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MAE 560 Computational Fluid Mechanics and Heat Transfer 3. Prerequisite: MA 501 or MA 512, MAE 550 or MAE 557, proficiency in the FORTRAN programming language is required.

Introduction to integration of the governing partial differential equations of fluid flow and heat transfer by numerical finite difference and finite volume means. Methods for parabolic, hyper-bolic and elliptical equations and application to model equations. Error analysis and physical considerations.

MA 512 Advanced Calculus II 3. Prerequisite: MA 341.

General theorems of partial differentiation; implicit function theorems; vector calculus in 3-space; line and surface integrals; classical integral theorems. Credit will not be given for both MA 426 and MA 512.

MA 532 Ordinary Differential Equations I 3. Prerequisite: MA 341, 405, 425 or 511, Corequisite: MA 426 or 512.

Existence and uniqueness theorems, systems of linear equations, fundamental matrices, matrix exponential, nonlinear systems, plane autonomous systems, stability theory.

MA 534 Introduction To Partial Differential Equations 3. Prerequisite: MA 425 or MA 511, MA 341, Corequisite: MA 426 or 512.

Linear first order equations, method of characteristics. Classification of second order equations. Solution techniques for the heat equation, wave equation and Laplace's equation. Maximum principles. Green's functions and fundamental solutions.

MA 785 Numerical Solution of Ordinary Differential Equations 3. Prerequisite: MA 511 or 512.

Numerical methods for initial value problems including predictor-corrector, Runge-Kutta, hybrid and extrapolation methods; stiff systems; shooting methods for two-point boundary value problems; weak, absolute and relative stability results.

PY 711 Advanced Quantum Mechanics I 3. Prerequisite: MA 512, PY 782.

Introduction to relativistic quantum theory of Dirac particles and the positron. Other topics including second quantization technique and its application to many-body problems, radiation theory and quantization of the electromagnetic field.

PY 781 Quantum Mechanics I 3. Prerequisite: MA 512; PY 411 or 414; Graduate standing.

Fundamental concepts and formulations, including interpretation and techniques, and the application of theory to simple physical systems, such as the free particle, the harmonic oscillator, the particle in a potential well and central force problems. Other topics including approximation methods, identical particles and spin, transformation theory, symmetries and invariance, and an introduction to quantum theory of scattering and angular momentum.

PY 782 Quantum Mechanics II 3. Prerequisite: MA 512; PY 411 or 414; Graduate standing.

Fundamental concepts and formulations, including interpretation and techniques, and the application of theory to simple physical systems, such as the free particle, the harmonic oscillator, the particle in a potential well and central force problems. Other topics including approximation methods, identical particles and spin, transformation theory, symmetries and invariance, and an introduction to quantum theory of scattering and angular momentum.

PY 783 Advanced Classical Mechanics I 3. Prerequisite: MA 512, PY 412, PY 414; Graduate standing.

Introduction to theoretical physics in preparation for advanced study. Emphasis on classical mechanics, special relativity and the motion of charged particles. Topics including variational principles, Hamiltonian dynamics and canonical transformation theory, structure of the Lorentz group and elementary dynamics of unquantized fields.