2008-2009 Bulletin â PDF - SEAS Bulletin - Columbia University
2008-2009 Bulletin â PDF - SEAS Bulletin - Columbia University
2008-2009 Bulletin â PDF - SEAS Bulletin - Columbia University
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APPLIED MATHEMATICS: THIRD AND FOURTH YEARS<br />
65<br />
SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII<br />
REQUIRED<br />
COURSES<br />
APMA E3101 (3) 1 APMA E3102 (3) 1 MATH W4061 (3) APMA E3900 (3) 3<br />
Linear algebra Partial differential equations Modern analysis Research<br />
(Applied math, I)<br />
(Applied math, II)<br />
APMA E4101 (3)<br />
APMA E4901 (0) Course from Group A Introduction to<br />
Seminar or Group B 2 dynamical systems<br />
(Applied math, III)<br />
Course from Group A APMA E4300 (3)<br />
or Group B 2 Introduction to APMA E4903 (4)<br />
numerical methods<br />
Seminar<br />
APMA E4204 (3) 1 (Computational math, I)<br />
Complex variables<br />
ELECTIVES<br />
APPH E4301y Introduction to plasma physics<br />
Lect: 3. 3 pts. Professor Maurer.<br />
Prerequisite: APPH E4300. Definition of a plasma.<br />
Plasmas in laboratories and nature, plasma production.<br />
Motion of charged particles in electric<br />
and magnetic fields, adiabatic invariants.<br />
Heuristic treatment of collisions, diffusion, trans-<br />
MAJOR-<br />
RELATED<br />
OTHER<br />
TECHNICAL<br />
NONTECH<br />
0 or 3 points<br />
Includes courses designated: MATH, APMA, STAT, and COMS<br />
3 points 3 points 3 points 3 or 6 points<br />
Other approved science, engineering, economics, or finance courses<br />
3 points 3 points 3 points 3 or 6 points<br />
TOTAL POINTS<br />
15 15 16 15<br />
1 MATH V2010 may be substituted for APMA E3101; APMA E4200 or MATH V3028 may be substituted for APMA E3102; MATH V3007 may be substituted for APMA E4204.<br />
2 One course from Group A and one course from Group B required for graduation. Group A: SIEO W3658: Probability; SIEO W4105: Probability; SIEO W3600: Introduction to<br />
probability and statistics; SIEO W4150: Introduction to probability and statistics; MATH W4155: Probability theory. Group B: STAT W3000: Introduction to statistics; STAT<br />
W3659: Statistical inference; STAT W4107: Statistical inference; STAT W4109: Probability and statistical inference; SIEO W 4606: Elementary stochastic processes; IEOR<br />
E3106: Introduction to stochastic models; IEOR E4106: Introduction to operations research: stochastic models; IEOR E4703: Monte Carlo simulation; COMS W4771:<br />
Machine learning.<br />
3 With an adviser’s permission, an approved technical elective may be substituted.<br />
CHAP E4120x Statistical mechanics<br />
Lect: 3. 3 pts. Professor O’Shaughnessy.<br />
Prerequisite: CHEN E3210 or equivalent thermodynamics<br />
course, or the instructor’s permission.<br />
Fundamental principles and underlying assumptions<br />
of statistical mechanics. Boltzmann’s entropy<br />
hypothesis and its restatement in terms of<br />
Helmholtz and Gibbs free energies and for<br />
open systems. Correlation times and lengths.<br />
Exploration of phase space and observation<br />
timescale. Correlation functions. Fermi-Dirac and<br />
Bose-Einstein statistics. Fluctuation-response<br />
theory. Applications to ideal gases, interfaces,<br />
liquid crystals, microemulsions and other complex<br />
fluids, polymers, Coulomb gas, interactions<br />
between charged polymers and charged interfaces,<br />
ordering transitions.<br />
APPH E4130y Physics of solar energy<br />
Lect: 3. 3 pts. Professor Chen.<br />
Prerequisites: general physics (PHYS C1403 or<br />
C1602), general chemistry (one term, such as<br />
CHEM C1403), and mathematics, including ordinary<br />
differential equations and complex numbers<br />
(such as MATH V1202 or E1210), or the instructor’s<br />
permission. The physics of solar energy,<br />
including solar radiation, the analemma, atmospheric<br />
effects, thermodynamics of solar energy,<br />
physics of solar cells, energy storage and transmission,<br />
and physics and economics in the solar<br />
era.<br />
APPH E4200x Physics of fluids<br />
Lect: 3. 3 pts. Professor Mauel.<br />
Prerequisites: APMA E3102 or the equivalent,<br />
PHYS C1401 or C1601 or the equivalent. An<br />
introduction to the physical behavior of fluids for<br />
science and engineering students. Derivation of<br />
basic equations of fluid dynamics: conservation<br />
of mass, momentum, and energy. Dimensional<br />
analysis. Vorticity. Laminar boundary layers.<br />
Potential flow. Effects of compressibility, stratification,<br />
and rotation. Waves on a free surface; shallow<br />
water equations. Turbulence.<br />
APPH E4210y Geophysical fluid dynamics<br />
Lect: 3. 3 pts. Professor Polvani.<br />
Prerequisites: APMA E3101 and E3102 or the<br />
equivalents and APPH E4200 or the equivalent,<br />
or permission of the instructor. Fundamental concepts<br />
in the dynamics of rotating, stratified flows.<br />
Geostrophic and hydrostatic balances, potential<br />
vorticity, f and beta plane approximations, gravity<br />
and Rossby waves, geostrophic adjustment and<br />
quasigeostrophy, baroclinic and barotropic instabilities,<br />
Sverdrup balance, boundary currents,<br />
Ekman layers.<br />
APPH E4300x Applied electrodynamics<br />
Lect: 3. 3 pts. Professor Boozer.<br />
Prerequisites: PHYS W3003 and APPH E3300<br />
or their equivalents. Overview of properties and<br />
interactions of static electric and magnetic fields.<br />
Study of phenomena of time-dependent electric<br />
and magnetic fields, including induction, waves,<br />
and radiation as well as special relativity.<br />
Applications are emphasized.<br />
<strong>SEAS</strong> <strong>2008</strong>–<strong>2009</strong>