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ANTH W4346: Laboratory Techniques
3.00 Credits
Columbia University in the City of New York
Training in general archaeological methods. Data recording techniques, preparation of reports and illustration, etc.
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APMA E4101: Introduction to Dynamical Systems
3.00 Credits
Columbia University in the City of New York
Prerequisites: APMA E2101 (or MATH E1210)and APMA E3101 An introduction to the analytic and geometric theory of dynamical systems; basic existence, uniqueness and parameter dependence of solutions to ordinary differential equations; constant coefficient and parametrically forced systems; Fundamental solutions; resonance; limit points, limit cycles and clasificiation of flows in the plane (poincare-Bendixson Therem); conservative and dissipative systems; linear and nonlinear stability analysis of equilibria and periodic solutions; stble and unstable manifoleds; bifurcations, e.g. Andronov-Hopf; sensitive depeneence and chaotic dynamics; slected applications.
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APMA E4300: Introduction to numerical methods
3.00 Credits
Columbia University in the City of New York
Prerequisites: MATH V1201, MATH E1210, and APMA E3101 or their equivalents. Some programming experience and Matlab will be extremely useful. Introduction to fundamental algorithms and analysis of numerical methods commonly used by scientists, mathematicians and engineers. This course is designed to give a fundamental understanding of the building blocks of scientific computing that will be used in more advanced courses in scientific computing and numerical methods for PDE?s. Topics include numerical solutions of algebraic systems, linear least-squares, eigenvalue problems, solution of non-linear systems, optimization, interpolation, numerical integration and differentiation, initial value problems and boundary value problems for systems of ODE?s. All programming exercises will be in Matlab.
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APMA E4300 - Introduction to numerical methods
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APPH E4200: Physics of fluids
3.00 Credits
Columbia University in the City of New York
Prerequisite: APMA E3102 or equivalent; PHYS 1401 or 1601 or equivalent. An introduction to the physical behavior of fluids for science and engineering students. Derivation of basic equations of fluid dynamics: conservation of mass, momentum, and energy. Dimensional analysis. Vorticity. Laminar boundary layers. Potential flow. Effects of compressibility, stratification, and rotation. Waves on a free surface; shallow water equations. Turbulence.
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APPH E4210: Geophysical fluid dynamics
3.00 Credits
Columbia University in the City of New York
Prerequisites: APMA E3101, APMA E3102 (or equivalents) and APPH E4200 (or equivalent), or permission from instructor. Fundamental concepts in the dynamics of rotating, stratified flows. Geostrophic and hydrostatic balances, potential vorticity, f and beta plane approxima-tions, gravity and Rossby waves, geostrophic adjustment and quasigeostrophy, baroclinic and barotropic instabilities, Sverdrup balance, boundary currents, Ekman layers.
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APPH E4210 - Geophysical fluid dynamics
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APPH E4901: Seminar: problems in applied physics
1.00 Credits
Columbia University in the City of New York
This course is required for, and can be taken only by, all applied physics majors and minors in the junior year. Discussion of specific and self-contained problems in areas such as applied electrodynamics, physics of solids, and plasma physics. Topics change yearly.
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APPH E4901 - Seminar: problems in applied physics
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APPH E4903: Seminar: problems in applied physics
2.00 Credits
Columbia University in the City of New York
This course is required for, and can be taken only by, all applied physics majors in the senior year. Discussion of specific and self-contained problems in areas such as applied electrodynamics, physics of solids, and plasma physics. Formal presentation of a term paper required. Topics change yearly.
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ARCH V1020: Introduction To Architectural Design and Visual Culture
3.00 Credits
Columbia University in the City of New York
Corequisites: Intended for the non-major, sophomore year and above. Enrollment limited to 18 students. Introductory design studio to introduce students to architectural design through readings and studio design projects. Intended to develop analytic skills to critique existing media and spaces. Process of analysis used as a generative tool for the students' own design work. Attendance is mandatory at the first class meeting in order to form class registration lists.
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ARCH V1020 - Introduction To Architectural Design and Visual Culture
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ARCH V3101: Architectural Representation: Abstraction
4.00 Credits
Columbia University in the City of New York
Prerequisites: Enrollment limited to 16 students per section. Recommended for the sophomore year. Students work in a studio environment. Introduction to design through analysis of abstract architectural space and form. Emphasis on the design process and principles of representations through architectural drawing and model making. Attendance is mandatory at the first class meeting in order to form class registration lists.
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ARCH V3103: Architectural Representation: Perception
4.00 Credits
Columbia University in the City of New York
Prerequisites: Students work in a studio environment. Recommended for the sophomore year. Enrollment limited to 16 students per section. Introduction to design through studies in the perception of architectural space and form. Emphasis on exploratory, inventive processes for the generation, development, and representation of ideas in a variety of media. Attendance is mandatory at the first class meeting in order to form class registration lists.
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