2009-2010 Bulletin – PDF - SEAS Bulletin - Columbia University

APPLIED MATHEMATICS: THIRD AND FOURTH YEARS
65
SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII
REQUIRED
COURSES
APMA E3101 (3) 1 APMA E3102 (3) 1 MATH W4061 (3) APMA E3900 (3) 3
Linear algebra Partial differential equations Modern analysis Research
(Applied math, I)
(Applied math, II)
APMA E4101 (3) Courses designated
APMA E4901 (0) Course from Group A Introduction to MATH, APMA, or STAT (3)
Seminar or Group B 2 dynamical systems
(Applied math, III)
Course from Group A APMA E4300 (3)
or Group B 2 Introduction to APMA E4903 (4)
numerical methods
Seminar
APMA E4204 (3) 1 (Computational math, I)
Complex variables
ELECTIVES
TECH 4
NONTECH
3 points 3 points 3 points 6 points
3 points 3 points 3 points 3 points
TOTAL POINTS
15 15 16 15
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.
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 probability and statistics; SIEO W4150: Introduction to probability and statistics; MATH W4155: Probability theory. Group B: STAT W3105: Introduction to statistics; STAT
W3107: Statistical inference; STAT W4107: Statistical inference; STAT W4109: Probability and statistical inference; SIEO W 4606: Elementary stochastic processes; IEOR
E3106: Introduction to stochastic models; IEOR E4106: Introduction to operations research: stochastic models; IEOR E4703: Monte Carlo simulation; COMS W4771:
Machine learning.
3 With an adviser’s permission, an approved technical elective may be substituted.
4 Any course in science or engineering at the 3000 level or above qualifies as a technical elective.
systems, rate processes, modulation, detection,
harmonic generation, and applications.
CHAP E4120x Statistical mechanics
Lect: 3. 3 pts. Professor O’Shaughnessy.
Prerequisite: CHEN E3210 or equivalent thermodynamics
course, or the instructor’s permission.
Fundamental principles and underlying assumptions
of statistical mechanics. Boltzmann’s entropy
hypothesis and its restatement in terms of
Helmholtz and Gibbs free energies and for
open systems. Correlation times and lengths.
Exploration of phase space and observation
timescale. Correlation functions. Fermi-Dirac and
Bose-Einstein statistics. Fluctuation-response
theory. Applications to ideal gases, interfaces,
liquid crystals, microemulsions and other complex
fluids, polymers, Coulomb gas, interactions
between charged polymers and charged interfaces,
ordering transitions.
APPH E4130y Physics of solar energy
Lect: 3. 3 pts. Professor Chen.
Prerequisites: General physics (PHYS C1403 or
C1602), general chemistry (one term, such as
CHEM C1403), and mathematics, including ordinary
differential equations and complex numbers
(such as MATH V1202 or E1210), or the instructor’s
permission. The physics of solar energy,
including solar radiation, the analemma, atmospheric
effects, thermodynamics of solar energy,
physics of solar cells, energy storage and transmission,
and physics and economics in the solar
era.
APPH E4200x Physics of fluids
Lect: 3. 3 pts. Professor Mauel.
Prerequisites: APMA E3102 or the equivalent,
PHYS C1401 or C1601 or the 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.
APPH E4210y Geophysical fluid dynamics
Lect: 3. 3 pts. Professor Polvani.
Prerequisites: APMA E3101 and E3102 or the
equivalents and APPH E4200 or the equivalent,
or permission of the instructor. Fundamental concepts
in the dynamics of rotating, stratified flows.
Geostrophic and hydrostatic balances, potential
vorticity, f and beta plane approximations, gravity
and Rossby waves, geostrophic adjustment and
quasigeostrophy, baroclinic and barotropic instabilities,
Sverdrup balance, boundary currents,
Ekman layers.
APPH E4300x Applied electrodynamics
Lect: 3. 3 pts. Professor Boozer.
Prerequisites: PHYS W3003 and APPH E3300
or their equivalents. Overview of properties and
interactions of static electric and magnetic fields.
Study of phenomena of time-dependent electric
and magnetic fields, including induction, waves,
and radiation as well as special relativity.
Applications are emphasized.
APPH E4301y Introduction to plasma physics
Lect: 3. 3 pts. Professor Maurer.
Prerequisite: APPH E4300. Definition of a plasma.
Plasmas in laboratories and nature, plasma production.
Motion of charged particles in electric
and magnetic fields, adiabatic invariants.
Heuristic treatment of collisions, diffusion, transport,
and resistivity. Plasma as a conducting fluid.
Electrostatic and magnetostatic equilibria of plasmas.
Waves in cold plasmas. Demonstration of
laboratory plasma behavior, measurement of
plasma properties. Illustrative problems in fusion,
space, and nonneutral or beam plasmas.
SEAS 2009–2010