Undergraduate Courses Open to Graduate Students
- Math 1070, Numerical Analysis
This course in numerical mathematics is designed for students interested
in solving scientific and engineering problems on computers and is
intended to expose students to a wide range of up
to date numerical methods. The emphasis is on algorithms, the mathematical
ideas behind them and their use in obtaining numerical solutions. Our
goal will be to understand how and when the
methods work. The concept of numerical error will be used to quantify the
accuracy of approximation. We will also study the stability and the
efficiency of algorithms.
- Math 1080, Numerical Linear Algebra
This course in NLA is for students interested in solving scientific and
engineering problems which involve lots of data and more than one
dimension. Basically, any such problem reduces
eventually to one in numerical linear algebra. The course gives an
introduction to the direct and iterative algorithms for solving linear
systems. The course will cover the development and
analysis of these numerical algorithms, to be used in the resolution of
linear systems , the algebraic eigenvalue problem and least squares
problems.
- Math 1110, Industrial Mathematics
This course introduces various methods of applied mathematics used to
solve industrial type problems. It addresses the five stages in
mathematical modeling: physical problem,
mathematical model, discrete (numerical) model, computation of a solution,
output data analysis. Central topics are differential equations
(continuous model) and matrix equations
(discrete model).
- Math 1100, Linear Programming
The course M1100 gives an introduction to the basic areas of linear
programming. The course will cover the development and analysis of
algorithms for linear programming, with an emphasis on the simplex
algorithm.
Graduate Courses in Computational Mathematics
- Our gateway course for students who have no experience with computing or
numerical analysis is:
Math 2070: Numerical Methods in Scientific Computing I, and
Math 2071: Numerical Methods in Scientific Computing II
The sequence M2070-M2071 gives an in-depth introduction to the basic areas
of numerical analysis. The courses will cover the development and
mathematical analysis of practical algorithms
for the basic areas of numerical analysis . The course M2071 does not
assume a knowledge of M2070; and material from M2070 that is needed in
M2071 will be reviewed as necessary .
These courses also include a Computational Laboratory (Offered
every year) that complement the lectures. In addition, in M2071, an introduction
to MPI and parallel computation is taught.
- Math 2030 Iterative Methods for Linear and Nonlinear Systems.
The course gives an introduction to the iterative algorithms for solving
linear and nonlinear systems. The course will cover the development and
analysis of these
numerical algorithms, to be used in the resolution of linear and nonlinear
systems. (Offered frequently )
- Math 2090: Numerical Solution of Ordinary Differential Equations.
This course aims to give an in-depth introduction to the numerical methods
for solving ordinary differential equations. Both initial value problems
and boundary value problems are
considered. Important practical issues such as stability, stiffness, error
estimation and control will be considered for Runge-Kutta methods,
multistep methods and finite difference
methods. If time permits, numerical techniques for differential-algebraic
equations will be also presented.
(Offered frequently )
- Math 2480 : Computational Approximation Theory
This course in Computational Approximation Theory is designed for students
interested the mathematical foundations of methods for solving scientific
and engineering problems on computers.
The emphasis is on the mathematical ideas behind approximating a function
with one determined by a finite number of degrees of freedom and
applications of this , such as quadrature
(numerical integration). (Offered intermittently according to interests
of students and faculty)
- Math 2601 Advanced Scientific Computing 1,
Math 2602 Advanced Scientific Computing 2,
Math 2603 Advanced Scientific Computing 3,
Math 2604 Advanced Scientific Computing 4:
The topics of these four courses rotate according to interests and
current trends in scientific computing. Examples include: Large Eddy
Simulation and Computational Turbulence; Domain
Decomposition for PDEs; Discontinuous Galerkin methods (Offered every term)
-
Math 2960 Computational Fluid Mechanics
This course studies the mathematical analysis of finite element methods
for approximating the flow of viscous incompressible fluids. This includes
the oldest area of mathematics up to the most
modern. We pick a path through the subject allowing a penetration of the
field that is both intuitive and rigorous.
Topics include:
1. Finite Element Approximation of Scalar PDEs.
2. Vectors ,Tensors and Conservation Laws.
3. Approximating Vector Functions: Mixed Methods.
4. The Equations of Fluid Motion.
5. Equilibrium Laminar Flows.
6. Approximating Equilibrium Laminar Flows.
7. The Time Dependent NSE
8. Approximating the Time Dependent NSE
9. Turbulence.
(Offered frequently according to interests of students and faculty)
-
Math 3030 Matrix Iterative Analysis
(Offered intermittently according to interests of students and faculty)
-
Math 3035 Difference Methods
(Offered intermittently according to interests of students and faculty)
-
Math 3040 Topics in Scientific Computing: High Performance Computing
(Offered according to interests of students and faculty)
-
Math 3070 Numerical Solution of Nonlinear Equations
(Offered intermittently according to interests of students and faculty)
- Math 3071 , Numerical Solutions of Partial Differential Equations
This course is an introduction to modern numerical methods for solving
partial differential equations. It will cover both finite difference and
finite element methods. Accuracy,
stability, and efficiency of the algorithms are studied from both
theoretical and computational standpoint.
(Offered frequently )
- Math 3072: Finite Element Method
This course is an introduction to the theoretical and computational
aspects of the finite element method for the solution of boundary value
problems for partial differential equations.
Emphasis will be on linear elliptic, self-adjoint, second order problems,
although some material on fourth order problems will be presented. Topics
include: variational formulation of
boundary value problems, natural and essential boundary conditions, Lax
Milgram lemma, approximation theory, error estimates, element
construction, continuous and discontinuous
finite element methods, and solution methods for the resulting finite
element systems.
(Offered frequently )
- Math 3075 Parallel Finite Element Methods
(Offered intermittently according to interests of students and faculty)
- Math 3077 Computational Fourier Analysis & Applications
(Offered intermittently according to interests of students and faculty)
- Math 3435 Computational Waveletts and Fractal Image Analysis
(Offered intermittently according to interests of students and faculty)
- Math 3480 Spline Approximation
(Offered intermittently according to interests of students and faculty)
- Math 3910 Seminar in Scientific Computing
(Offered intermittently according to interests of students and faculty)
- Math 3965 Advanced Computational Fluid Mechanics
(Offered intermittently according to interests of students and faculty)
Last updated 11/17/2005.
U. Pittsburgh
Dept. Mathematics
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