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ACM 232 abc: Computational Fluid Dynamics
9.00 Credits
California Institute of Technology
Development and analysis of algorithms used in the solution of fluid mechanics problems. Numerical analysis of discretization schemes for partial differential equations including interpolation, integration, spatial discretization, systems of ordinary differential equations; stability, accuracy, aliasing, Gibbs and Runge phenomena, numerical dissipation and dispersion; boundary conditions. Survey of finite difference, finite element, finite volume and spectral approximations for the numerical solution of the incompressible and compressible Euler and Navier-Stokes equations, including shock-capturing methods. Instructors: Colonius, Koumoutsakos, Meiron.
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ACM 232 abc - Computational Fluid Dynamics
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ACM 256 ab: Special Topics in Applied Mathematics
9.00 Credits
California Institute of Technology
Introduction to finite element methods. Development of the most commonly used method—continuous, piecewise-linear finite elements on triangles for scalar elliptic partial differential equations; practical (a posteriori) error estimation techniques and adaptive improvement; formulation of finite element methods, with a few concrete examples of important equations that are not adequately treated by continuous, piecewise-linear finite elements, together with choices of finite elements that are appropriate for those problems. Homogenization and optimal design. Topics covered include periodic homogenization, G- and H-convergence, Gamma-convergence, G-closure problems, bounds on effective properties, and optimal composites. Instructor: Farrell; Part b not offered 2012–13.
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ACM 256 ab - Special Topics in Applied Mathematics
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ACM 257: Special Topics in Financial Mathematics
9.00 Credits
California Institute of Technology
This course develops some of the techniques of stochastic calculus and applies them to the theory of financial asset modeling. The mathematical concepts/tools developed will include introductions to random walks, Brownian motion, quadratic variation, and Ito-calculus. Connections to PDEs will be made by Feynman-Kac theorems. Concepts of risk-neutral pricing and martingale representation are introduced in the pricing of options. Topics covered will be selected from standard options, exotic options, American derivative securities, term-structure models, and jump processes. Not offered 2012–13.
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ACM 257 - Special Topics in Financial Mathematics
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ACM 270: Advanced Topics in Applied and Computational Mathematics
1.00 - 9.00 Credits
California Institute of Technology
Advanced topics in applied and computational mathematics that will vary according to student and instructor interest. May be repeated for credit. Instructor: Chandrasekaran.
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ACM 270 - Advanced Topics in Applied and Computational Mathematics
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ACM 290 abc: Applied and Computational Mathematics Colloquium
1.00 Credits
California Institute of Technology
A seminar course in applied and computational mathematics. Weekly lectures on current developments are presented by staff members, graduate students, and visiting scientists and engineers. Graded pass/fail only.
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ACM 290 abc - Applied and Computational Mathematics Colloquium
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ACM 300: Research in Applied and Computational Mathematics
1.00 - 9.00 Credits
California Institute of Technology
No course description available.
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ACM 300 - Research in Applied and Computational Mathematics
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ACM 95/100 abc: Introductory Methods of Applied Mathematics
12.00 Credits
California Institute of Technology
First term: complex analysis: analyticity, Laurent series, singularities, branch cuts, contour integration, residue calculus. Second term: ordinary differential equations. Linear initial value problems: Laplace transforms, series solutions. Linear boundary value problems: eigenvalue problems, Fourier series, Sturm-Liouville theory, eigenfunction expansions, the Fredholm alternative, Green’s functions, nonlinear equations, stability theory, Lyapunov functions, numerical methods. Third term: linear partial differential equations: heat equation separation of variables, Fourier transforms, special functions, Green’s functions, wave equation, Laplace equation, method of characteristics, numerical methods. Instructors: Pierce, Meiron, Hou.
Prerequisite:
Ma 1 abc, Ma 2 ab (may be taken concurrently), or equivalents.
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ACM 95/100 abc - Introductory Methods of Applied Mathematics
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Ae 100: Research in Aerospace
1.00 - 9.00 Credits
California Institute of Technology
Open to suitably qualified undergraduates and first-year graduate students under the direction of the staff. Credit is based on the satisfactory completion of a substantive research report, which must be approved by the Ae 100 adviser and by the option representative.
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Ae 100 - Research in Aerospace
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Ae 101 abc: Fluid Mechanics
9.00 Credits
California Institute of Technology
Fundamentals of fluid mechanics. Microscopic and macroscopic properties of liquids and gases; the continuum hypothesis; review of thermodynamics; general equations of motion; kinematics; stresses; constitutive relations; vorticity, circulation; Bernoulli’s equation; potential flow; thin-airfoil theory; surface gravity waves; buoyancy-driven flows; rotating flows; viscous creeping flow; viscous boundary layers; introduction to stability and turbulence; quasi one-dimensional compressible flow; shock waves; unsteady compressible flow; and acoustics. Instructors: Pullin, Dimotakis.
Prerequisite:
APh 17 or ME 18, and ME 19 or equivalent, ACM 95/100 or equivalent (may be taken concurrently).
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Ae 101 abc - Fluid Mechanics
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Ae 102 abc: Mechanics of Structures and Solids
9.00 Credits
California Institute of Technology
Static and dynamic stress analysis. Two- and three-dimensional theory of stressed elastic solids. Analysis of structural elements with applications in a variety of fields. Variational theorems and approximate solutions, finite elements. A variety of special topics will be discussed in the third term such as, but not limited to, elastic stability, wave propagation, and introductory fracture mechanics. Instructors: Bhattacharya, Ravichandran.
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Ae 102 abc - Mechanics of Structures and Solids
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