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 firstorder differential equations  
Sections 30.3 & 30.4  First order linear differential equations, first/second order constant coefficient linear differential equations  