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Course Criteria
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3.00 Credits
Introduces phase-space methods, elementary bifurcation theory and perturbation theory, and applies them to the study of stability in the contexts of nonlinear dynamical systems and nonlinear waves, including free and forces nonlinear vibrations and wave motions. Examples are drawn from mechanics and fluid dynamics, and include transitions to periodic oscillations and chaotic oscillations. Also cross-listed as MAE 624.
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3.00 Credits
Topics include the solution of systems of linear and nonlinear equations, calculations of matrix eigenvalues, least squares problems, and boundary value problems in ordinary and partial differential equations.
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3.00 Credits
Analyses of regular perturbations; roots of polynomials; singular perturbations in ODE’s; periodic solutions of simple nonlinear differential equations; multiple-Scales method; WKBJ approximation; turning-point problems; Langer’s method of uniform approximation; asymptotic behavior of integrals; Laplace Integrals; stationary phase; and steepest descents. Examples are drawn from physical systems. Cross-listed as MAE 637.
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3.00 Credits
Review of ordinary differential equations. Initial value problems, boundary value problems, and various physical applications. Linear algebra, including systems of linear equations, matrices, eigenvalues, eigenvectors, diagonalization, and various applications. Scalar and vector field theory, including the divergence theorem, Green’s theorem, Stokes theorem, and various applications. Partial differential equations that govern physical phenomena in science and engineering. Solution of partial differential equations by separation of variables, superposition, Fourier series, variation of parameters, d’ Alembert’s solution. Eigenfunction expansion techniques for nonhomogeneous initial-value, boundary-value problems. Particular focus on various physical applications of the heat equation, the potential (Laplace) equation, and the wave equation in rectangular, cylindrical, and spherical coordinates. Cross-listed as MAE 641.
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3.00 Credits
Further and deeper understanding of partial differential equations that govern physical phenomena in science and engineering. Solution of linear partial differential equations by eigenfunction expansion techniques. Green’s functions for time-independent and time-dependent boundary value problems. Fourier transform methods, and Laplace transform methods. Solution of a variety of initial-value, boundary-value problems. Various physical applications. Study of complex variable theory. Functions of a complex variable, and complex integral calculus, Taylor series, Laurent series, and the residue theorem, and various applications. Serious work and efforts in the further development of analytical skills and expertise. Cross-listed as MAE 642.
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3.00 Credits
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.
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3.00 Credits
Includes first order partial differential equations (linear, quasilinear, nonlinear); classification of equations and characteristics; and well-posedness of initial and boundary value problems. Cross-listed as MAE 644.
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3.00 Credits
Topics vary from year to year and are selected to fill special needs of graduate students.
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3.00 Credits
Topics include the solution of flow and heat transfer problems involving steady and transient convective and diffusive transport; superposition and panel methods for inviscid flow; finite-difference methods for elliptic, parabolic, and hyperbolic partial differential equations; elementary grid generation for odd geometries; and primitive variable and vorticity-steam function algorithms for incompressible, multidimensional flows. Extensive use of personal computers/workstations including graphics. Cross-listed as MAE 672.
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1.00 - 12.00 Credits
Detailed study of graduate-level material on an independent basis under the guidance of a faculty member.
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