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Course Criteria
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3.00 Credits
Credits: 3 Covers more advanced topics in computational fluid dynamics, including high-resolution schemes for hyperbolic PDEs, advanced Euler solvers, Navier-Stokes solvers, grid generation, adaptive mesh refinement, efficient use of supercomputing hardware, and future trends. Projects include topics in grid generation and adaptive refinement. Students expected to write their own codes. Prerequisites CSI 721 or permission of instructor. Hours of Lecture or Seminar per week 3 Hours of Lab or Studio per week 0
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3.00 Credits
Credits: 3 Covers gas dynamics, shock waves, method of characteristics, boundary layer flows, instabilities, and turbulence modeling. Special topics include biological, non-Newtonian, and free surface flows; aeroelasticity; and magneto-hydrodynamics. Prerequisites CSI 720 or permission of instructor. Hours of Lecture or Seminar per week 3 Hours of Lab or Studio per week 0
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3.00 Credits
Credits: 3 Covers selected topics in the computational aspects of continuum systems not covered in fixed-content courses in dynamical systems. Possible topics are smooth-particle hydrodynamics, radiation hydrodynamics, algorithms for continuum systems, adaptive grids for continuum computations, spectral methods in computational fluid dynamics, algorithms for concurrent machines, formation of highenergy particle jets in astrophysical applications, application to Earth atmospheric problems, and flow considerations in molten materials. Prerequisites Permission of instructor. Notes May be repeated for credit as needed. Hours of Lecture or Seminar per week 3 Hours of Lab or Studio per week 0
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3.00 Credits
Credits: 3 Selected topics in bioinformatics not covered in fixed-content bioinformatics courses. Prerequisites Permission of instructor. Notes May be repeated for credit as needed. Hours of Lecture or Seminar per week 3 Hours of Lab or Studio per week 0
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3.00 Credits
Credits: 3 Cross-Listed with MATH 625 Covers computational methods for matrix systems; theory and development of numerical algorithms for the solution of linear systems of equations, including direct and iterative methods; analysis of sensitivity of system to computer round off; and solution of least squares problems using orthogonal matrices. Also covers computation of eigenvalues and eigenvectors, singular value decomposition, and applications. Prerequisites MATH 203 and some programming experience. Hours of Lecture or Seminar per week 3 Hours of Lab or Studio per week 0
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3.00 Credits
Credits: 3 The finite element method is commonly used for developing numerical approximations to problems involving ordinary and partial differential equations. Course develops underlying mathematical foundation, examines specific types of finite elements, analyzes convergence rates and approximation properties, and uses method to solve important equations. Students develop their own codes and are expected to complete independent projects. Prerequisites MATH 446 or 685, or permission of instructor. Hours of Lecture or Seminar per week 3 Hours of Lab or Studio per week 0
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3.00 Credits
Credits: 3 Develops tools of mathematical modeling while carrying out numerical simulations. Considers examples from across the sciences. Topics include basic issues such as models, simplification, linearity, and nonlinearity; dimensionless parameters; dimensional analysis; models involving differential equations; examples from population growth and chemical kinetics; models involving partial differential equations; diffusion, transport, nonlinearity and shocks; probabilistic modeling; perturbation methods; extrapolation; and introduction to stability. Prerequisites Permission of instructor. Hours of Lecture or Seminar per week 3 Hours of Lab or Studio per week 0
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3.00 Credits
Credits: 3 Cross-Listed with MATH 772 Studies theory and computational aspects of wavelets and wavelet transform. Emphasizes computational aspects of wavelets. Defines Fast Wavelet Transform in one and two dimensions, and develops appropriate numerical algorithms, and theory of wavelet bases on the real line. Covers multiresolution analysis, splines, time-frequency localization, and wavelet packets. Prerequisites Knowledge of convolution and Fourier transforms of sequences; some familiarity with Hilbert space theory helpful but not required; knowledge of scientific programming language. Hours of Lecture or Seminar per week 3 Hours of Lab or Studio per week 0
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3.00 Credits
Credits: 3 Introduction to practical aspects of nonlinear optimization. Covers applications of optimization algorithms to solving problems in science and engineering. Applications include data analysis, materials science, nanotechnology, mechanics, optical design, shape design, and trajectory optimization. Prerequisites MATH 213 and 216, or permission of instructor. Hours of Lecture or Seminar per week 3 Hours of Lab or Studio per week 0
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3.00 Credits
Credits: 3 Provides mathematical and computational background for computational algebraic geometry and its applications. Includes algebra, geometry, algorithms, concept of Groebner bases, automatic theorem proving, and serial and parallel algorithms and their complexity. Topics are related to applications in engineering and computer science. Students expected to complete projects. Prerequisites Undergraduate degree in scientific discipline and course in abstract algebra. Hours of Lecture or Seminar per week 3 Hours of Lab or Studio per week 0
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