MAT137 Calculus! 2018-2019 L0601

Lecturer: Qin Deng

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

Class Time: T9-10, W9-11 @MP203

Office hours: W12-2 @ PG003




Unit 12: Improper integrals

Date Topic Videos Slides Textbook section
T 26/02/19 Improper integrals 12.1 - 12.6 - 7.8, 7.9
W 27/02/19 BCT, LCT 12.7 - 12.10 - 7.8, 7.9



Unit 11: Sequences
Date Topic Videos Slides Textbook section
W 06/02/19 Sequences 11.1, 11.2 Lec 11.1 slides 8.1, 8.2
T 12/02/19 Properties of sequences 11.3, 11.4 Lec 11.2 slides 8.1,8.2
W 13/02/19 Theorems about sequences, the Big Theorem 11.5 - 11.8 Lec 11.3 slides 8.2



Unit 10: Volumes
Date Topic Videos Slides Textbook section
T 05/02/19 Volume 10.1 Lec 10.1 slides TBA
W 06/02/19 Volume 10.2 See Lec 11.1 TBA



Unit 9: Integration methods
Date Topic Videos Slides Textbook section
W 23/01/19 Integration by substitution 9.1 - 9.4 Lec 9.1 slides 6.1
T 29/01/19 Integration by parts 9.5 - 9.9 Lec 9.2 slides 6.2
W 30/01/19 Integration of trig functions, rational functions 9.10 - 9.12, 9.15 - 9.17 Lec 9.3 slides 6.3



Unit 8: The definition of integral
Date Topic Videos Slides Textbook section
W 16/01/19 Antiderivative, indefinite integrals 8.1, 8.2 Lec 8.1 slides 5.5, 5.6
T 22/01/19 FTC I 8.3, 8.4 Lec 8.2 slides 5.6
W 23/01/19 FTC II 8.5 - 8.7 See Lec 9.1 5.6



Unit 7: The definition of integral
Date Topic Videos Slides Textbook section
T 08/01/19 Sums and sigmas 7.1, 7.2 Lec 7.1 slides -
W 09/01/19 Suprema, infima and integrable functions 7.3 - 7.7 Lec 7.2 slides -
T 15/01/19 More integrable functions 7.8, 7.9 Lec 7.3 slides -
W 16/01/19 Riemann sums 7.10 - 7.12 See Lec 8.1 -



Unit 6: Applications of the derivative
Date Topic Videos Slides Textbook section
T 27/11/18 Applied optimizations 6.1, 6.2 Lec 6.1 slides 4.8
W 28/11/18 Indeterminate forms, L’Hopital’s Rule 6.3 - 6.10 Lec 6.2 slides 4.4 - 4.6
T 4/12/18 Concavity 6.11, 6.12 Lec 6.3 slides 2.1, 4.9
W 5/12/18 Asymptotes, Curve sketching 6.13 - 6.16 Lec 6.4 slides 4.9



Unit 5: Mean Value Theorem and applications

Date Topic Videos Slides Textbook section
W 14/11/18 Inverse trig functions, Local extrema 4.6 - 4.8, 5.1 - 5.4 Lec 5.1 slides 3.5, 4.1
T 20/11/18 Rolle’s Theorem 5.5, 5.6 Lec 5.2 slides 4.2
W 21/11/18 MVT, Monotonicity 5.7 - 5.12 Lec 5.3 slides 4.2, 4.3



Unit 4: Inverse functions and inverse trig functions

Date Topic Videos Slides Textbook section
W 31/10/18 Related rates, inverse functions 3.19, 3.20, 4.1, 4.2 Lec 4.1 slides 4.7, 1.5, 1.7
T 13/10/18 One-to-one functions 4.3, 4.4, 4.5 Lec 4.2 slides 1.7, 3.6



Unit 3: Derivatives

Date Topic Videos Slides Textbook section
W 17/10/18 Definition of derivatives, differentiation rules 3.1, 3.2, 3.3, 3.4, 3.5, 3.8 Lec 3.1 slides 3.1 - 3.3
T 23/10/18 Proof of the differentiation rules 3.6, 3.7, 3.9 Lec 3.2 slides 3.1,3.3
W 24/10/18 Chain rule, implicit differentiation, trig 3.10, 3.11, 3.12 Lec 3.3 slides 3.4, 3.5, 3.7
T 30/10/18 Derivatives of exponentials and logarithms 3.13 - 3.18 Lec 3.4 slides 3.4, 3.6, 3.7



Unit 2: Limit and Continuity

Date Topic Videos Slides Textbook section
T 25/09/18 Inequalties, absolute values 2.4 Lec 2.1 slides 1.2, 1.8
W 26/09/18 Intuitive idea and definition of a limit 2.1, 2.2, 2.3, 2.5, 2.6 Lec 2.2 slides 2.1, 2.2
T 2/10/18 Proof from definition of limits 2.7, 2.8, 2.9 Lec 2.3 slides 2.2
W 3/10/18 Limit laws, squeeze theorem 2.10, 2.11, 2.12, 2.13 Lec 2.4 slides 2.3
T 9/10/18 Continuity 2.14, 2.15 Lec 2.5 slides 2.4
W 10/10/17 Continuity theorems, computations 2.16, 2.17, 2.18, 2.19, 2.20 Lec 2.6 slides 2.1, 2.3, 2.4
T 16/10/17 IVT, EVT 2.21, 2.22 Lec 2.7 slides 2.5



Unit 1: Set Theory and Logic

Date Topic Videos Slides Textbook section
T 11/09/18 Introduction - Lec 1.1 slides -
W 12/09/18 Sets, quantifiers 1.1, 1.2, 1.3, 1.4, 1.5, 1.6 Lec 1.2 slides 1.1, 1.2, 1.3
T 18/09/18 Conditionals, negation 1.7, 1.8, 1.9 Lec 1.3 slides 1.3
W 19/09/18 Definitions, proofs, induction 1.10, 1.11, 1.12, 1.13, 1.14, 1.15 Lec 1.4 slides 1.4