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

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APAM E4999x and y–S4999 Curricular
practical training
1 pt. Members of the faculty.
Prerequisite: Obtained internship and approval
from adviser. Only for master’s students in the
Department of Applied Physics and Applied
Mathematics who may need relevant work
experience as part of their program of study.
Final report required. This course may not be
taken for pass/fail or audited.
APPH E6081x Solid state physics, I
3 pts. Lect: 3. Professor Pinczuk.
Prerequisites: APPH E3100 or the equivalent.
Knowledge of statistical physics on the level
of MSAE E3111 or PHYS G4023 strongly
recommended. Crystal structure, reciprocal
lattices, classification of solids, lattice dynamics,
anharmonic effects in crystals, classical electron
models of metals, electron band structure, and
low-dimensional electron structures.
APPH E6082y Solid state physics, II
3 pts. Lect: 3. Professor Kim.
Prerequisite: APPH E6081 or the instructor’s
permission. Semiclassical and quantum
mechanical electron dynamics and
conduction, dielectric properties of insulators,
semiconductors, defects, magnetism,
superconductivity, low-dimensional structures,
and soft matter.
APPH E6085x Computing the electronic
structure of complex materials
3 pts. Lect: 3. Offered in alternate years.
Prerequisite: APPH E3100 or equivalent. Basics
of density functional theory (DFT) and its
application to complex materials. Computation
of electronics and mechanical properties of
materials. Group theory, numerical methods,
basis sets, computing, and running open source
DFT codes. Problem sets and a small project.
APPH E6091y Magnetism and magnetic
materials
3 pts. Lect. 3. Offered in alternate years.
Professor Bailey.
Prerequisites: MSAE E4206, APPH E6081, or
equivalent. Types of magnetism. Band theory
of ferromagnetism. Magnetic metals, insulators,
and semiconductors. Magnetic nanostructures:
ultrathin films, superlattices, and particles.
Surface magnetism and spectroscopies. High
speed magnetization dynamics. Spin electronics.
APPH E6101x Plasma physics, I
3 pts. Lect: 3. Instructor to be announced.
Prerequisite: APPH E4300. Debye screening.
Motion of charged particles in space- and
time-varying electromagnetic fields. Two-fluid
description of plasmas. Linear electrostatic and
electromagnetic waves in unmagnetized and
magnetized plasmas. The magnetohydrodynamic
(MHD) model, including MHD equilibrium,
stability, and MHD waves in simple geometries.
Fluid theory of transport.
APPH E6102y Plasma physics, II
3 pts. Lect: 3. Professor Boozer.
Prerequisite: APPH E6101. Magnetic coordinates.
Equilibrium, stability, and transport of torodial
plasmas. Ballooning and tearing instabilities.
Kinetic theory, including Vlasov equation,
Fokker-Planck equation, Landau damping, kinetic
transport theory. Drift instabilities.
APPH E6110x Laser interactions with matter
3 pts. Lect: 3. Not offered in 2011–2012.
Prerequisites: APPH E4112 or equivalent, and
quantum mechanics. Principles and applications
of laser-matter coupling, nonlinear optics, threeand
four-wave mixing, harmonic generation,
laser processing of surfaces, laser probing of
materials, spontaneous and stimulated light
scattering, saturation spectroscopy, multiphoton
excitation, laser isotope separation, transient
optical effects.
APAM E6650x and y–S6650 Research project
1–6 pts. Members of the faculty.
This course may be repeated for credit. A special
investigation of a problem in nuclear engineering,
medical physics, applied mathematics, applied
physics, and/or plasma physics consisting of
independent work on the part of the student and
embodied in a formal report.
APPH E9142x-E9143y Applied physics seminar
3 pts. Sem: 3. Not offered in 2011–2012.
These courses may be repeated for credit.
Selected topics in applied physics.
APAM E9301x and y–S9301 Doctoral research
0–15 pts. Members of the faculty.
Prerequisite: Qualifying examination for the
doctorate. Required of doctoral candidates.
APAM E9800x and y–S9800 Doctoral
research instruction
3, 6, 9, or 12 pts. Members of the faculty.
A candidate for the Eng.Sc.D. degree must
register for 12 points of doctoral research
instruction. Registration for APAM E9800 may
not be used to satisfy the minimum residence
requirement for the degree.
APAM E9900x and y–S9900 Doctoral
dissertation
0 pts. Members of the faculty.
A candidate for the doctorate may be required
to register for this course every term after the
coursework has been completed, and until the
dissertation has been accepted.
Courses in Applied
Mathematics
APMA E2101y Inroduction to applied
mathematics
3 pts. Lect: 3. Professor Spiegelman.
Prerequisite: Calculus III. A unified, singlesemester
introduction to differential equations
and linear algebra with emphases on
(1) elementary analytical and numerical
technique and (2) discovering the analogs
on the continuous and discrete sides of the
mathematics of linear operators: superposition,
diagonalization, fundamental solutions. Concepts
are illustrated with applications using the
language of engineering, the natural sciences,
and the social sciences. Students execute
scripts in Mathematica and MATLAB (or the
like) to illustrate and visualize course concepts
(programming not required).
APMA E3101x Linear algebra
3 pts. Lect: 3. Professor Duchêne.
Matrix algebra, elementary matrices, inverses,
rank, determinants. Computational aspects of
solving systems of linear equations: existenceuniqueness
of solutions, Gaussian elimination,
scaling, ill-conditioned systems, iterative
techniques. Vector spaces, bases, dimension.
Eigenvalue problems, diagonalization, inner
products, unitary matrices.
APMA E3102y Partial differential equations
3 pts. Lect: 3. Professor Sobel.
Prerequisite: MATH E1210 or equivalent.
Introduction to partial differential equations;
integral theorems of vector calculus. Partial
differential equations of engineering in
rectangular, cylindrical, and spherical
coordinates. Separation of the variables.
Characteristic-value problems. Bessel functions,
Legendre polynomials, other orthogonal
functions; their use in boundary value problems.
Illustrative examples from the fields of
electromagnetic theory, vibrations, heat flow, and
fluid mechanics.
APAM E3105x Programming methods for
scientists and engineers
3 pts. Lect: 2.5. Lab: 1. Not offered in 2011–2012.
Introduction to modern techniques of computer
programming for the numerical solutions to
familiarity with basic and advanced concepts
of modern numerical programming and acquire
practical experience solving representative
problems in math and physics.
APMA E3900x and y Undergraduate research
in applied mathematics
0–4 pts. Members of the faculty.
This course may be repeated for credit, but
no more than 6 points of this course may be
counted toward the satisfaction of the B.S.
degree requirements. Candidates for the B.S.
degree may conduct an investigation in applied
mathematics or carry out a special project
under the supervision of the staff. Credit for the
course is contingent upon the submission of an
acceptable thesis or final report.
APMA E4001y Principles of applied
mathematics
3 pts. Lect: 3. Professor Duchêne.
Prerequisites: Introductory Linear Algebra
required. Ordinary Differential Equations
recommended. Review of finite-dimensional
vector spaces and elementary matrix theory.
Linear transformations, change of basis,
eigenspaces. Matrix representation of linear
operators and diagonalization. Applications
to difference equations, Markov processes,
ordinary differential equations, and stability of
nonlinear dynamical systems. Inner product
spaces, projection operators, orthogonal
bases, Gram-Schmidt orthogonalization. Least
engineering 2011–2012