Methods of Applied Mathematics I

Math 601-602 — Spring 2009

Instructor: Dr. Francis J. Narcowich

Office: 302 Milner Hall

E-mail: fnarc@math.tamu.edu

Phone: 845-7369

URL: /~francis.narcowich/

Office Hours: MWF 9:30-10:30, and by appointment.

Catalogue Description

Methods of linear algebra, vector analysis, and complex variables. PREREQUISITE: MATH 308.

Time & Place

MWF 11:30-12:20, BLOC 117.

Grading

Homework, 20%

Two in-class tests, 25% each (Dates: TBA)

Final Examination, 30% (Wednesday, May 13, 10:30 am - 12:30 pm)

Texts

1. Jim Hefferon, Saint Michael's College, Linear Algebra (online text), published via Open Textbooks Project.
2. George Cain and James Herod, Georgia Institute of Technology, Multivariable Calculus (online text), published via Open Textbooks Project.
3. Matthias Beck, Gerald Marchesi, and Dennis Pixton, A First Course in Complex Analysis (online text) published via Open Textbooks Project.
4. Instructor's Notes
   • Notes on Row Reduction
   • The Rank of a Matrix
   • Coordinate Vectors and Examples
   • Methods of Finding Bases
   • Notes on Special Functions

Syllabus

1. Linear algebra
   • Systems of linear equations and matrix operations
   • vector spaces, subspaces, important examples
   • linear independence, linear dependence, basis, dimension, coordinates, change of coordinates
   • inner products, bi-orthogonal and orthonormal sets, covariant and contravariant coordinates, Gram-Schmidt, least squares
   • linear transformations, eigenvalues, eigenvectors, diagonalization, applications
2. Vector analysis
   • scalar and vector valued functions, surfaces
   • limits, continuity, gradient, divergence, curl — coordinate independent definitions
   • integral calculus — Green's Theorem, Divergence Theorem, Stokes's Theorem
3. Complex variables
   • Analytic functions — Cauchy-Riemann equations; examples: exponential, log, trig functions, etc.
   • Cauchy's Theorem, power series
   • Residue Theorem, conformal maps, applications

Make-up Policy: I will give make-ups (or satisfactory equivalents) only in cases authorized under TAMU Regulations. In borderline cases, I will decide whether or not the excuse is authorized. Also, if you miss a test, contact me as soon as possible.

Academic Integrity

Copying Course Materials:   "All printed hand-outs and web-materials are protected by US Copyright Laws. No multiple copies can be made without written permission by the instructor."

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