MAS 565 Syllabus 2017

Professor Kwak, Do Young,

Office Nat. Sci. Building 2405, Tel: 2720

Text:(ref only!) Numerical Analysis by Rainer Kress, Springer GTM series, 1998.

Schedule

week 1 Nonlinear equation- convergence, Newton's Method

week 2 Nonlinear equation-system, Jacobi G-S

week 3 piecewise linear apporx, Lagrange- Newton interpolation

week 4 Chebyshev polynomial, Cubic Spline

week 5 Gaussian quadrature

week 6 Numerical sol. of ODE

week 7 Linear Algebra-Preliminary, Gaussian Elim

week 8 Mid Term Exam

week 9 Iterative Schemes

week10  Eigenvalue problem-Givens Householder

week11  Nonsymmetric QR

week 12 Power Method, condition Number

week 13 Elliptic problem

week 14 Irregular boundary

week 15 Error analysis

week 16 Parabolic problem-Final Exam

References.

Burden, R. and J.Douglas Faires, Numerical Analysis 6th ed, Brooks/Cole 1997

Ueberhuber, Christoph. Numerical Computation 1, 2. New York, Springer 1997(Graduate)

Greenbaum, A. Iterative Methods for Solving linear systems, SIAM 1997(graduate level)

Stewart, G. W. Matrix Algorithm Vol II, Basic Eigensystem SIAM 2001.

Numerical Analysis in Modern Scientific Computing (P. Deuflhard/Hohman)

Other references:

Braess, Dietrich. Finite elements. Theory, fast solvers, and applications in solid mechanics  Cambridge University Press, Cambridge, 1997

Brenner, S. and C.; Scott, L. R. The mathematical theory of finite element methods

Texts in Applied Mathematics, 15. Springer-Verlag, New York, 1994

Ciarlet, Philippe G. The finite element method for elliptic problems. N-H. 1978

Golub, Gene H.; Van Loan, Charles F. Matrix computations, Johns Hopkins University Press, Baltimore, MD, 1996

Johnson, Claes. Numerical solution of partial differential equations by the finite element method, Cambridge University Press, Cambridge-New York, 1987

Lambert, J. D. Computational methods in ordinary differential equations

Introductory Mathematics for Scientists and Engineers. John Wiley & Sons, London-New York-Sydney, 1973

Stoer, Josef; Bulirsch, Roland. Introduction to numerical analysis

Second edition. Texts in Applied Mathematics, 12. Springer-Verlag, New York, 1993

Young, David. Iterative Solution of Large Linear Systems

Academic Press, London, 1971

2: Scientific Computing with Ordinary Differential Equations

(Deuflhard/Bornemann)

3: Adaptive Numerical Solution of Partial Differential Equations

(Deuflhard/Weiser, presently translated)

Wilkinson, J.H. The algebraic eigenvalue Problem(Classic reference on eigenvalue problem)

Wilkinson, J.H. and C. Reinsch 1971 Handbook of Automatic Computation. II Springer.

Softwares:

Go to the site and download C++(Visual_Studio)   http://circnts.kaist.ac.kr/

http://www.physics.drexel.edu/courses/Comp_Phys/General/C_basics/

http://www.cprogramming.com/tutorial.html

Or use freeware available from

1 Visual C++  Express  http://www.visualstudio.com/downloads

2 Turbo C++ 3.0

3 http://gcc.gnu.org/

4. http://www.brothersoft.com/dev-c++-download-65296.html

See for general software packages:

http://www.netlib.org

LINPACK, LAPACK, EISPACK, IMSL, MATLAB, MAPLE, MATHEMATICA, CEMTOOL(Korean)