MATH 300 - Advanced Boundary Value Problems I

★ 3 (fi 6)(EITH/SP/SU, 3-0-0)

Derivation of the classical partial differential equations of applied mathematics, solutions using separation of variables. Fourier expansions and their applications to boundary value problems. Introduction to Fourier Transforms. Emphasis on building an appropriate mathematical model from a physical problem, solving the mathematical problem, and carefully interpreting the mathematical results in the context of the original physical problem. Prerequisites: MATH 201 and 209. Notes: (1) Open only to students in Engineering, Specialization Physics, and Specialization Geophysics. (2) Credit can be obtained in at most one of MATH 300 and 337. (3) Course cannot be taken for credit if credit has been obtained in ECE 341.

MATH 337 - Introduction to Partial Differential Equations

★ 3 (fi 6)(EITHER, 3-0-0)

Boundary value problems of classical Math Physics, orthogonal expansions, classical special functions. Advanced transform techniques. Prerequisites: One of MATH 209, 215, or 217, and one of MATH 201, 334 or 336. Notes: (1) Credit can be obtained in at most one of MATH 300 or 337. (2) Course cannot be taken for credit if credit has been obtained in ECE 341.

MATH 436 - Intermediate Partial Differential Equations I

★ 3 (fi 6)(FIRST, 3-0-0)

Partial differential equations as physical models. Introduction to basic generalized functions. Theory of linear and quasi-linear first-order equations: general solution, initial value problem, generalized solutions and propagation of singularities, characteristic surfaces, shock formation. Theory of fully nonlinear first order equations: complete solution and the initial value problem. Hamilton-Jacobi equation and its applications. Second order linear equations in n dimensions: classification, canonical form, characteristic surfaces and shock formation, initial and boundary value problem. Prerequisite: MATH 337.

MATH 201 - Differential Equations

★ 3 (fi 6)(EITH/SP/SU, 3-0-1)

First-order equations; second-order linear equations: reduction of order, variation of parameters; Laplace transform; linear systems; power series; solution by series; separation of variables for PDEs. Prerequisite or corequisite: MATH 209 or 214. Notes: (1) Open only to students in Engineering, Specialization Physics, and Specialization Geophysics. (2) Credit can be obtained in at most one of MATH 201, 334 or 336. (3) Students in all sections of this course will write a common final examination. Non-Engineering students who take this course will receive *3.0.

MATH 336 - Honors Ordinary Differential Equations

★ 3 (fi 6)(EITHER, 3-0-0)

First order differential equations. Linear systems of differential equations and linear differential equations of higher order. Stability and qualitative theory of 2-dimensional linear and non-linear systems. Laplace transform methods. Existences and uniqueness theorems. Prerequisites: MATH 225 or 227, and either MATH 209, 217, 314 or both 214 and 216. Note: Credit can be obtained in at most one of MATH 201, 334 and 336.