Week
Topics covered
1
Sequences and Convergence;  Infinite Series; Convergence Tests for Positive Series; Absolute and Conditional Convergence
2
Power Series;  Taylor and Maclaurin Series; Applications of Taylor and Maclaurin Series; The Binomial Theorem and Binomial Series
3
 Analytic Geometry in Three Dimensions;  Vectors ; The Cross Product in 3-Space;  Planes and Lines
4
 Quadric Surfaces;  Conics (only Classifying General Conics);  Vector Functions of One Variable; Curves and Parametrizations; Arc Length and Surface Area (up to Areas of Surfaces of Revolution)
5
 Functions of Several Variables; Limits and Continuity
6
Partial Derivatives (omit Distance from a Point to a Surface);  Higher-Order Derivatives;  The Chain Rule (omit Homogeneous Functions);  Linear Approximations, Differentiability, and Differentials; (up to Differentials in Applications)
7
 Gradients and Directional Derivatives;  Implicit Functions; Taylor Series and Approximations (omit Approximating Implicit Functions)
8
Extreme Values;  Extreme Values of Functions Defined on Restricted Domains (omit Linear Programming); Lagrange Multipliers (omit Nonlinear Programming)
9
 Parametric Problems (only Differentiating Integrals with Parameters);  Double Integrals;  Iteration of Double Integrals in Cartesian Coordinates;  Improper Integrals and a Mean-Value Theorem
10
 Polar Coordinates and Polar Curves (omit Polar Conics);  Double Integrals in Polar Coordinates;  Slopes, Areas, and Arc Lengths for Polar Curves (only Areas Bounded by Polar Curves); Triple Integrals
11
 Cylindrical and Spherical Coordinates; Change of Variables in Triple Integrals
12
Vector and Scalar Fields(up to Fields Lines);  Conservative Fields (omit Sources, Sinks, and Dipoles);  Line Integrals; Line Integrals of Vector Fields
13
Surfaces and Surface Integrals (omit The Attraction of a Spherical Shell );  Arc Length and Surface Area (only Areas of Surfaces of Revolution);  Oriented Surfaces and Flux Integrals
14
Gradient, Divergence, and Curl (up to Interpretation of the Divergence);  Some Identities Involving Grad, Div, and Curl;  Green's Theorem in the Plane.