Loyola University Chicago

Mathematics and Statistics

MATH 263: Multivariable Calculus

Course Details
Credit Hours: 4
Prerequisites: 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.

Dwyer and Gruenward. Calculus Resequenced for Students in STEM, preliminary edition. Wiley. ISBN: 978-1119321590.

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    Double Integrals in Polar Coordinates
    15.4    Green’s Theorem
    15.5    Parametric Surfaces
    15.6    Surface Integrals
    15.7    Divergence Theorem
    15.8    Stokes’ Theorem