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Course Criteria
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0.00 - 4.00 Credits
Principal features of modern climate, including dominant modes of variability. The Earth's energy and water cycles, and their role in climate change. Processes determining the principal atmospheric and ocean circulation features, and their variability on seasonal to decadal time scales. Factors that determine past and future climates, including climate feedbacks. Detection and attribution of climate change.
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0.00 - 4.00 Credits
The chemical composition of the oceans and the nature of the physical and chemical processes governing this composition in the past and present. The cycles of major and minor oceanic constituents, including interactions with the biosphere and at the ocean-atmosphere and ocean-sediment interfaces.
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0.00 - 4.00 Credits
An intro to differential equations. Both applications and fundamental theory will be discussed. Basic second order differential equations (including the wave, heat and Poisson equations); separation of variables and solution by Fourier series and Fourier integrals; boundary value problem and Green's function; variational methods; normal mode analysis and perturbation methods; nonlinear first order (Hamilton-Jacobi) equations and method of characteristics; reaction-diffusion equations; in addition, application of these equations and methods to e.g. finance and control. Necessary background material in ODEs will be covered.
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0.00 - 4.00 Credits
Asymptotic methods, Dominant balance, ODEs: initial and Boundary value problems, Wronskian, Green's functions, Complex Variables: Cauchy's theorem, Taylor and Laurent expansions, Approximate Solution of Differential Equations, singularity type, Series expansions. Asymptotic Expansions. Stationary Phase, Saddle Points, Stokes phenomena. WKB Theory: Stokes constants, Airy function, Derivation of Heading's rules, bound states, barrier transmission. Asymptotic evaluation of integrals, Laplace's method, Stirling approximation, Integral representations, Gamma function, Riemann zeta function. Boundary Layer problems, Multiple Scale Analysis
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0.00 - 4.00 Credits
This course will concern itself with the analysis of high dimensional data sets using spectral methods. There has been significant progress in the development of methods for dimensionality reduction of high dimensional data. We will discuss these methods and how to perform data analysis tasks such as clustering and classification, regression and out-of-sample extension of empirical functions, semi-supervised learning, and independent component analysis (ICA). We will emphasize applications to image and signal processing, structural biology, dynamical systems, text and document analysis, search and data mining, finance, and more.
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0.00 - 4.00 Credits
A broad introduction to scientific computation using examples drawn from astrophysics. From computer science, practical topics including processor architecture, parallel systems, structured programming, and scientific visualization will be presented in tutorial style. Basic principles of numerical analysis, including sources of error, stability, and convergence of algorithms. The theory and implementation of techniques for linear and nonlinear systems of equations, ordinary and partial differential equations will be demonstrated with problems in stellar structure and evolution, stellar and galactic dynamics, and cosmology.
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0.00 - 4.00 Credits
The goal of this course is to teach basic tools and principles of writing good code, in the context of scientific computing. Specific topics include an overview of relevant compiled and interpreted languages, build tools and source managers, design patterns, design of interfaces, debugging and testing, profiling and improving performance, portability, and an introduction to parallel computing in both shared memory and distributed memory environments. The focus is on writing code that is easy to maintain and share with others. Students will develop these skills through a series of programming assignments and a group project.
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0.00 - 4.00 Credits
This is a general introduction to multiscale modeling. Topics to be covered include: analytical methods (averaging, homogenization, hydrodynamic and continuum limits, renormalization group methods); classical numerical methods (multi-grid, fast multi-pole methods, etc); modern numerical methods; variational model reduction, coupling techniques and hybrid schemes. Applications to PDEs with multiscale data, coupling kinetic and hydrodynamic models, coupling continuum and molecular dynamics models, etc.
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0.00 - 4.00 Credits
In this course, students are trained, through the use of an audio/visual method, to speak, understand, read and write Modern Standard Arabic, the form of Arabic shared by all Arab countries. Classroom time is devoted to conversation (skits and discussions) and grammar exercises (including skim-reading tasks) stemming from the text book. Consistent emphasis is placed on authentic materials that derive from the living cultural context.
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0.00 - 4.00 Credits
This course continues the study of Modern Standard Arabic commenced in Arabic 101. Emphasis is placed on grammatical analysis; writing and reading of increasingly longer, unvocalized texts; further vocabulary acquisition, and continued practice in listening and speaking Modern Standard Arabic.
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