# MATH 263: Multivariable Calculus

Course Details
Credit Hours: 4
Prerequisites: MATH 162
Description:  This course covers the differential and integral calculus of multivariable and vector valued functions, and sequences and infinite series, culminating with Green's Theorem, the Divergence Theorem, and Stokes' Theorem.

Dwyer and Grunwald, “Calculus: Resequenced for Students in STEM”, Preliminary Edition, Wiley.

Chapter 12: Infinite Series

12.1    Sequences
12.2    Series
12.3    Integral Test
12.4    Comparison Tests
12.5    Alternating Series
12.6    Ratio and Root Tests
12.7    Power Series
12.8    Power Series Representations of Functions
12.9    Taylor Series

Chapter 13: Vector-Valued Functions

13.1    Review of Vectors
13.2    Vector-Valued Functions
13.3    Differentiation & Integration of Vector-Valued Functions
13.4    Arc Length and Curvature
13.5    Motion in Space
13.6    Tangent, Normal, and Binormal Vectors

Chapter 14: Surfaces, Solids, and Multiple Integrals

14.1    Cylinders and Quadric Surfaces
14.2    Review of Double Integrals
14.3    Surface Area
14.4    Integrals Over Solids: Triple Integrals
14.5    Cylindrical and Spherical Coordinates
14.6    Triple Integrals in Cylindrical and Spherical Coordinates
14.7    Change of Variables: The Jacobian

Chapter 15: Vector Analysis

15.1    Vector Fields
15.2    Line Integrals
15.3    Conservative Vector Fields
15.4    Green’s Theorem
15.5    Parametric Surfaces
15.6    Surface Integrals
15.7    Divergence Theorem
15.8    Stokes’ Theorem