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

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and programming ability in C/C++ or FORTRAN/F90.
An introduction to the concepts, the hardware and
software environments, and selected algorithms
and applications of parallel scientific computing,
with an emphasis on tightly coupled computations
that are capable of scaling to thousands of
processors. Includes high-level descriptions of
motivating applications and low-level details of
implementation, in order to expose the algorithmic
kernels and the shifting balances of computation
and communication between them. Students run
demonstration codes provided on a Linux cluster.
Modest programming assignments using MPI and
PETSc culminate in an independent project leading
to an in-class report.
APMA E4400y Introduction to biophysical
modeling
Lect: 3. 3 pts. Professor Wiggins.
Prerequisites: PHYS W1401 or the equivalent and
APMA E2101 or MATH E1210 or the equivalent.
Introduction to physical and mathematical models
of cellular and molecular biology. Physics at the
cellular scale (viscosity, heat, diffusion, statistical
mechanics). RNA transcription and regulation of
genetic expression. Genetic and biochemical networks.
Bioinformatics as applied to reverse engineering
of naturally occurring networks and to
forward engineering of synthetic biological networks.
Mathematical and physical aspects of
functional genomics.
APMA E4901x Seminar: problems in
applied mathematics
Lect: 1. 0 pt. Professor Wiggins.
This course is required for, and can be taken only
by, all applied mathematics majors in the junior
year. Prerequisites or corequisites: APMA E4200
and E4204, or their equivalents. Introductory seminars
on problems and techniques in applied mathematics.
Typical topics are nonlinear dynamics,
scientific computation, economics, operations
research, etc.
APMA E4903x Seminar: problems in
applied mathematics
Lect: 1. Tutorial: 2. 3 or 4 pts. Professor Wiggins.
This course is required for, and can be taken only
by, all applied mathematics majors in the senior
year. Prerequisites or corequisites: APMA E4200
and E4204, or their equivalents. For 4 pts. credit,
term paper required. Examples of problem areas
are nonlinear dynamics, asymptotics, approximation
theory, numerical methods, etc.
Approximately three problem areas are studied
per term.
APMA E4990x and y Special topics in
applied mathematics
Lect: 3. 1–3 pts. Instructors 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 advanced undergraduate students
and graduate students in engineering, physical
sciences, biological sciences, and other fields.
APMA E6209x Approximation theory
Lect: 3. 3 pts. Offered in alternate years.
Not given in 2009–2010.
Prerequisite: MATH W4061 or some knowledge
of modern analysis. Theory and application of
approximate methods of analysis from the viewpoint
of functional analysis. Approximate numerical
and analytical treatment of linear and nonlinear
algebraic, differential, and integral equations.
Topics include function spaces, operators in
normed and metric spaces, fixed point theorems
and their applications.
APMA E6301y Analytic methods for partial
differential equations
Lect: 3. 3 pts. Professor Bal.
Prerequisite: Advanced calculus, basic concepts
in analysis, APMA E3101 and E4200 or their
equivalents, or permission of the instructor.
Introduction to analytic theory of PDEs of fundamental
and applied science; wave (hyperbolic),
Laplace and Poisson equations (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
Lect: 3. 3 pts. Offered in alternate years.
Not given in 2009–2010.
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
Lect: 3. 3 pts. Not given in 2009–2010.
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 Special topics in
applied mathematics
Lect: 3. 3 pts. x: Professor Langmore;
y: Not given in 2009–2010.
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
Lect: 3. 3 pts. Offered in alternate years.
Professor Marzuola.
Prerequisite: APMA E4204 or the 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 and S9101-S9102
Research
1 to 4 pts. Members of the faculty.
Prerequisite: The permission of the supervising
faculty member. This course may be repeated.
Advanced study in a special area.
APMA E9810x or y Mathematical earth
sciences seminar
Lect. 1. 0 pts. Professor Polvani.
Current research in problems at the interface
between applied mathematics and earth and
environmental sciences.
APMA E9815x or y Geophysical fluid
dynamics seminar
Lect. 3. 1 to 3 pts. Instructors to be announced.
Problems in the dynamics of geophysical fluid
flows. May be repeated for up to 10 points of
credit.
COURSES IN MATERIALS
SCIENCE AND ENGINEERING
See page 171.
SEAS 2009–2010