Evangelos A. Coutsias, Math 311

Math 311: Vector Analysis

Instructor: Evangelos A. Coutsias

Required Text: H.F. Davis and A.D. Snyder Introduction to Vector Analysis 7th Edition

Also required: Murray R. Spiegel Schaum's Outlines: Vector Analysis (problems book)

Supplement (recommended): H.M. Schey Div, Grad, Curl and all that: an informal text on Vector Calculus

Outline

This course develops the geometrical ideas of two and three dimensional calculus. It is good preparation for advanced engineering and physics courses, Classical Mechanics, Statics, Dynamics and Vibrations, Electromagnetics and Wave Propagation, Fluid Flow and Elasticity.

  • Topics to be covered include:

    Vector Algebra; Scalar and Vector Products; vector identities; lines, planes and vector geometry. Vector functions; diferentiation; space curves, velocity, acceleration; curvature and torsion. Scalar and Vector Fields; gradients and level lines; flow lines; divergence and flux; curl and circulation; Laplacian and tension. Orthogonal curvilinear coordinates. Line, surface and volume integrals. The theorems of Gauss and Stokes. Orthogonal matrices and rotations in 3 dimensions. Vector equations of Classical Mechanics.

    Quiz Dates

    Unless announced otherwise, there will be a 15' quiz every Friday, with the first graded quiz being on Friday, Jan. 29, 1999.

    Grades to date

    Syllabus and Homework Problems

    Computing

    Many of the calculations for this class can be performed by judicious use of a symbolic manipulation program, such as Maple, Mathematica, Macsyma, Derive etc. I highly recommend you familiarize yourselves with one of these programs. I will be probably using Maple for any and all computer-related work.

    Maple V:

    If you are unfamiliar with Maple, click here for some help to get started.

    Return to: Department of Mathematics and Statistics, University of New Mexico.

    <vageli@math.unm.edu>
    Last updated: September 15, 1997