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University of Utah

Department of Computer Science

Department of Mathematics

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CES Course Descriptions

**CS 5210/6210: Introduction to Scientific Computing ** (3) Prereq.:
CS 3200, CS3510, MATH 3150. This course is offered every third semester,
beginning in Fall 1999.

*Course Outline*: This course provides an introduction to existing
classical and modern numerical methods and a knowledge of their
algorithmic development and efficient implementation. Topics include:
numerical linear algebra, approximation methods and parallel
computation methods for nonlinear equations, ordinary differential
equations, and partial differential equations. Students will learn
about existing algorithms, and develop and implement new algorithms
for parallel and distributed environments.

**MATH 5610: Introduction to Numerical Analysis I** (4) Sem: A. Prereq:
MATH 2210, either MATH 2250 or 2270, and computing experience.

*Course Outline*: Numerical linear algebra,
interpolation, integration, differentiation, approximation (including
discrete and continuous least squares, Fourier analysis, and
wavelets).

**CS 6220: Advanced
Scientific Computing ** (3) Prereq.: CS 5210/6210 or MATH 5610
(Offered every third semester, beginning in Spring 2000).

*Course Outline*: A study of the numerical
solution of two and three dimensional partial differential equations that
arise in science and engineering problems. Topics include: finite
difference methods, finite element methods, boundary element methods,
multigrid methods, sinc methods, domain decomposition, mesh generation,
storage optimization methods, and adaptive methods.

**5620 Introduction to Numerical Analysis II ** (4) Sem:
S. Recommended Prereq.: MATH 5610.

*Course Outline*: Computational solution of initial and
boundary value problems of ordinary and partial differential
equations.

**MATH 5740: Mathematical Modeling** (2) Sem: S. Prereq.: CS 5220 or
MATH 5620 .

*Course Outline*: Development of mathematical models for
physical, biological, engineering, and industrial phenomena and
problems, using mainly ordinary and partial differential
equations. Involvement of analytical and numerical tools suitable for
analysis and visualization of the solutions of these problems,
including packages such as LAPACK, EISPACK, Maple and Matlab.

**CS 5630/6630: Scientific Visualization** (3) Prereq.: CS 3510,
CS 3200 or CS 5210 or MATH 5610 (Offered every third semester, beginning Fall
2000).

*Course Outline*: An introduction to the techniques and
tools needed for the visual display of data. Students will explore
mmany aspects of visualization, using a ``from concepts to results''
format. The course begins with an overview of the important issues
involved in visualization, continues through an overview of graphics
tools relating to visualization, and ends with instruction in the
utilization and customization of a variety of scientific visualization
software packages.

** MATH 6790 Case Studies in Computational Engineering and
Science ** (2) Sem: S. Prereq.: MATH 5740 and either MATH 5620 or CS 5220.

*Course Outline*: Two to five faculty members from
various disciplines will describe in detail a project in which they
are engaged that involves all ingredients of computational engineering
and science: a scientific or engineering problem, a mathematical
problem leading to mathematical questions, and the solution and
interpretation of these questions obtained by the use of modern
computing techniques. Participating faculty will vary from year to
year. To be offered on the basis of need.

**CS 6938/MATH 6795: Seminar in Computational Engineering
and Science** (1-3). Prereq.: MATH 6790.

*Course Outline*: Students in the final semester of the
Computational Engineering and Science program will present their own
CES-related research.

Students in the CES program are encouraged to take additional courses
in the various areas above. Some courses that may be of interest
are:

**CS 5020: Algorithms and Data Structures **

**CS 5010: Software Practice **

**CS 6820: Parallel Computer Architecture **

**CS 7120: Information Based Complexity **

**CS 7240: Sinc Methods **

**CS 5600/6600, 5610/6610: Computer Graphics**

**CS 6670, 6680: Computer-Aided Geometric Design**

**CS 6939: Seminar in Inverse Problems** (1-3).

**MATH 5110, 5120 Mathematical Biology **

**MATH 5410, 5420 Introduction to Ordinary Differential Equations **

**MATH 5440 Introduction to Partial Differential Equations **

**MATH 5470 Applied Dynamical Systems **

**MATH 5660 Parallel Numerical Methods**

**MATH 5710, 5720 Introduction to Applied Mathematics **

**MATH 6610, 6620 Analysis of Numerical Methods **

**MATH 6630 Numerical Solutions of Partial Differential
Equations **

**MATH 6710 Applied Linear Operator and Spectral Methods **

**MATH 6720 Appl Complex Variables, Asymptotic Methods **

**MATH 6730 Asymptotic and Perturbation Methods **

**MATH 6750, 6760 Continuum Mechanics: Fluids, Solids **

**MATH 6770, 6780 Mathematical Biology **