Date | Topics | Required videos | Textbook sections | Lecture slides |
---|---|---|---|---|
Fri, 7 Sep | Introduction | --- | --- | slides |
Mon, 10 Sep | Sets | 1.1, 1.2, 1.3 | 1.1, 1.2 | slides |
Wed, 12 Sep | Quantifiers | 1.4, 1.5, 1.6 | 1.3 | slides |
Fri, 14 Sep | Conditionals | 1.7, 1.8, 1.9 | 1.3 | slides |
Mon, 17 Sep | Definitions and proofs | 1.10, 1.11, 1.12, 1.13 | 1.4 | slides |
Wed, 19 Sep | Induction | 1.14, 1.15 | 1.4 | slides |
Date | Topics | Required videos | Supplementary videos | Textbook sections | Lecture slides |
---|---|---|---|---|---|
Fri, 21 Sep | Distance and absolute value | 2.4 | --- | 1.2, 1.8 | slides |
Mon, 24 Sep | The intuitive idea of limit | 2.1, 2.2, 2.3 | --- | 2.1 | slides |
Wed, 26 Sep | The definition of limit | 2.5, 2.6 | --- | 2.2 | slides |
Fri, 28 Sep | Proofs from the definition of limit | 2.7, 2.8 | 2.9 | 2.2 | slides |
Mon, 1 Oct | Limit laws | 2.10, 2.11 | --- | 2.3 | slides |
Wed, 3 Oct | Squeeze theorem and more proofs with limits | 2.12, 2.13 | --- | 2.3 | slides |
Fri, 5 Oct | Continuity | 2.14, 2.15 | --- | 2.4 | slides |
Wed, 10 Oct | More on continuity | 2.16, 2.17 | 2.18 | 2.4 | slides |
Fri, 12 Oct | Computations | 2.19, 2.20 | --- | 2.1, 2.3, 2.4 | slides |
Mon, 15 Oct | IVT and EVT | 2.21, 2.22 | --- | 2.5 | slides |
Date | Topics | Required videos | Supplementary videos | Textbook sections | Lecture slides |
---|---|---|---|---|---|
Wed, 17 Oct | Definition of derivative | 3.1, 3.2, 3.3 | --- | 3.1 | slides |
Fri, 19 Oct | Differentiation rules | 3.4, 3.5, 3.8 | --- | 3.2, 3.3 | slides |
Mon, 22 Oct | Proof of the differentiation rules | 3.6, 3.7, 3.9 | --- | 3.1, 3.3 | slides |
Wed, 24 Oct | The chain rule | 3.10 | --- | 3.5 | slides |
Fri, 26 Oct | Trig derivatives and implicit differentiation | 3.11, 3.12 | --- | 3.4, 3.7 | slides |
Mon, 29 Oct | Derivatives of exponentials and logarithms | 3.13, 3.15, 3.16, 3.17, 3.18 | 3.14 | 3.4, 3.6, 3.7 | slides |
Wed, 31 Oct | Related rates | 3.19, 3.20 | --- | 4.7 | slides |
Date | Topics | Required videos | Textbook sections | Lecture slides |
---|---|---|---|---|
Fri, 2 Nov | Inverse functions | 4.1, 4.2 | 1.5, 1.7 | slides |
Mon, 12 Nov | One-to-one functions | 4.3, 4.4, 4.5 | 1.7, 3.6 | slides |
Wed, 14 Nov | Inverse trig functions | 4.6, 4.7, 4.8 | 3.5 | slides |
Date | Topics | Required videos | Supplementary videos | Textbook sections | Lecture slides |
---|---|---|---|---|---|
Fri, 16 Nov | Local extrema | 5.2, 5.3, 5.4 | 5.1 | 4.1 | slides |
Mon, 19 Nov | Rolle's Theorem | 5.5, 5.6 | --- | 4.2 | slides |
Wed, 21 Nov | MVT | 5.7, 5.8, 5.9 | --- | 4.2 | slides |
Fri, 23 Nov | Monotonocity | 5.10, 5.11, 5.12 | --- | 4.3 | slides |
Date | Topics | Required videos | Supplementary videos | Textbook sections | Lecture slides |
---|---|---|---|---|---|
Mon, 26 Nov | Applied optimization | 6.1, 6.2 | --- | 4.8 | slides |
Wed, 28 Nov | Indeterminate forms and L'Hôpital's Rule | 6.4, 6.5, 6.7 | 6.3, 6.6 | 4.4, 4.5, 4.6 | slides |
Fri, 30 Nov | Indeterminate forms and L'Hôpital's Rule | 6.8, 6.10 | 6.9 | 4.4, 4.5, 4.6 | slides |
Mon, 3 Dec | Concavity | 6.11, 6.12 | --- | 4.9 | slides |
Wed, 5 Dec | Asymptotes | 6.13, 6.14, 6.15 | 6.16 | 2.1, 4.9 | slides |
Thu, 6 Dec | Curve sketching | --- | --- | 4.9 | slides |
Date | Topics | Required videos | Lecture slides |
---|---|---|---|
Mon, 7 Jan | Sums and sigmas | 7.1, 7.2 | slides |
Wed, 9 Jan | Suprema and infima | 7.3, 7.4 | slides |
Fri, 11 Jan | Integrable functions | 7.5, 7.6, 7.7, 7.8, 7.9 | slides |
Mon, 14 Jan | More integrable functions | 7.5, 7.6, 7.7, 7.8, 7.9 | slides |
Wed, 16 Jan | Riemann sums | 7.10, 7.11, 7.12 | slides |
Date | Topics | Required videos | Supplementary videos | Textbook sections | Lecture slides |
---|---|---|---|---|---|
Fri, 18 Jan | Antiderivatives, indefinite integrals | 8.1, 8.2 | --- | 5.5, 5.6 | slides |
Mon, 21 Jan | FTC Part 1 | 8.3, 8.4 | --- | 5.6 | slides |
Wed, 23 Jan | FTC Part 2 | 8.5, 8.6 | 8.7 | 5.6 | slides |
Note: We are skipping Videos 9.13, 9.14.
Date | Topics | Required videos | Supplementary videos | Textbook sections | Lecture slides |
---|---|---|---|---|---|
Fri, 25 Jan | Integration by substitution | 9.1 | 9.1--9.4 | 6.1 | slides |
Mon, 28 Jan | Integration by parts | 9.6 | 9.5--9.9 | 6.2 | slides |
Wed, 30 Jan | Integration of trigonometric functions | 9.10 | 9.10--9.12 | 6.3 | slides |
Fri, 1 Feb | Integration of rational functions | 9.15 | 9.15--9.17 | 6.5 | slides |
Date | Topics | Required videos | Textbook sections | Lecture slides |
---|---|---|---|---|
Mon, 4 Feb | Volumes | 10.1 | 7.4 | slides |
Wed, 6 Feb | Volumes | 10.2 | 7.5 | slides |
Date | Topics | Required videos | Textbook sections | Lecture slides |
---|---|---|---|---|
Fri, 8 Feb | Sequences | 11.1, 11.2 | 8.1, 8.2 | slides |
Mon, 11 Feb | Properties of sequences | 11.3, 11.4 | 8.1, 8,2 | slides |
Wed, 13 Feb | Theorems about sequences | 11.5, 11.6 | 8.2 | slides |
Fri, 15 Feb | The Big Theorem | 11.7, 11.8 | --- | slides |
Date | Topics | Required videos | Supplementary videos | Textbook sections | Lecture slides |
---|---|---|---|---|---|
Mon, 25 Feb | Improper integrals | 12.1, 12.4 | 12.1--12.6 | 7.8, 7.9 | posted after lecture |
Wed, 27 Feb | BCT for integrals | 12.7, 12.8 | --- | 7.8, 7.9 | posted after lecture |
Fri, 1 Mar | LCT for integrals | 12.9, 12.10 | --- | 7.8, 7.9 | posted after lecture |
Date | Topics | Required videos | Supplementary videos | Textbook sections | Lecture slides |
---|---|---|---|---|---|
Mon, 4 Mar | Definition of series | 13.2, 13.3, 13.4 | 13.1 | 8.3 | posted after lecture |
Wed, 6 Mar | Properties of series | 13.5, 13.6, 13.7 | --- | 8.3, 8.4 | posted after lecture |
Fri, 8 Mar | Properties of series | 13.8, 13.9 | --- | 8.4 | posted after lecture |
Mon, 11 Mar | Integral and comparison tests | 13.10, 13.11, 13.12 | --- | 8.5, 8.7 | posted after lecture |
Wed, 13 Mar | Alternating series | 13.13, 13.14 | --- | 8.6 | posted after lecture |
Fri, 15 Mar | Conditional and absolute convergence | 13.15 | 13.16, 13.17 | 8.6 | posted after lecture |
Mon, 18 Mar | Ratio test | 13.18, 13.19 | --- | 8.7 | posted after lecture |
Date | Topics | Required videos | Textbook sections | Lecture slides |
---|---|---|---|---|
Wed, 20 Mar | Power series | 14.1, 14.2 | 9.1 | posted after lecture |
Fri, 22 Mar | Taylor polynomials | 14.3, 14.4 | 9.1, 9.2, 9.3 | posted after lecture |
Mon, 25 Mar | Taylor series | 14.5, 14.6 | 9.1, 9.2, 9.3 | posted after lecture |
Wed, 27 Mar | Analytic functions | 14.7, 14.8 | 9.1, 9.2, 9.3 | posted after lecture |
Fri, 29 Mar | New power series | 14.9, 14.10 | 9.1, 9.2, 9.3 | posted after lecture |
Mon, 1 Apr | Applications | 14.12, 14.14 | 9.1, 9.2, 9.3, 9.4 | posted after lecture |
Wed, 3 Apr | Applications | 14.11, 14.13 | 9.1, 9.2, 9.3, 9.4 | posted after lecture |
Fri, 5 Apr | Applications | 14.15 | 9.4 | posted after lecture |