Loyola University Chicago

Mathematics and Statistics

MATH 263: Multivariable Calculus

Course Details
Credit Hours: 4

MATH 162 with a grade of C- or higher

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 (WebAssign eBook) 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