MA 253

MA 253 - Calculus III

  1. Solid "Analytic Geometry"
    a) Coordinates: the distance formula
    b) Vectors in space
    c) Equation of a line in space
    d) Equation of a plane, Angles
    e) Distance from a point to a plane
    f) Spheres and cylinders
    g) Quadric surfaces
    h) Other coordinate systems: cylindrical and spherical

  2. Partial Differentiation
    a) Limits and continuity of functions of several variables
    b) Partial derivatives
    c) The total differential; applications
    d) The Chain Rule; applications
    e) Second and higher order derivatives
    f) Directional derivatives and gradients
    g) Maxima and minima

  3. Multiple Integration
    a) Definition of the integral
    b) Double and triple integrals
    c) Interpretation as area and volume
    d) Double integral in polar coordinates
    e) Volumes by double integrals in cylindrical coordinates
    f) Triple integrals in cylindrical and spherical coordinates
    g) Change of variables

  4. Vector Analysis
    a) Vector fields
    b) Divergence and curl of a vector field
    c) Line integrals
    d) Conservative vector fields and independence of path
    e) Green's Theorem
    f) Surfaces
    g) Surface integrals
    h Divergence Theorem and applications
    i) Stokes' Theorem and applications


    Learning Outcome 1: The student will understand the basic geometry of three-dimensional space.

    Learning Outcome 2: The student will understand differentiation of functions of several variables.

    Learning Outcome 3: The student will understand integration of functions of several variables.