides 8.1,8.2
W 12/02/20 The Big Theorem 11.7, 11.8 Lec 11.3 slides 8.2



Unit 12: Improper integrals
Date Topic Videos Slides Textbook section
T 25/02/20 Improper integrals, BCT for integrals 12.1 - 12.8 Lec 12.1 slides 7.8, 7.9
W 26/02/20 LCT for integrals 12.9, 12.10 Lec 12.2 slides 7.8, 7.9



Unit 13: Series
Date Topic Videos Slides Textbook section
T 03/03/20 Definition of series, properties of series 13.1 - 13.7 Lec 13.1 slides 8.3, 8.4
W 04/03/20 Properties of series 13.8, 13.9 Lec 13.2 slides 8.4
T 10/03/20 Integral and comparison tests, alternating series 13.10 - 13.14 Lec 13.3 slides 8.5 - 8.7
W 11/03/20 Conditional and absolute convergence 13.15 - 13.17 Lec 13.4 slides 8.6



Unit 14: Power series and Taylor series
Date Topic Videos Slides Textbook section
T 17/03/20 Ratio test, Power series 13.18, 13.19, 14.1, 14.2 Lec 14.1 slides 8.7, 9.1
W 18/03/20 Taylor polynomials 14.3, 14.4 Lec 14.2 slides 9.1 - 9.3
T 24/03/20 Taylor series, analytic functions 14.5 - 14.8 Lec 14.3 slides 9.1 - 9.3
W 25/03/20 New power series 14.9, 14.10 Lec 14.4 slides 9.1 - 9.3
T 02/04/20 Applications 14.11 - 14.14 Lec 14.5 slides 9.1 - 9.4
W 03/04/20 Outroduction - Lec 14.6 slides -