2011-2012 Bulletin â PDF - SEAS Bulletin - Columbia University

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68 (elliptic), heat (parabolic) and Schroedinger (dispersive) equations; fundamental solutions, Green’s functions, weak/distribution solutions, maximum principle, energy estimates, variational methods, method of characteristics; elementary functional analysis and applications to PDEs; introduction to nonlinear PDEs, shocks; selected applications. APMA E6302x Numerical analysis of partial differential equations 3 pts. Lect: 2. Not offered in 2011–2012. Prerequisite: APMA E3102 or E4200. Numerical analysis of initial and boundary value problems for partial differential equations. Convergence and stability of the finite difference method, the spectral method, the finite element method and applications to elliptic, parabolic, and hyperbolic equations. APMA E6304y Integral transforms 3 pts. Lect: 2. Not offered in 2011–2012. Prerequisites: APMA E4204 and MATH E1210, or their equivalents. Laplace, Fourier, Hankel, and Mellin transforms. Selection of suitable transform for a given partial differential equation boundary value problem. Operational properties of transforms. Inversion theorems. Approximate evaluation of inversion integrals for small and large values of parameter. Application to the solution of integral equations. APMA E6901x and y–E6901y Special topics in applied mathematics 3 pts. Lect: 3. Instructor to be announced. Prerequisites: Advanced calculus and junior year applied mathematics, or their equivalents. This course may be repeated for credit. Topics and instructors from the Applied Mathematics Committee and the staff change from year to year. For students in engineering, physical sciences, biological sciences, and other fields. APMA E8308y Asymptotic methods in applied mathematics 3 pts. Lect: 2. Not offered in 2011–2012. Prerequisite: APMA E4204 or equivalent. Asymptotic treatment of ordinary and partial differential equations in problems arising in applied mathematics. Asymptotic series. Asymptotic evaluation of integrals. Expansion of solutions of ordinary differential equations: connection problem and turning points. Stoke’s phenomenon. Differential equations with a parameter: “boundary layer” phenomenon. Application to partial differential equations: problems from fluid dynamics, wave propagation theory, electromagnetic theory. APMA E9101x-E9102y Research 1–4 pts. Members of the faculty. Prerequisite: Permission of the supervising faculty member. This course may be repeated. Advanced study in a special area. APMA E9810x or y Mathematical earth science seminar 0 pts. Lect: 1. Professor Polvani. Prerequisite: Instructor’s permission. Current research in problems at the interface between applied mathematics and earth and environmental sciences. APMA E9815x or y Geophysical fluid dynamics seminar 1–3 pts. May be repeated for up to 10 points of credit. Not offered in 2011–2012. Prerequisite: Instructor’s permission. Problems in the dynamics of geophysical fluid flows. Courses in Materials science and engineering See page 172. engineering 2011–2012
iomedical engineering 351 Engineering Terrace, MC 8904 Phone: 212-854-4460 E-mail: bme@columbia.edu www.bme.columbia.edu 69 Interim Chair Andreas H. Hielscher Departmental Administrator Shila Maghji Business Manager Kidest Shenkoru Administrative Coordinator for Student Affairs Jarmaine Lomax Administrative Assistant for Fiscal Affairs Michelle Cintron Administrative Assistant for Departmental Affairs Paulette Louissaint Laboratory Manager Keith Yeager Computer Systems Administrator Robert J. Foster Chair of Undergraduate Studies X. Edward Guo Chair of Graduate Studies Helen H. Lu Ombuds Lance Kam Professors Gerard H. A. Ateshian X. Edward Guo Andreas H. Hielscher Clark T. Hung Andrew F. Laine Edward F. Leonard Van C. Mow, Stanley Dicker Professor Gordana Vunjak- Novakovic Associate Professors Henry Hess Christopher R. Jacobs Elisa E. Konofagou Helen H. Lu Jeremy J. Mao Barclay Morrison III Paul Sajda Assistant Professors Elizabeth Hillman Hayden Huang Lance C. Kam Samuel K. Sia Lecturer in Discipline Aaron Matthew Kyle Joint Faculty Dimitris Anastassiou, Professor of Electrical Engineering Aniruddha Das, Assistant Professor of Psychiatry Shunichi Homma, Professor of Medicine Elizabeth S. Olson, Assistant Professor of Otolaryngology/Head and Neck Surgery Lawrence Schwartz, Professor of Radiology Michael P. Sheetz, Professor of Cell Biology R. Theodore Smith, Associate Professor of Ophthalmology Adjunct Professors Ernest Feleppa Shiro Matsuoka Adjunct Associate Professor Nicolas W. Chbat Affiliates Peter K. Allen, Professor of Computer Science Robert DeLaPaz, Professor of Radiology Kung Ming Jan, Associate Professor of Clinical Medicine Jung-Chi Liao, Assistant Professor of Mechanical Engineering Zheng Feng Lu, Associate Professor of Clinical Radiology John Pile-Spellman, Professor of Radiology and Neurosurgery Henry M. Spotnitz, Professor of Surgery Biomedical engineering is an evolving discipline in engineering that draws on collaboration among engineers, physicians, and scientists to provide interdisciplinary insight into medical and biological problems. The field has developed its own knowledge base and principles that are the foundation for the academic programs designed by the Department of Biomedical Engineering at Columbia. The programs in biomedical engineering at Columbia (B.S., M.S., Ph.D., Eng.Sc.D., and M.D./ Ph.D.) prepare students to apply engineering and applied science to problems in biology, medicine, and the understanding of living systems and their behavior, and to develop biomedical systems and devices. Modern engineering encompasses sophisticated approaches to measurement, data acquisition and analysis, simulation, and systems identification. These approaches are useful in the study of individual cells, organs, entire organisms, and populations of organisms. The increasing value of mathematical models in the analysis of living systems is an important sign of the success of contemporary activity. The programs offered in the Department of Biomedical Engineering seek to emphasize the confluence of basic engineering science and applied engineering with the physical and biological sciences, particularly in the areas of biomechanics, cell and tissue engineering, and biosignals and biomedical imaging. Programs in biomedical engineering are taught by its own faculty, members of other Engineering departments, and faculty from other University divisions who have strong interests and involvement in biomedical engineering. Several of the faculty hold joint appointments in Biomedical Engineering and other University departments. Courses offered by the Department of Biomedical Engineering are complemented by courses offered by other departments in The Fu Foundation School of Engineering and Applied Science, and by many departments in the Faculty of Medicine, the School of Dentistry and Oral Surgery, and the Mailman School of Public Health, as well as the science departments within the Graduate School of Arts and Sciences. The availability of these courses in a university that contains a large medical center and enjoys a basic commitment to interdisciplinary research is important to the quality and strength of the program. Educational programs at all levels are based on engineering and biological fundamentals. From this basis, the program branches into concentrations along three tracks: biomechanics, cell and tissue engineering, and biosignals and biomedical imaging. The intrinsic engineering 2011–2012
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Bulletin 2011 -2012
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Bulletin 2011 -2012
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a message from the dean As students
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About the School and University
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3 After receiving a master’s degr
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Resources and Facilities 5 A Colleg
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• CourseWorks is the University c
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Undergraduate Studies
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students improve their ability to e
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transistors, first order RC and RL
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possible overseas destinations and
Page 23 and 24: more than 68 transfer points toward
Page 25 and 26: Programs Registered with the New Yo
Page 27 and 28: Applicants may submit results of th
Page 29 and 30: Undergraduate Tuition, Fees, and Pa
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Page 37 and 38: statements covering these special r
Page 39 and 40: 33 Completion of Requirements The r
Page 41 and 42: graduate admissions 35 Office of Gr
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Page 47 and 48: esearch assistantships, readerships
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Page 51 and 52: 45 Xi Chen Associate Professor of E
Page 53 and 54: S. G. Steven Kou Professor of Indus
Page 55 and 56: Tiffany Shaw Assistant Professor of
Page 57 and 58: Enders Robinson Maurice Ewing and J
Page 59 and 60: Departments and Academic Programs
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Page 63 and 64: techniques based on the theory of g
Page 65 and 66: Applied Physics: Third and Fourth Y
Page 67 and 68: Applied mathematics: Third and Four
Page 69 and 70: are determined in consultation with
Page 71 and 72: APPH E4110x Modern optics 3 pts. Le
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Page 83 and 84: BMEN E4420y Biomedical signal proce
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Page 99 and 100: Program Objectives In developing an
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Page 103 and 104: engineering mechanics: Third and Fo
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Page 107 and 108: ENME E4363y Multiscale computationa
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COMS E6902x and y Thesis 1-9 pts. A
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Engineer, and the doctorate degrees
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Scholarships, Fellowships, and Inte
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earth and environmental engineering
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sludge or cake that must be dispose
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theory and practical aspects of dat
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EAEE E4241x Solids handling and tra
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permission. Critical discussion of
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engineering. Details on those progr
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electrical engineering: Third and F
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electrical engineering: Third and F
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outside of engineering and science
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knowledge of elementary algebra. EL
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ELEN E4488x Optical systems 3 pts.
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ELEN E6321y Advanced digital electr
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and different topics rotate through
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ELEN E6781y Topics in modeling and
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Current Research Activities In indu
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take one additional 3-point course.
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optimization applied probability fi
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industrial engineering: Third and F
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operations research: Third and Four
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OPERATIONS RESEARCH: engineering ma
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OPERATIONS RESEARCH: FINANCIAL engi
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applications. Review of elements of
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Current Research Activities Current
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materials science and engineering:
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Chemistry, Earth and Environmental
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cations, grain boundaries, electron
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Biomechanics and Mechanics of Mater
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processing for sample preparation a
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mechanical engineering: third and f
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mechanical engineering: third and f
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prescribed design problems. Problem
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iophysics of molecular motors, mech
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Undergraduate Minors
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take the core BME requirements, as
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MINOR IN Entrepreneurship and Innov
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Interdisciplinary Courses and Cours
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Courses in Other Divisions of the U
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EESC V1201y Environmental risks and
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process of critical listening, both
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to Riemann geometry. Motion of part
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Campus and Student Life
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Preprofessional Advising The Office
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three Greek councils: The Interfrat
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student services 211 university hou
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Upperclass and Graduate Students Ma
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Scholarships, Fellowships, Awards,
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Class of 1900 (1940) Gift of the Cl
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James M. and Elizabeth S. Li Endowe
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Max Yablick Memorial Scholarship (1
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Applied Physics Faculty Award Award
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time to that member of the graduati
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228 Academic Procedures and Standar
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230 calendar day, not a 24-hour tim
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232 Academic standing Academic Hono
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234 Policy on Conduct and Disciplin
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236 • Understand what instructors
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238 Student Grievances, Academic Co
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240 C. Discrimination and sexual ha
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242 columbia university resource li
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244 Medical Services John Jay Hall,
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246 The Morningside Heights Area of
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248 Center for Career Education (CC
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250 See also payments fellowships,
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252 parents contributions to educat
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254 notes engineering 2011-2012
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256 notes engineering 2011-2012
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500 West 120th Street New York, New
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