# MAT137: Calculus with proofs 2020-2021 LEC 0501

Lecturer: Qin Deng

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

Class Time: M, Th, F 2-3

Office hours: Th 3-5

Class TAs: Dong Hao (David) Ou Yang, Aaron Tronsgard

Date Topic Videos Slides
Th 10/09/20 Introduction - Lec 1.1 slides
F 11/09/20 Sets 1.1, 1.2, 1.3 Lec 1.2 slides
M 14/09/20 Quantifiers 1.4, 1.5, 1.6 Lec 1.3 slides
Th 17/09/20 Conditionals 1.7, 1.8, 1.9 Lec 1.4 slides
F 18/09/20 Definitions and proofs 1.10 - 1.13 Lec 1.5 slides
M 21/09/20 Induction 1.14, 1.15 Lec 1.6 slides

Unit 2: Limits and Continuity

Date Topic Videos Slides
Th 24/09/20 Distance and absolute value 2.4 Lec 2.1 slides
F 25/09/20 Limits geometrically 2.1, 2.2, 2.3 Lec 2.2 slides
M 28/09/20 The definition of limit 2.5, 2.6 Lec 2.3 slides
Th 01/10/20 Proofs from the definition of limit 2.7, 2.8, 2.9 Lec 2.4 slides
F 02/10/20 Limit laws 2.10, 2.11 Lec 2.5 slides
M 05/10/20 Squeeze theorem and more proofs with limits 2.12, 2.13 Lec 2.6 slides
Th 08/10/20 Continuity 2.14, 2.15 Lec 2.7 slides
F 09/10/20 More on continuity 2.16, 2.17, 2.18 Lec 2.8 slides
Th 15/10/20 Computations 2.19, 2.20 Lec 2.9 slides
F 16/10/20 IVT, EVT 2.21, 2.22 Lec 2.10 slides, computation hints

Unit 3: Derivatives

Date Topic Videos Slides
M 19/10/20 Definition of derivative 3.1, 3.2, 3.3 Lec 3.1 slides
Th 22/10/20 Differentiation rules 3.4, 3.5, 3.8 Lec 3.2 slides
F 23/10/20 Proof of the differentiation rules 3.6, 3.7, 3.9 Lec 3.3 slides
M 26/10/20 The chain rule 3.10, 3.11 Lec 3.4 slides
Th 29/10/20 Trig derivatives, implicit differentiation 3.12, 3.13 Lec 3.5 slides

Unit 4: Transcendental functions

Date Topic Videos Slides
F 30/10/20 Inverse functions 4.1, 4.2 Lec 4.1 slides
M 02/11/20 Inverse functions 4.3, 4.4 Lec 4.2 slides
Th 05/11/20 Exponentials and logarithms 4.5, 4.7 - 4.9 (4.6, 4.10, 4.11) Lec 4.3 slides
F 06/11/20 Inverse trig functions 4.12, 4.13, 4.14 Lec 4.4 slides

Unit 5: The Mean Value Theorem and applications

Date Topic Videos Slides
M 16/11/20 Local and global extrema 5.1 - 5.4 Lec 5.1 slides
Th 19/11/20 Rolle's Theorem 5.5, 5.6 Lec 5.2 slides
F 20/11/20 MVT 5,7, 5.8, 5.9 Lec 5.3 slides
M 23/10/20 Monotonicity 5.10, 5.11, 5.12 Lec 5.4 slides

Unit 6: Applications of derivatives and limits

Date Topic Videos Slides
Th 26/11/20 Related rates 6.1, 6.2 Lec 6.1 slides
F 27/11/20 Applied optimization 6.3, 6.4 Lec 6.2 slides
M 30/11/20 Indeterminate form and L'Hôpital's Rule 6.6, 6.7, 6.9 (6.5, 6.8) Lec 6.3 slides
Th 03/12/20 Indeterminate form and L'Hôpital's Rule 6.10, 6.12 (6.11) Lec 6.4 slides
F 04/12/20 Concavity 6.13, 6.14 Lec 6.5 slides
M 07/12/20 Asymptotes 6.15 - 6.17 (6.18) Lec 6.6 slides
Th 10/12/20 Curve sketching - Lec 6.7 slides

Unit 7: The definition of integral

Date Topic Videos Slides
M 11/01/21 Sums and sigmas 7.1, 7.2 Lec 7.1 slides
Th 14/01/21 Suprema and infima 7.3, 7.4 Lec 7.2 slides
F 15/01/21 The definition of integral 7.5, 7.6 Lec 7.3 slides
M 18/01/21 Examples and properties of the integral 7.7, 7.8, 7.11 Lec 7.4 slides
Th 21/01/21 Integrals as limits 7.9, 7.10 Lec 7.5 slides

Unit 8: The Fundamental Theorem of Calculus

Date Topic Videos Slides
F 22/01/21 Antiderivatives and indefinite integrals 8.1, 8.2 Lec 8.1 slides
M 25/01/21 FTC - Part 1 8.3, 8.4 Lec 8.2 slides
Th 28/01/21 FTC - Part 2 8.5, 8.6 (8.7) Lec 8.3 slides

Unit 9: Integration methods

Date Topic Videos Slides
F 29/01/21 Integration by substitution 9.1, 9.2 (9.3) Lec 9.1 slides
M 01/02/21 Integration by parts 9.4 (9.5, 9.6) Lec 9.2 slides
Th 04/02/21 Integration of products of trigonometric functions 9.7 (9.8, 9.9) Lec 9.3 slides
F 05/02/21 Integration of rational functionsl 9.10 (9.11, 9.12) Lec 9.4 slides

Unit 10: Applications of the integrals

Date Topic Videos Slides
M 08/02/21 Volumes 10.1 Lec 10.1 slides
Th 11/02/21 Volumes 10.2 Lec 10.2 slides

Unit 11: Sequences

Date Topic Videos Slides
F 12/02/21 Sequences 11.1, 11.2 Lec 11.1 slides
M 22/02/21 Properties of sequences 11.3, 11.4 Lec 11.2 slides
Th 25/02/21 Theorems about sequences 11.5, 11.6 Lec 11.3 slides
F 26/02/21 The Big Theorem 11.7, 11.8 Lec 11.4 slides

Unit 12: Improper integrals

Date Topic Videos Slides
M 01/03/21 Improper integrals 12.1, 12.4, 12.5 (12.2, 12.3, 12.6) Lec 12.1 slides
Th 04/03/21 The Basic Comparison Test 12.7, 12.8 Lec 12.2 slides
F 05/03/21 The Limit Comparison Test 12.9, 12.10 Lec 12.3 slides

Unit 13: Series

Date Topic Videos Slides
M 08/03/21 Definition of series 13.2, 13.3, 13.4 (13.1) Lec 13.1 slides
Th 11/03/21 Properties of series 13.5, 13.6, 13.7 Lec 13.2 slides
F 12/03/21 Properties of series 13.8, 13.9 Lec 13.3 slides
M 15/03/21 Integral test and comparison test 13.10, 13.12 (13.11) Lec 13.4 slides
Th 18/03/21 Alternating series 13.13 (13.14) Lec 13.5 slides
F 19/03/21 Absolute and conditional convergence 13.15 (13.16, 13.17) Lec 13.6 slides
M 22/03/21 Ratio test 13.18, 13.19 Lec 13.7 slides

Unit 14: Power series and Taylor series

Date Topic Videos Slides
Th 25/03/21 Power series 14.1, 14.2 Lec 14.1 slides
F 26/03/21 Taylor polynomials 14.3, 14.4 Lec 14.2 slides
M 29/03/21 Taylor series 14.5, 14.6 Lec 14.3 slides
Th 01/04/21 Analytic functions 14.7, 14.8 Lec 14.4 slides
M 05/04/21 Constructing new Taylor series 14.9, 14.10 Lec 14.5 slides
Th 08/04/21 Applications 14.12, 14.14 Lec 14.6 slides
F 09/04/21 Applications 14.11, 14.13 (14.15) Lec 14.7 slides
M 12/04/21 Outroduction - Lec 14.8 slides