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APMA 2810P: Perturbation Methods
1.00 Credits
Brown University
Basic concepts of asymptotic approximations with examples with examples such as evaluation of integrals and functions. Regular and singular perturbation problems for differential equations arising in fluid mechanics, wave propagation or nonlinear oscillators. Methods include matched asymptotic expansions and multiple scales. Methods and results will be discussed in the context of applications to physical problems.
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APMA 2810P - Perturbation Methods
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APMA 2810Q: Discontinous Galerkin Methods
1.00 Credits
Brown University
In this seminar course we will cover the algorithm formulation, stability analysis and error estimates, and implementation and applications of discontinuous Galerkin finite element methods for solving hyperbolic conservation laws, convection diffusion equations, dispersive wave equations, and other linear and nonlinear partial differential equations. Prerequisite: AM 255
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APMA 2810Q - Discontinous Galerkin Methods
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APMA 2810R: Computational Biology Methods for Gene/Protein Networks and Structural Proteomics
1.00 Credits
Brown University
The course presents computational and statistical methods for gene and protein networks and structural proteomics; it emphasizes: (1) Probablistic models for gene regulatory networks via microarray, chromatin immunoprecipitation, and cis-regulatory data; (2) Signal transduction pathways via tandem mass spectrometry data; (3) Molecular Modeling forligand-receptor coupling and docking. The course is recommended for graduate students.
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APMA 2810R - Computational Biology Methods for Gene/Protein Networks and Structural Proteomics
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APMA 2810S: Topics in Control
1.00 Credits
Brown University
No description available.
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APMA 2810S - Topics in Control
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APMA 2810T: Nonlinear Partial Differential Equations
1.00 Credits
Brown University
This course introduces techniques useful for solving many nonlinear partial differential equations, with emphasis on elliptic problems. PDE from a variety of applications will be discussed. Contact the instructor about prerequisites.
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APMA 2810T - Nonlinear Partial Differential Equations
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APMA 2810U: Topics in Differnetial Equations
1.00 Credits
Brown University
No description available.
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APMA 2810U - Topics in Differnetial Equations
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APMA 2810V: Topics in Partial Differential Equations
1.00 Credits
Brown University
The course will cover an introduction of the L_p theory of second order elliptic and parabolic equations, finite difference approximations of elliptic and parabolic equations, and some recent developments in the Navier¿Stokes equations and quasi¿geostrophic equations. Some knowledge of real analysis will be expected.
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APMA 2810V - Topics in Partial Differential Equations
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APMA 2810W: Advanced Topics in High Order Numerical Methods for Convection Dominated Problems
1.00 Credits
Brown University
This is an advanced seminar course. We will cover several topics in high order numercial methods for convection dominated problems, including methods for solving Boltzman type equations, methods for solving unsteady and steady Hamilton¿Jacobi equations, and methods for solving moment models in semi¿conductor device simulations. Prerequisite: AM 255 or equivalent knowledge of numerical analysis.
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APMA 2810W - Advanced Topics in High Order Numerical Methods for Convection Dominated Problems
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APMA 2810X: Introduction to the Theory of Large Deviations
1.00 Credits
Brown University
The theory of large deviations attempts to estimate the probability of rare events and identify the most likely way they happen. The course will begin with a review of the general framework, standard techniques (change-of-measure, PDE, weak convergence, etc.), and basic examples (e.g., Sanov's and Cramer's Theorems). We then will cover the Wentsel-Freidlin theory. The last part of the course will be one or two related topics, possibly drawn from (but not limited to) risk-sensitive control and Monte Carlo methods. Prerequisites: APMA 2630 and 2640.
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APMA 2810X - Introduction to the Theory of Large Deviations
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APMA 2810Y: Discrete high-D Inferences in Genomics
1.00 Credits
Brown University
Genomics is revolutionizing biology and biomedicine and generated a mass of clearly relevant high-D data along with many important high-D discreet inference problems. Topics: special characteristics of discrete high-D inference including Bayesian posterior inference; point estimation; interval estimation; hypothesis tests; model selection; and statistical decision theory.
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APMA 2810Y - Discrete high-D Inferences in Genomics
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