300

The study of functions in several variables: vectors, matrices, partial derivatives, gradients, optimization, and integration. Differentiation and integration of vector-valued functions, line integrals, surface integrals, curl, divergence, Green's Theorem, and Stokes' Theorem.

Computational techniques for solving physics and chemistry problems as well as for simulating, analyzing, and graphically visualizing physical systems and processes. Offered fall of odd years.

Complex numbers and functions of a complex variable; limits, differentiability; Cauchy's theorem; power series, Laurent series, residue theorem with applications, maximum modulus theorem, Liouville's theorem; conformal mapping and applications.

Topics may include: set theory, logic, methods of proof, combinatorics, recurrence relations, graphs, and Boolean algebra.

Introduction to elementary ordinary differential equations with applications to physical processes with emphasis on first and second order equations, systems of linear equations, and Laplace transforms.

Fourier series. Inner product spaces. Solutions to heat, wave, and Laplace's equations. Green's functions.

This course introduces the basic concepts and techniques in the study of dynamical systems, including nonlinear ordinary differential equations, difference equations, and systems of equations. Using a wide variety of applications from the physical sciences, we will cover analytical methods such as linear stability, bifurcations, phase plane analysis, limit cycles, Lorenz equations, chaos, iterated maps, period doubling, and fractals.

This course surveys many of the ideas, methods and applications of graph theory. Topics may include: connectivity, matchings, graph algorithms, network flows, graph colorings, planarity, circuits, cycles, and tournaments.

Systems of linear equations and matrices, determinants, vector spaces, linear transformations, eigenvalues and eigenvectors.

An introduction to the study of the integers and related objects. Topics are taken from among the following: divisibility, primes and the Euclidean algorithm, the Euler phi function, special primes and perfect numbers, congruences mod n, quadratic residues, continued fractions, quadratic forms, Diophantine equations.

Ordinary differential equations, complex variables and matrices are developed and illustrated through applications in physics with emphasis on examples from the fields of vibrations and waves.

An introduction to statistical methods utilized across disciplines. Topics include experimental design, randomization and sampling distributions, tests of statistical significance, normal model, confidence intervals, t-procedures, two-sample comparisons, one-way analysis of variance, simple linear regression, and bootstrapping. The course makes substantial use of programming in a statistical software package.

Survey of applied mathematics with an emphasis on modeling problems from science and engineering. Process of formulating the model, solving/simulating, and analyzing/interpreting results. Applications may include: continuous- and discrete-time population models, models of physical and biological phenomena, and statistical models.

Credit arranged.

Credit arranged.

Faculty-directed student research. Before enrolling, a student must consult with a faculty member to define project. May be repeated for credit. Credit arranged.

Practical field experience in selected industries or agencies. Department permission and supervision is required. Students may receive an IP (In Progress) grade until the completion of their internship. 

Credit arranged.