CSC/MAT 320 - 3 Semester Hours

Numerical Analysis I

The use of numerical methods to solve mathematical problems such as the solutions of equations, interpolation, differentiation, and integration. Computer proficiency is gained by programming the solutions, studying algorithm efficiency, error propagation.

MAT 220 and MAT 230 and CSC 212

The subject of numerical analysis deals with computational methods to approximate, in an efficient manner, the solutions to mathematical problems that do not have a an analytic solution. Such mathematical problems occur in physical problems. As such, numerical analysis is required in the science and engineering disciplines. Numerical models are also used to solve economics problems.

Upon successful completion of this course, students will be able to:

1. Recognize types of problems and identify numerical methods that are used to solve the problems.
2. Efficiently program solutions to problems.

1. Solution of equations in one variable
   1. bisection method
   2. Newton's method
   3. fixed-point iteration
   4. error analysis
2. interpolation and polynomial approximation
   1. Taylor polynomials
   2. interpolation and the Lagrange polynomial
   3. iterated interpolation
   4. cubic spline interpolation
   5. isoparametric interpolation
3. numerical differentiation and integration
   1. adaptive quadrature methods
   2. Gaussian quadrature
4. initial-value problems for ordinary differential equations
   1. Euler's method
   2. Runge-Kutta methods
   3. multistep and variable step-size multistep methods
5. direct methods for solving linear systems
   1. Gaussian elimination and backward substitution
   2. pivoting strategies
   3. special types of matrices
6. iterative techniques in matrix algebra
   1. norms of vectors and matrices
   2. Eigenvalues and Eigenvectors
   3. iterative techniques
7. approximation theory
   1. discrete least-squares approximation
   2. Chebyshev polynomials
   3. Fast Fourier Transforms

1. lecture
2. discussion
3. homework assignments
4. programming assignments
5. examination

1. Readings from the textbook.
2. Design and implementation of programs.

1. programs
2. examinations

No additional resources are required.

R. L. Burden and J. D. Faires. Numerical Analysis (7ed). Brooks Cole, Pacific Grove, 2000.

S. C. Chapra and R. P. Canale. Numerical Methods for Engineers (4ed). McGraw-Hill Science/Engineering/Math, New York, 2001.

E. W. Cheney and D. R. Kincaid. Numerical Mathematics and Computing (4ed). Brooks Cole, Pacific Grove, 1999.

R. Hamming. Numerical Methods for Scientists and Engineers (2ed). Dover Publications, Mineola, New York, 1987.

W. H. Press (ed), S.A. Teukolsky (ed), W. T. Vetterling, and B. P. Flannery (ed). Numerical Recipes in C(++): The Art of Scientific Computing (2ed). Cambridge University Press, Cambridge, 2002.

D. Yang. C++ and Object-Oriented Numeric Computing for Scientists and Engineers. Springer Verlag, New York, 2000.