# MATH 263A: Multivariable Calculus Alternate

Course Details
Credit Hours: 4
Prerequisites: Transfer credit or AP credit for MATH 162
Description:  Vectors and vector algebra, curves and surfaces in space, functions of several variables, partial derivatives, the chain rule, the gradient vector, Lagrange multipliers, multiple integrals, volume, surface area, the Change of Variables Theorem, line integrals, surface integrals, Green's Theorem, the Divergence Theorem, and Stokes' Theorem.

James Stewart. Calculus: Early Transcendentals (packaged with WebAssign) 8th ed. 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)
14.8    Lagrange Multipliers

Chapter 15: V-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