Courses

Brief review of conditional probability and expectation followed by a study of Markov chains, both discrete and continuous time. Queuing theory, terminology, and single queue systems are studied with some introduction to networks of queues. Uses Monte Carlo simulation of random variables throughout the semester to gain insight into the processes under study. Prereq., APPM 3570 or equivalent. Same as APPM 5560.

Covers discrete and continuous probability laws, random variables; expectations; laws of large numbers and central limit theorem; estimation, testing hypothesis, analysis of variance, regression analysis, and nonparametric methods. Emphasizes applications with an introduction to packaged computer programs. Prereq., APPM 1360 or equivalent Calculus 2 course. Same as APPM 5570.

Combines statistical methods with practical applications and computer software. Develops commonly used statistical models such as analysis of variance as well as linear and logistic regression. The statistical models are implemented and interpreted in the context of actual data sets using available statistical software. Continuation of APPM 4570. Prereq., APPM 4570 or any course in statistics. Same as APPM 5580.

Focuses on numerical solution of nonlinear equations, interpolation, methods in numerical integration, numerical solution of linear systems, and matrix eigenvalue problems. Stresses significant computer applications and software. Prereqs., APPM 3310 or MATH 3130, and knowledge of a programming language. Same as MATH 4650.

Continuation of APPM 4650. Examines numerical solution of initial-value problems and two-point boundary-value problems for ordinary differential equations. Also looks at numerical methods for solving partial differential equations. Prereq., APPM 4650 and knowledge of a programming language. Same as MATH 4660.

Provides a vehicle for the development and presentation of new topics that may be incorporated into the core courses in applied mathematics. May be repeated up to 6 total credit hours. Prereqs., variable, depending on the topic. See instructor. Same as APPM 5720.

Introduces undergraduate students to the research foci of the Department of Applied Mathematics. May be repeated up to 9 total credit hours. Prereq., APPM 3310 or MATH 3130. Recommended prereq., a course in ordinary or partial differential equations.

Introduces undergraduate students to the research foci of the program in applied mathematics. It is also designed to be a capstone experience for the program's majors. May be repeated up to 6 total credit hours. Prereq., APPM 3310 or MATH 3130. Recommended prereq., course in ordinary or partial differential equations. Similar to APPM 4955.

Same as APPM 4120 and MATH 5120. Prerequisites: Restricted to Graduate Students only.

Restricted to graduate students. Same as APPM 4350. Prerequisites: Restricted to Graduate Students only.

Prereq., graduate status in engineering or arts and sciences, or instructor consent. Same as APPM 4360. Prerequisites: Restricted to Graduate Students only.

Same as APPM 4380. Prerequisites: Restricted to Graduate Students only.

Same as APPM 4390. Prerequisites: Restricted to Graduate Students only.

Reviews basic ideas of complex analysis, including solutions of ODEs and PDEs of physical interest via complex analysis; conformal mapping, including Schwarz-Christoffel transformations and generalizations; computational methods; Riemann-Hilbert problems; and topics in asymptotic methods. Prereq., APPM 4360 or 5360, or instructor consent.

Discusses the elements of basic real and complex analysis, Banach spaces, Lp spaces, and many relevant inequalities. Includes applications of existence and uniqueness of solutions to various types of ordinary differential equations, partial differential equations, and integral equations. Prereqs., APPM 4440 and 4450 or equivalent, or instructor consent. Prerequisites: Restricted to Graduate Students only.

Continuation of APPM 5440. Prereq., APPM 5440 or instructor consent. Prerequisites: Restricted to Graduate Students only.

Introduces the theory and applications of dynamical systems through solutions to differential equations.Covers existence and uniqueness theory, local stability properties, qualitative analysis, global phase portraits, perturbation theory, and bifurcation theory. Special topics may include Melnikov methods, averaging methods, bifurcations to chaos, and Hamiltonian systems. Prereqs., undergraduate courses equivalent to APPM 2360, 3310, and 4440.

Studies properties and solutions of partial differential equations. Covers methods of characteristics, well-posedness, wave, heat and Laplace equations, Green's functions, and related integral equations. Prereqs., APPM 4350 and 4360, or MATH 4430, or equivalent. Prerequisites: Restricted to Graduate Students only.

Covers asymptotic evaluation of integrals (stationary phase and steepest descent), perturbation methods (regular and singular methods, and inner and outer expansions), multiple scale methods, and applications to differential and integral equations. Prereq., APPM 5470 or instructor consent. Prerequisites: Restricted to Graduate Students only.

Prereq., one semester calculus-based probability course, such as MATH 4510 or APPM 3570. Same as APPM 4520 and MATH 5520. Prerequisites: Restricted to Graduate Students only.

Same as APPM 4540 and MATH 5540. Prerequisites: Restricted to Graduate Students only.

Prereq., APPM 3570 or equivalent. Same as APPM 4560. Prerequisites: Restricted to Graduate Students only.

Same as APPM 4570. Prerequisites: Restricted to Graduate Students only.

Continuation of APPM 5570. Prereq., one semester of statistics. Same as APPM 4580. Prerequisites: Restricted to Graduate Students only.

Solution of nonlinear algebraic equations, interpolation, integration, approximation, and numerical linear algebra. Prereq., APPM 3310 or MATH 3130, and experience with a scientific programming language. Prerequisites: Restricted to Graduate Students only.