Special topics in applied mathematics

Partial differential equations that govern physical phenomena in science and engineering. Separation of variables, superposition, Fourier series, Sturm-Liouville eigenvalue problems, eigenfunction expansion techniques. Particular focus on the heat, wave, and Laplace partial differential equations in rectangular, cylindrical, and spherical coordinates. Prerequisites: (APMA 2120 or MATH 2310 or MATH 2315) AND (APMA 2130 or MATH 3250 or APMA 2501 topic Diff Equations & Linear Algebra)

Analyzes the role of statistics in science; hypothesis tests of significance; confidence intervals; design of experiments; regression; correlation analysis; analysis of variance; and introduction to statistical computing with statistical software libraries. Prerequisite: Admission to graduate studies.

This course uses a Case-Study approach to teach statistical techniques with R: confidence intervals, hypotheses tests, regression, and anova. Also, it covers major statistical learning techniques for both supervised and unsupervised learning. Supervised learning topics cover regression and classification, and unsupervised learning topics cover clustering & principal component analysis. Prior basic statistic skills are needed.

Topics vary from year to year and are selected to fill special needs of graduate students.

Advanced Special topics in Applied Mathematics

Topics include analytic functions, Cauchy Theorems and formulas, power series, Taylor and Laurent series, complex integration, residue theorem, conformal mapping, and Laplace transforms. Prerequisite: APMA 2120 or MATH 2310 or APMA 2512 - Honors Engineering Mathematics II.

Covers the fundamental concepts necessary for success in engineering courses and Applied Mathemtics courses.

The focus will be on solving systems of ordinary differential equations using basic linear algebra. Techniques for both homogeneous and nonhomogenous systems will be introduced. Time permitting, solving differential equations with the unit step and unit impulse functions will also be covered. Prerequisite: Differential Equations from Virginia Community College or equivalent

Advanced special topics in Applied Mathematics