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Course Criteria
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2.00 Credits
Analysis and practice of mathematical writing. Oral and poster conference presentations. Academic job interview skills. Mathematics on the web. Offered: jointly with MATH 500 and STAT 500.
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5.00 Credits
Projectoriented computational approach to solving problems arising in the physical/engineering sciences, finance/economics, medical, social and biological sciences. Problems requiring use of advanced MATLAB routines and toolboxes. Covers graphical techniques for data presentation and communication of scientific results.
Prerequisite:
Proficiency in basic MATLAB or AMATH 301, or permission of instructor
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5.00 Credits
Numerical methods for solving linear systems of equations, linear least squares problems, matrix eigen value problems, nonlinear systems of equations, interpolation, quadrature, and initial value ordinary differential equations. Offered: jointly with MATH 584; A.
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5.00 Credits
Numerical methods for steady-state differential equations. Two-point boundary value problems and elliptic equations. Iterative methods for sparse symmetric and nonsymmetric linear systems: conjugate-gradients, preconditioners. Offered: jointly with MATH 585; W.
Prerequisite:
AMATH 584/MATH 584 which may be taken concurrently
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5.00 Credits
Numerical methods for time-dependent differential equations, including explicit and implicit methods for hyperbolic and parabolic equations. Stability, accuracy, and convergence theory. Spectral and pseudospectral methods. Offered: jointly with ATM S 581/MATH 586; Sp.
Prerequisite:
AMATH 581 or AMATH 584
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3.00 Credits
Origin and properties of higher transcendental functions; theoretical basis and applications of Laplace, Fourier, Bessel, Mellin transforms; asymptotic analysis, including methods of steepest descent and stationary phase, WKB.
Prerequisite:
AMATH 567, AMATH 568, AMATH 569, or equivalent
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3.00 Credits
Review of Sturm-Liouville theory. Green’s functions and integral representation of solution to PDEs. Fredholm and Volterra integral equations. Hilbert-Schmidt theory. Singular integral equations of Cauchy type. Applications to science and engineering.
Prerequisite:
AMATH 567, AMATH 568, AMATH 569, or equivalent
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5.00 Credits
Stochastic techniques and models with applications. Markov process and diffusion, stochastic differential equations, randomly perturbed dynamical systems, and statistical mechanics.
Prerequisite:
AMATH 572, or permission of instructor
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2.00 - 3.00 Credits
Various advanced topics in numerical analysis and scientific computing, such as iterative methods, eigenvalue computations, approximation theory, finite element methods, inverse problems, nonlinear conservation laws, computational fluid dynamics. Offered: jointly with MATH 594.
Prerequisite:
AMATH 584, 585, 586, or equivalent
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2.00 - 3.00 Credits
Various advanced topics in numerical analysis and scientific computing. See the description for 594 for sample topics. Offered: jointly with MATH 595.
Prerequisite:
AMATH 584, 585, 586, or equivalent
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