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 |
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 |
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 |
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 |
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 |
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 |
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 | - |
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 |
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 |
Date | Topic | Videos | Slides | Textbook section |
---|---|---|---|---|
T 04/02/20 | Volume | 10.1, 10.2 | Lec 10.1 slides | 7.4, 7.5 |
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 |
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 |
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 |
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 | - |