# The Calculus Lifesaver: All The Tools You Need To Excel At Calculus by Adrian Banner

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!

 An Interview with Adrian Banner (8:18) "How I Wrote The Calculus Lifesaver"

### Videos of lectures by Adrian Banner

Chapters / Sections Contents Video
File 1: Chapters 1 & 2 Functions, trig
File 2: Chapters 3 & 4 Limits: theory and polynomial examples
File 3: Chapter 5 & 6
Sections 7.1.1 & 7.1.2
Continuity, differentiability, trig limits
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
Chapter 8 Implicit differentiation, related rates
Chapter 9 (except 9.6 & 9.7)
Section 14.2
Exponentials, review of topics so far
Sections 10.1, 10.2 &
13.2 (except 13.2.4)
Inverse functions, inverse trig functions, linearization
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.)
Section 11.5
Chapter 12
Classifying critical points, sketching graphs
Sections 13.1 & 14.1 Optimization, L'Hopital's Rule
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
Chapter 17
Section 18.1
Fundamental Theorems, integration by substitution
Sections 18.1, 18.2, & 19.1 Substitution revisited, integration by parts, integrals involving trig limits
Section 18.3 Partial fractions
Sections 19.2, 19.3 & 19.4 Trig integrals, trig substitutions, and summary of integration techniques
Chapter 29 (except 29.2) Volumes of revolution, arc lengths, and surface areas
Chapter 20, Sections 21.1 & 21.3.1 Improper integrals, part 1
Sections 21.3, 21.4, & 21.5 Improper integrals, part 2
Sections 22.1, 22.2, 22.5.1, 22.5.2, 23.1, 23.2, 23.3, & 23.4 Sequences and series, part 1
Sections 22.5.3, 22.5.4, 23.5, 23.6, 23.7 & 24.1 Sequences and series, part 2, introduction to power
Section 24.2, Chapter 25,
Section 26.1
Estimation using Taylor series, the remainder/error term, radius of convergence of power series
Chapter 26, Section 28.1 More about power and Taylor series, introduction to complex numbers
Sections 28.1.1, 28.2, 28.3, 28.4, 30.1 & 30.2 Complex numbers, separable first-order differential equations
Sections 30.3 & 30.4 First order linear differential equations, first/second order constant coefficient linear differential equations

File updated: 7/15/2014