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Please note that these lectures were originally given as review sessions for the Princeton introductory calculus courses MAT103 and MAT104 during the 2006/7 academic year. As a result, some of the topics are covered out of order, and some sections of The Calculus Lifesaver aren't covered at all. Each lecture lasts for about 2 hours. We hope that you find them useful! RealPlayer is required to view the streaming videos. If you don't have it installed, click here http://www.real.com/player to download it. To copy the Vodcast (MPEG-4) or WindowsMedia files, right-click the links and "save as."
Videos of lectures by Adrian Banner
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| Chapters / Sections | Contents | Streaming
(RealPlayer) | Download
(Vodcast) | Download
(WMV) |
| Chapters 1 & 2 | Functions, trig | Video 1 | File 1 | File 1 |
| Chapters 3 & 4 | Limits: theory and polynomial examples | Video 2 | File 2 | File 2 |
Chapter 5 &
Sections 7.1.1 & 7.1.2 | Continuity, differentiability, trig limits | Video 3 | File 3 | File 3 |
Sections 7.1.3 & 7.1.4
Chapter 6 (except 6.6 & 6.7)
Section 7.2, excluding 7.2.3 | Trig limits (continued), how to solve differentiation problems, trig derivatives, simple harmonic motion | Video 4 | File 4 | File 4 |
| Chapter 8 | Implicit differentiation, related rates | Video 5 | File 5 | File 5 |
Chapter 9 (except 9.6 & 9.7)
Section 14.2 | Exponentials, review of topics so far | Video 6 | File 6 | File 6 |
Sections 10.1, 10.2 &
13.2 (except 13.2.4) | Inverse functions, inverse trig functions, linearization | Video 7 | File 7 | File 7 |
Section 13.2.2
Chapter 11 | More on the differential, extrema, Rolle/Mean Value Theorem, critical points and the second derivatives (Note: The lecture stops suddenly but is made up at the beginning of the next video.) | Video 8 | File 8 | File 8 |
Section 11.5
Chapter 12 | Classifying critical points, sketching graphs | Video 9 | File 9 | File 9 |
| Sections 13.1 & 14.1 | Optimization, L’Hôpital's Rule | Video 10 | File 10 | File 10 |
Chapter 15 (except 15.1.2)
Chapter 16 (except 16.7)
Sections 17.1, 17.2, & 17.3 | Sigma notation, Riemann sums, integration, introduction to the Fundamental Theorems | Video 11 | File 11 | File 11 |
Chapter 17
Section 18.1 | Fundamental Theorems, integration by substitution | Video 12 | File 12 | File 12 |
| Sections 18.1, 18.2, & 19.1 | Substitution revisited, integration by parts, integrals involving trig limits | Video 13 | File 13 | File 13 |
| Section 18.3 | Partial fractions | Video 14 | File 14 | File 14 |
| Sections 19.2, 19.3 & 19.4 | Trig integrals, trig substitutions, and summary of integration techniques | Video 15 | File 15 | File 15 |
| Chapter 29 (except 29.2) | Volumes of revolution, arc lengths, and surface areas | Video 16 | File 16 | File 16 |
| Chapter 20, Sections 21.1 & 21.3.1 | Improper integrals, part 1 | Video 17 | File 17 | File 17 |
| Sections 21.3, 21.4, & 21.5 | Improper integrals, part 2 | Video 18 | File 18 | File 18 |
| Sections 22.1, 22.2, 22.5.1, 22.5.2, 23.1, 23.2, 23.3, & 23.4 | Sequences and series, part 1 | Video 19 | File 19 | File 19 |
| Sections 22.5.3, 22.5.4, 23.5, 23.6, 23.7 & 24.1 | Sequences and series, part 2, introduction to power | Video 20 | File 20 | File 20 |
Section 24.2, Chapter 25,
Section 26.1 | Estimation using Taylor series, the remainder/error term, radius of convergence of power series | Video 21 | File 21 | File 21 |
| Chapter 26, Section 28.1 | More about power and Taylor series, introduction to complex numbers | Video 22 | File 22 | File 22 |
| Sections 28.1.1, 28.2, 28.3, 28.4, 30.1 & 30.2 | Complex numbers, separable first-order differential equations | Video 23 | File 23 | File 23 |
| Sections 30.3 & 30.4 | First order linear differential equations, first/second order constant coefficient linear differential equations | Video 24 | File 24 | File 24 |
File updated: 9/11/2007 |
