| Date | Topics | Videos to watch before lecture | Slides used in lecture |
|---|---|---|---|
| Thu, Sep 7 | Introduction+Sets | 1.1, 1.2, 1.3 | Lecture 1 slides |
| Mon, Sep 11 | Negation+Quantifiers | 1.4, 1.5, 1.6 | Lecture 2 slides |
| Thu, Sep 14 | Conditionals+Definitions | 1.7 to 1.13 | Lecture 3 slides |
| Mon, Sep 18 | Induction | 1.14, 1.15 | Lecture 4 slides |
| Date | Topics | Videos to watch before lecture | Slides used in lecture |
|---|---|---|---|
| Thu, Sep 21 | Inequalities and absolute values
Intuitive definition of limit |
2.4, 2.1, 2.2, 2.3 | Lecture 5 slides |
| Mon, Sep 25 | The formal definition of limit | 2.5, 2.6, 2.7 | Lecture 6 slides |
| Thu, Sep 28 | More on definitions of limit
Limit laws, squeeze theorem |
2.8, 2.9, 2.10, 2.11, 2.12 | Lecture 7 slides |
| Mon, Oct 2 | Continuity | 2.13, 2.14, 2.15 | Lecture 8 slides |
| Thu, Oct 5 | Discontinuities, Trigonometric Limits | 2.16, 2.17, 2.18 | Lecture 9 slides |
| Thu, Oct 12 | IVT, EVT, Definition of Derivative | 2.19, 2.20, 3.1, 3.2, 3.3, 3.4 | Lecture 10 slides |
| Date | Topics | Videos to watch before lecture | Slides used in lecture |
|---|---|---|---|
| Mon, Oct 16 |
Differentiability implies continuity
Proofs of differentiation rules |
3.5, 3.6, 3.7 | Lecture 11 slides |
| Thu, Oct 19 |
Higher-order derivatives
The chain rule Derivatives of trigonometric functions |
3.8, 3.9, 3.10, 3.11 | Lecture 12 slides |
| Mon, Oct 23 | Implicit Differentiation | 3.12 | Lecture 13 slides |
| Thu, Oct 26 | Exponentials and Logarithms | 3.13, 3.14, 3.15, 3.16, 3.17, 3.18 | Lecture 14 slides |
| Date | Topics | Videos to watch before lecture | Slides used in lecture |
|---|---|---|---|
| Mon, Oct 30 | Inverse Functions | 4.1, 4.2, 4.3, 4.4 | Lecture 15 slides |
| Thu, Nov 2 |
Inverse trigonometric functions Related rates |
4.5, 4.6, 4.7, 4.8 No videos |
Lecture 16 slides
Related rates |
| Date | Topics | Videos to watch before lecture | Slides used in lecture |
|---|---|---|---|
| Mon, Nov 13 | Local extrema | 5.1, 5.2, 5.3, 5.4 | Lecture 17 slides |
| Thu, Nov 16 | Rolle's Theorem, MVT | 5.5, 5.6, 5.7, 5.8, 5.9 | Lecture 18 slides |
| Mon, Nov 20 | Increasing and decreasing functions | 5.10, 5.11, 5.12 | Lecture 19 slides |
| Date | Topics | Videos to watch before lecture | Slides used in lecture |
|---|---|---|---|
| Thu, Nov 23 |
Applied optimization problems Limit at $\infty$ |
No videos | Applied Optimization Problems Limits at Infinity |
| Mon, Nov 27 |
Limit at $\infty$ (continued) L'Hopital's Rule |
No videos | Limits at Infinity (Cont.) |
| Thu, Nov 30 |
L'Hopital's Rule Curve sketching |
No videos | L'Hopital's Rule |
| Mon, Dec 4 | Concavity, Curve sketching | No videos | Curve Sketching |
| Thu, Dec 7 (makeup) | Curve sketching (continued) | No videos |
| Date | Topics | Videos to watch before lecture | Slides used in lecture |
|---|---|---|---|
| Thu, Jan 4 | Sums and sigmas, suprema, infima | 7.1, 7.2, 7.3, 7.4 | Lecture 20 slides |
| Mon, Jan 8 | Integrable functions | 7.5, 7.6, 7.7, 7.8, 7.9 | Lecture 21 slides |
| Thu, Jan 11 | Integrable functions, Riemann sums | 7.5 to 7.12 | Lecture 22 slides |
| Date | Topics | Videos to watch before lecture | Slides used in lecture |
|---|---|---|---|
| Mon, Jan 15 |
Antiderivatives, indefinite integrals FTC Part 1 |
8.1, 8.2, 8.3 | Lecture 23 slides |
| Thu, Jan 18 | FTC Part 1 + Part 2 | 8.3, 8.4, 8.5, 8.6, 8.7 | Lecture 24 slides |
| Date | Topics | Videos to watch before lecture | Slides used in lecture |
|---|---|---|---|
| Mon, Jan 22 | Substitution rule | 9.1, 9.2, 9.3 | Lecture 25 slides |
| Thu, Jan 25 |
Substitution rule (continued) Integration by parts |
9.4, 9.5, 9.6, 9.7, 9.8, 9.9 | Lecture 26 slides |
| Mon, Jan 29 |
Integration of trigonometric functions Integration by trigonometric substitution |
9.10, 9.11, 9.12, 9.13, 9.14 | Lecture 27 slides |
| Thu, Feb 1 |
Trig substitution (continued) Volumes: washer method |
9.15, 9.16, 9.17 No videos |
Lecture 28 slides Volume1 |
| Mon, Feb 5 | Volumes: shell method | No videos | Volume2 |
| Date | Topics | Videos to watch before lecture | Slides used in lecture |
|---|---|---|---|
| Thu, Feb 8 |
Convergence of sequences Bounded and monotonic sequences |
11.1, 11.2, 11.3, 11.4, 11.5 | Lecture 29 slides |
| Mon, Feb 12 |
The monotone convergence theorem for sequences The big theorem for sequences |
11.6, 11.7, 11.8 | Lecture 30 slides |
| Date | Topics | Required videos | Recommended videos | Slides used in lecture |
|---|---|---|---|---|
| Thu, Feb 15 |
Definition of improper integrals The basic comparison test |
12.1, 12.4 12.7, 12.8 |
12.1--12.6 |
Lecture 31 slides |
| Mon, Feb 26 | The limit comparison test | 12.9, 12.10 | Lecture 32 slides |
| Date | Topics | Required videos | Recommended videos | Slides used in lecture |
|---|---|---|---|---|
| Thu, March 1 |
Definition of series Properties of series |
13.2, 13.3, 13.4 13.5, 13.6 |
13.1 | Lecture 33 slides |
| Mon, March 5 | The divergence test | 13.7, 13.8, 13.9 | Lecture 34 slides | |
| Thu, March 8 |
Integral test and comparison test Alternating series |
13.10, 13.11, 13.12 13.13, 13.14 |
Lecture 35 slides | |
| Mon, March 12 | Absolute and conditional convergence | 13.15 | 13.6, 13.7 | Lecture 36 slides |
| Thu, March 15 |
The ratio test Power series |
13.18, 13.19 14.1, 14.2 |
Lecture 37 slides |
| Date | Topics | Required videos | Recommended videos | Slides used in lecture |
|---|---|---|---|---|
| Mon, March 19 | Taylor polynomials | 14.3, 14.4 | Taylor Series | Lecture 38 slides |
| Thu, March 22 |
Taylor series Analytic functions |
14.5, 14.6 14.7, 14.8 |
Lecture 39 slides | |
| Mon, March 26 | New power series | 14.9, 14.10 | Lecture 40 slides | |
| Thu, March 29 | Applications | 14.11, 14.12, 14.13, 14.14 | Lecture 41 slides | |
| Mon, April 2 | Applications | 14.5 | Lecture 42 slides |