Description

An introduction to multivariable calculus, including vectors and vector-valued functions, partial derivatives and applications of partial derivatives (such as tangent planes and Lagrange multipliers), multiple integrals, volume, surface area, and the classical theorems of Green, Stokes and Gauss. All sections of the course will use the software package MATLAB.

Prerequisites

MATH 141

Topics

(by chapter) XI. Vectors, Lines and Planes.
Cartesian coordinates of space
Vectors
Lines
Planes
Dot and cross product
XII. Vector-valued Functions
Vector-valued functions
Tangents
Normals
Curvature
XIII. Partial Derivatives
Quadric surfaces
Partial derivatives
Chain rule
Directional derivatives
Gradients
Extreme values
Lagrange multipliers
XIV. Multiple Integrals
Double and triple integrals
Change of variable
Volume
Surface area
Moments and centers of gravity
XV. Calculus of Vector Fields
Line and surface integrals
Green's theorem
Stokes' theorem
Divergence theorem