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APMA 2820J: Numerical Linear Algebra
1.00 Credits
Brown University
Solving large systems of linear equations: The course will use the text of Treften and BAO that includes all the modern concepts of solving linear equations.
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APMA 2820J - Numerical Linear Algebra
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APMA 2820K: Numerical Solution of Ordinary Differential Equations
1.00 Credits
Brown University
We discuss the construction and general theory of multistep and multistage methods for numerically solving systems of ODE's, including stiff and nonlinear problems. Different notions to stability and error estimation and control. As time permits we shall discuss more advanced topics such as order reduction, general linear and additive methods, symplectic methods, and methods for DAE. Prerequisites: AM 219 and AM 255 or equivalent. Some programming experience is expected.
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APMA 2820K - Numerical Solution of Ordinary Differential Equations
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APMA 2820L: Random Processes in Mechanics
1.00 Credits
Brown University
No description available.
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APMA 2820L - Random Processes in Mechanics
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APMA 2820M: Singularities in Eliptic Problems and their Treatment by High-Order Finite Element Methods
1.00 Credits
Brown University
Singular solutions for elliptic problems (elasticity and heat transfer) are discussed. These may arise around corners in 2-D and along edges and vertices in 3-D domains. Derivation of singular solutions, charactized by eigenpairs and generalized stress/flux intensity factors (GSIF/GFIFs) are a major engineering importance (because of failure initiation and propagation). High-order FE methods are introduced, and special algorithms for extracting eigenpairs and GSIF/GFIFs are studied (Steklov, dual-function, ERR method, and others).
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APMA 2820M - Singularities in Eliptic Problems and their Treatment by High-Order Finite Element Methods
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APMA 2820N: Topics in Scientific Computing
1.00 Credits
Brown University
No description available.
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APMA 2820N - Topics in Scientific Computing
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APMA 2820O: The Mathematics of Shape with Applications to Computer Vision
1.00 Credits
Brown University
Methods of representing shape, the geometry of the space of shapes, warping and matching of shapes, and some applications to problems in computer vision and medical imaging. Prerequsite: See instructor for prerequisites.
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APMA 2820O - The Mathematics of Shape with Applications to Computer Vision
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APMA 2820P: Foundations in Statistical Inference in Molecular Biology
1.00 Credits
Brown University
In molecular biology, inferences in high dimensions with missing data are common. A conceptual framework for Bayesian and frequentist inferrnces in this setting including: sequence alignment, RNA secondary structure prediction, database search, and functional genomics. Statistical topics: parameter estimation, hypothesis testing, and characterization of posterior spaces. Core course in proposed PhD program in computational molecular biology.
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APMA 2820P - Foundations in Statistical Inference in Molecular Biology
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APMA 2820Q: Topics in Kinetic Theory
1.00 Credits
Brown University
This course will introduce current mathematical study for Boltzmann equation and Vlasov equation. We will study large time behavior and hydrodynamic limits for Boltzmann theory and instabilities in the Vlasov theory. Graduate PDE course is required.
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APMA 2820Q - Topics in Kinetic Theory
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APMA 2820R: Structure Theory of Control Systems
1.00 Credits
Brown University
The course deals with the following problems: given a family of control systems S and a family of control systems S', when does there exist an appropriate embedding of S into S' ? Most of the course will deal with the families of linear control systems. Knowledge of control theory and mathematical sophistication are required.
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APMA 2820R - Structure Theory of Control Systems
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APMA 2820S: Topics in Differential Equations
1.00 Credits
Brown University
A sequal to AM 221 concentrating on similar material.
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APMA 2820S - Topics in Differential Equations
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