MATH 263: Multivariable Calculus

Credit Hours

4

Prerequisites

MATH 162

Description

Vectors and vector algebra, vector-valued functions, functions of several variables, differential and integral calculus of functions of several variables, and advanced topics including change of variables in multiple integration, Green's Theorem, the Divergence Theorem, and Stokes' Theorem. Software such as MAPLE may be utilized.

James Stewart. Calculus: Early Transcendentals (packaged with WebAssign) 8th edition. Cengage Learning

Chapter 12: Vectors and the Geometry of Space
12.1    Three-Dimensional Coordinate Systems
12.2    Vectors
12.3    The Dot Product
12.4    The Cross Product
12.5    Equations of Lines and Planes
12.6    Optional: Cylinders and Quadric Surfaces
Chapter 13: Vector Functions
13.1    Vector Functions and Space Curves
13.2    Derivatives and Integrals of Vector Functions
13.3    Arc Length and Curvature
13.4    Motion in Space: Velocity and Acceleration
Chapter 14: Partial Derivatives
14.1    Functions of Several Variables
14.2    Limits and Continuity
14.3    Partial Derivatives
14.4    Tangent Planes and Linear Approximation
14.5    The Chain Rule
14.6    Directional Derivatives and the Gradient Vector
14.7    Maximum and Minimum Values (Optional: Discovery Project “Quadratic Approximations and Critical Points”)
14.8    Lagrange Multipliers
Chapter 15: Multiple Integrals
15.1    Double Integrals over Rectangles
15.2    Double Integrals over General Regions
15.3    Double Integrals in Polar Coordinates
15.4    Applications of Double Integrals
15.5    Surface Area
15.6    Triple Integrals
15.7    Triple Integrals in Cylindrical Coordinates
15.8    Triple Integrals in Spherical Coordinates
15.9    Change of Variables in Multiple Integrals
Chapter 16: Vector Calculus
16.1    Vector Fields
16.2    Line Integrals
16.3    The Fundamental Theorem for Line Integrals
16.4    Green’s Theorem
16.5    Curl and Divergence
16.6    Parametric Surfaces and Their Areas
16.7    Surface Integrals
16.8    Stokes’ Theorem
16.9    The Divergence Theorem