Date | Topics | Required videos | Supplementary videos | Lecture slides |
---|---|---|---|---|
Thu, 10 Sep | Introduction | --- | --- | To be posted |
Fri, 11 Sep | Sets | 1.1, 1.2, 1.3 | --- | slide |
Mon, 14 Sep | Quantifiers | 1.4, 1.5, 1.6 | --- | slide |
Thu, 17 Sep | Conditionals | 1.7, 1.8 | 1.9 | slide |
Fri, 18 Sep | Definitions and proofs | 1.10, 1.11, 1.12, 1.13 | --- | slide |
Mon, 21 Sep | Induction | 1.14, 1.15 | --- | slide |
Date | Topics | Required videos | Supplementary videos | Lecture slides |
---|---|---|---|---|
Thu, 24 Sep | Distance and absolute value | 2.4 | --- | slide |
Fri, 25 Sep | Limits geometrically | 2.1, 2.2, 2.3 | --- | slide |
Mon, 28 Sep | The definition of limit | 2.5, 2.6 | --- | slide |
Thu, 1 Oct | Proofs from the definition of limit | 2.7, 2.8 | 2.9 | slide |
Fri, 2 Oct | Limit laws | 2.10, 2.11 | --- | slide |
Mon, 5 Oct | Squeeze theorem and more proofs with limits | 2.12, 2.13 | --- | slide |
Thu, 9 Oct | Continuity | 2.14, 2.15 | --- | slide |
Fri, 10 Oct | More on continuity | 2.16, 2.17 | 2.18 | slide |
Thu, 15 Oct | Computations | 2.19, 2.20 | --- | slide |
Fri, 16 Oct | IVT and EVT | 2.21, 2.22 | --- | slide |
Date | Topics | Required videos | Supplementary videos | Lecture slides |
---|---|---|---|---|
Mon, 19 Oct | Definition of derivative | 3.1, 3.2, 3.3 | --- | slide |
Thu, 22 Oct | Differentiation rules | 3.4, 3.5, 3.8 | --- | slide |
Fri, 23 Oct | Proof of the differentiation rules | 3.6, 3.7, 3.9 | --- | slide |
Mon, 26 Oct | The chain rule | 3.10, 3.11 | --- | slide |
Thu, 29 Oct | Trig derivatives and implicit differentiation | 3.12, 3.13 | --- | slide |
Date | Topics | Required videos | Supplementary videos | Lecture slides |
---|---|---|---|---|
Fri, 30 Oct | Inverse functions | 4.1, 4.2 | --- | slide |
Mon, 2 Nov | Inverse functions | 4.3, 4.4 | --- | slide |
Thu, 5 Nov | Exponentials and logarithms | 4.5, 4.7, 4.8, 4.9 | 4.6, 4.10, 4.11 | slide |
Fri, 6 Nov | Inverse trig functions | 4.12, 4.13, 4.14 | --- | slide |
Date | Topics | Required videos | Supplementary videos | Lecture slides |
---|---|---|---|---|
Mon, 16 Nov | Local extrema | 5.2, 5.3, 5.4 | 5.1 | slide |
Thu, 19 Nov | Rolle's Theorem | 5.5, 5.6 | --- | slide |
Fri, 20 Nov | MVT | 5.7, 5.8, 5.9 | --- | slide |
Mon, 23 Nov | Monotonocity | 5.10, 5.11 | 5.12 | slide |
Date | Topics | Required videos | Supplementary videos | Lecture slides |
---|---|---|---|---|
Thu, 26 Nov | Related rates | 6.1, 6.2 | --- | slide |
Fri, 27 Nov | Applied optimization | 6.3, 6.4 | --- | slide |
Mon, 30 Nov | Indeterminate forms and L'Hôpital's Rule | 6.6, 6.7, 6.9 | 6.5, 6.8 | slide |
Thu, 3 Dec | Indeterminate forms and L'Hôpital's Rule | 6.10, 6.12 | 6.11 | slide |
Fri, 4 Dec | Concavity | 6.13, 6.14 | -- | slide |
Mon, 7 Dec | Asymptotes | 6.15, 6.16, 6.17 | 6.18 | slide |
Thu, 10 Dec | Curve sketching | --- | --- | slide |
Date | Topics | Required videos | Supplementary videos | Lecture slides |
---|---|---|---|---|
Mon, 11 Jan | Sums and sigmas | 7.1, 7.2 | --- | slide |
Thu, 14 Jan | Suprema and infima | 7.3, 7.4 | --- | slide |
Fri, 15 Jan | The definition of integral | 7.5, 7.6 | --- | slide |
Mon, 18 Jan | Examples and properties of the integral | 7.7, 7.8, 7.11 | --- | slide |
Thu, 21 Jan | Integrals as limits | 7.9, 7.10 | -- | slide |
Date | Topics | Required videos | Supplementary videos | Lecture slides |
---|---|---|---|---|
Fri, 22 Jan | Antiderivatives and indefinite integrals | 8.1, 8.2 | --- | slide |
Mon, 25 Jan | FTC - Part 1 | 8.3, 8.4 | --- | slide |
Thu, 28 Jan | FTC - Part 2 | 8.5, 8.6 | 8.7 | slide |
Date | Topics | Required videos | Supplementary videos | Lecture slides |
---|---|---|---|---|
Fri, 29 Jan | Integration by substitution | 9.1, 9.3 | 9.2 | slide |
Mon, 1 Feb | Integration by parts | 9.4 | 9.5, 9.6 | slide |
Thu, 4 Feb | Integration of products of trigonometric functions | 9.7 | 9.8, 9.9 | slide |
Fri, 5 Feb | Integration of rational functions | 9.10 | 9.11, 9.12 | slide |
Date | Topics | Required videos | Supplementary videos | Lecture slides |
---|---|---|---|---|
Mon, 8 Feb | Volumes | 10.1 | --- | slide |
Thu, 11 Feb | Volumes | 10.2 | --- | slide |
Date | Topics | Required videos | Supplementary videos | Lecture slides |
---|---|---|---|---|
Fri, 12 Feb | Sequences | 11.1, 11.2 | --- | slide |
Mon, 22 Feb | Properties of sequences | 11.3, 11.4 | --- | slide |
Thu, 25 Feb | Theorems about sequences | 11.5, 11.6 | --- | slide |
Fri, 26 Feb | The Big Theorem | 11.7, 11.8 | --- | slide |
Date | Topics | Required videos | Supplementary videos | Lecture slides |
---|---|---|---|---|
Mon, 1 Mar | Improper integrals | 12.1, 12.4, 12.5 | 12.2, 12.3, 12.6 | slide |
Thu, 4 Mar | The Basic Comparison Test | 12.7, 12.8 | --- | slide |
Fri, 5 Mar | The Limit Comparison Test | 12.9, 12.10 | --- | slide |
Date | Topics | Required videos | Supplementary videos | Lecture slides |
---|---|---|---|---|
Mon, 8 Mar | Definition of series | 13,2, 13.3, 13.4 | 13.1 | slide |
Thu, 11 Mar | Properties of series | 13.5, 13.6, 13.7 | --- | slide |
Fri, 12 Mar | Properties of series | 13.8, 13.9 | --- | slide |
Mon, 15 Mar | Integral test and comparison tests | 13.10, 13.12 | 13.11 | slide |
Thu, 18 Mar | Alternating series | 13.13 | 13.14 | slide |
Fri, 19 Mar | Absolute and conditional convergence | 13.15 | 13.16, 13.17 | slide |
Mon, 22 Mar | Ratio test | 13.18, 13.19 | --- | slide |
Date | Topics | Required videos | Supplementary videos | Lecture slides |
---|---|---|---|---|
Thu, 25 Mar | Power series | 14.1, 14.2 | --- | slide |
Fri, 26 Mar | Taylor polynomials | 14.3, 14.4 | --- | slide |
Mon, 29 Mar | Taylor series | 14.5, 14.6 | --- | slide |
Thu, 1 Apr | Analytic functions | 14.7, 14.8 | --- | slide |
Fri, 2 Apr | GOOD FRIDAY (no class) | --- | --- | (no class) |
Mon, 5 Apr | Constructing new Taylor series | 14.9, 14.10 | --- | slide |
Thu, 8 Apr | Applications | 14.12, 14.14 | --- | slide |
Fri, 9 Apr | Applications | 14.11, 14.13 | 14.15 | slide |
Mon, 12 Apr | Outroduction | --- | --- | slide |