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APMA 2810F: Introduction to Non-linear Optics
1.00 Credits
Brown University
No description available.
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APMA 2810F - Introduction to Non-linear Optics
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APMA 2810G: Large Deviations
1.00 Credits
Brown University
No description available.
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APMA 2810G - Large Deviations
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APMA 2810H: Math of Finance
1.00 Credits
Brown University
No description available.
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APMA 2810H - Math of Finance
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APMA 2810I: Mathematical Models and Numerical Analysis in Computational Quantum Chemistry
1.00 Credits
Brown University
We shall present on some models in the quantum chemistry field (Thomas Fermi and related, Hartree Fock, Kohn Sham) the basic tools of functional analysis for the study of their solutions. Then some of the discretization methods and iterative algorithms to solve these problems will be presented and analyzed. Some of the open problems that flourish in this field will also be presented all along the lectures.
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APMA 2810I - Mathematical Models and Numerical Analysis in Computational Quantum Chemistry
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APMA 2810J: Mathematical Techniques for Neural Modeling
1.00 Credits
Brown University
No description available.
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APMA 2810J - Mathematical Techniques for Neural Modeling
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APMA 2810K: Methods of Algebraic Geometry in Control Theory I
1.00 Credits
Brown University
Develops the ideas of algebraic geometry in the context of control theory. The first semester examines scalar linear systems and affine algebraic geometry while the second semester addresses multivariable linear systems and projective algebraic geometry.
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APMA 2810K - Methods of Algebraic Geometry in Control Theory I
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APMA 2810L: Numerical Solution of Hyperbolic PDE's
1.00 Credits
Brown University
No description available.
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APMA 2810L - Numerical Solution of Hyperbolic PDE's
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APMA 2810M: Some Topics in Kinetic Theory
1.00 Credits
Brown University
Nonlinear instabilities as well as boundary effects in a collisionless plasmas; Stable galaxy configurations; A nonlinear energy method in the Boltzmann theory will also be introduced. Self-contained solutions to specific concrete problems. Focus on ideas but not on technical aspects. Open problems and possible future research directions will then be discussed so that students can gain a broader perspective. Prerequisite: One semester of PDE (graduate level) is required.
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APMA 2810M - Some Topics in Kinetic Theory
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APMA 2810N: Topics in Nonlinear PDEs
1.00 Credits
Brown University
Aspects of the theory on nonlinear evolution equations, which includes kinetic theory, nonlinear wave equations, variational problems, and dynamical stability.
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APMA 2810N - Topics in Nonlinear PDEs
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APMA 2810O: Stochastic Differentail Equations
1.00 Credits
Brown University
This course develops the theory and some applications of stochastic differential equations. Topics include: stochastic integral with respect to Brownian motion, existence and uniqueness for solutions of SDEs, Markov property of solutions, sample path properties, Girsanov's Theorem, weak existence and uniqueness, and connections with partial differential equations. Possible additional topics include stochastic stability, reflected diffusions, numerical approximation, and stochastic control. Prerequisite: APMA 2640
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APMA 2810O - Stochastic Differentail Equations
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