Preface: The course textbook (Stewart, Clegg and Watson, Calculus, Ninth Edition, Cengage Publishing Co., 2020) is phenomenal. Reading the respective textbook chapters will serve you well in this course. However, many of us learn better through different mediums. Thus, I have created this study plan which consists of YouTube videos which will also take you through the respective course content. I suggest watching the videos and then doing the suggested problems from the course textbook. The videos are primarily taken from MAT137: Calculus with Proofs. It is appropriate as ESC194 and ESC195 provide a transfer credit for that course. The videos are made by Alfonso Gracia-Saz who unfortunately passed away in 2021. See here to learn more about his legacy: ‘Passionate, principled and caring’: U of T remembers math professor Alfonso Gracia-Saz. The multivariable portion of this course has videos taken from Alexandra Niedden. She teaches the content straight out of the course textbook so it will do well for this course.
Note: The MAT137 videos are appropriately rigorous, however, the videos are decently more rigorous than Professor Davis' lectures.
| Lecture | Topic | Resources |
|---|---|---|
| 1 | 6.7 Hyperbolic Functions | See Course Textbook for 6.7 |
| 2 | 6.8 Indeterminate Forms and l'Hospital's Rule |
Indeterminate Forms (6.5, 6.9, 6.10, 6.11, 6.12) L'Hôpital's Rule (6.6, 6.7, 6.8) |
| 3 | 7.1 Integration by Parts | Integration by Parts (9.4, 9.5, 9.6) |
| 4 |
7.2 Trigonometric Integrals 7.3 Trigonometric Substitution |
Integration of Trigonometric Functions (9.7, 9.8, 9.9) See Course Textbook for 7.3 |
| 5 | 7.4 Partial Fractions | Integration of Rational Functions (9.10, 9.11, 9.12) |
| 6 | 7.8 Improper Integrals | Improper Integrals (12.1, 12.2, 12.3, 12.4, 12.5, 12.6, 12.7, 12.8, 12.9, 12.10) |
| 7 |
8.1 Arc Length 8.2 Area of a Surface of Revolution |
See Course Textbook for 8.1 - 8.3 and 10.1 - 10.4 |
| 8 | 8.3 Applications to Physics and Engineering | |
| 9 |
10.1 Curves Defined by Parametric Equations 10.2 Calculus with Parametric Curves |
|
| 10 | 10.3 Polar Coordinates | |
| 11 | 10.4 Areas and Lengths in Polar Coordinates | |
| 12 | 11.1 Sequences Part 1 | Sequences and their Properties (11.1, 11.2, 11.3, 11.4) |
| 13 | 11.1 Sequences Part 2 | Theorems About Sequences (11.5, 11.6) The Big Theorem (11.7, 11.8) |
| 14 | 11.2 Series | Series (13.1, 13.2, 13.3, 13.4, 13.5, 13.6, 13.7, 13.8, 13.9) |
| 15 |
11.3 The Integral Test and Estimates of Sums 11.4 The comparison Tests |
The Integral Test (13.10, 13.11) Estimating the Value of an Alternating Series (13.14) Comparison Tests for Series (13.12) |
| 16 |
11.5 Alternating Series and Absolute Convergence 11.6 The Ratio and Root Tests |
Alternating Series (13.13) Absolute and Conditional Convergence (13.15, 13.16) Infinite Sums are not Commutative! (13.17) Ratio Test (13.18, 13.19) |
| 17 |
11.8 Power Series 11.9 Representations of Functions as Power Series |
Power Series (14.1, 14.2) How to Write Functions as Power Series Quickly (14.9, 14.10) |
| 18 | 11.10 Taylor and Maclaurin Series Part 1 | Taylor Polynomials (14.3, 14.4, 14.5) |
| 19 | 11.10 Taylor and Maclaurin Series Part 2 | The Four Main Maclaurin Series (14.6) |
| 20 |
11.11 Applications of Taylor Polynomials 11.12 The Binomial Series |
Analytic Functions and the Remainder Theorems (14.7, 14.8) Taylor Applications (14.11, 14.12, 14.13, 14.14, 14.15) Excerpt from Stewart on Binomial Series |
| 21 |
11.13 Fourier Series 12.5 Equations of Lines and Planes |
Stewart on Fourier Series Niedden - Equations of Lines & Planes |
| 22 |
12.6 Cylinders and Quadric Surfaces 13.1 Vector Functions and Space Curves |
Niedden - Cylinders & Quadric Surfaces Niedden - Vector Functions and Space Curves |
| 23 | 13.2 Derivatives and Integrals of Vector Functions | Niedden - Derivatives and Integrals of Vector Functions |
| 24 | 13.3 Arc Length and Curvature | Niedden - Arc Length and Curvature |
| 25 | 13.4 Motion in Space: Velocity and Acceleration | Niedden - Motion in Space: Velocity and Acceleration |
| 26 | Charged Particle Motions in Electric and Magnetic Fields | Go to Lecture |
| 27 |
14.1 Functions of Several Variables 14.2 Limits and Continuity |
Niedden - Functions of Several Variables Niedden - Limits and Continuity |
| 28 | 14.3 Partial Derivatives | Niedden - Partial Derivatives |
| 29 | 14.4 & 14.6 Directional Derivatives and the Gradient Vector Part 1 |
Niedden - Directional Derivatives and the Gradient Vector Part 1 Niedden - The Chain Rule |
| 30 |
14.4 & 14.6 Directional Derivatives and the Gradient Vector Part 2 14.5 The Chain Rule |
|
| 31 | 14.6 & 14.4 Tangent Planes and Linear Approximations | Niedden - Tangent Planes and Linear Approximations |
| 32 | 14.7 Maximum and Minimum Values Part 1 | Niedden - Maximum and Minimum Values |
| 33 | 14.7 Maximum and Minimum Values Part 2 | |
| 34 |
14.8 Lagrange Multipliers 14.9 Reconstructing a Function from its Gradient |
Niedden - Lagrange Multipliers Hale - Reconstructing a Function from its Gradient |
| 35 | Rocket Science | Go to Lecture |
| 36 | 14.10 Differentiability of an Integral wrt its Parameter | Goldmakher on Differentiation Under the Integral Sign |
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