Loyola University Chicago

Mathematics and Statistics

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