CSc 2262 Numerical Methods
Fall 2004
Schedule: TTh 9:10-10:30 am Room:
Prescott 114
Instructor: Donald H. Kraft Office: 286 Coates Phone: 578-2253
Office Hours: TTh 10:30am-Noon Email: kraft@bit.csc.lsu.edu
Web: http://www.csc.lsu.edu/~kraft
Text: Atkinson and Han, Elementary
Numerical Analysis, 3rd edition, John Wiley & Sons, Inc.,
2004
References:
Leader,
Numerical Analysis and Scientific Computing, Pearson, 2004
Schilling and Harris, Applied Numerical Methods
for Engineering Using Matlab and C, Brooks/Cole, 2000
Chapra, Applied Numerical Methods with Matlab for
Engineer and Scientists, Addison-Wesley, 2005
Chapra
and Canale, Numerical Methods for Engineers with Software and
Programming Applications, 4th
edition,
McGraw-Hill, 2002
Heath, Scientific Computing An Introductory Survey,
2nd edition, McGraw-Hill, 2002
Mathews and Fink, Numerical Methods Using Matlab,
4th edition, Pearson Prentice Hall, 2004
Numerical
Recipes in C: The Art of Scientific Computing, Cambridge University
Press,
http://www.library.cornell.edu/nr/bookcpdf.html
In
addition, there are journals with articles of interest, including the ACM Transactions on Mathematical Software. Also, check out http://www.math.jct.ac.il/~naiman/nm/
http://www.ma.utexas.edu/CNA/NA/sample.html
http://mathews.ecs.fullerton.edu/n2003/
http://www.cs.nyu.edu/courses/fall03/G22.2420-001/
http://www.rpi.edu/~lvovy/Fall2003/node7.html
Abstract: The course will cover computer-oriented methods for
solving numerical problems in science and engineering, including finding roots
(including iterative solutions such as Newton’s method), interpolation and
approximation (including curve fitting), numerical integration and
differentiation (including Simpson’s rule), solving linear equations (including
linear algebra), solving differential equations (including Euler’s method),
and, possibly, optimization and simulation.
There will be a bit of numerical analysis, i.e., the mathematics and
theory behind the numerical methods (including floating point arithmetic,
errors, stability, convergence, Taylor‘s series, explicit and implicit methods,
and possibly, finite differences), plus a short discussion of history leading
to the current interest in scientific computing.
Prerequisites: Math 1552; CSc
1251 or CSc 1351 or CSc 2290
Grading:
|
Midterm Exam Final Exam Homework Class Participation |
35% 35% 25% 5% |
No
late work will be accepted. Make-up exams will not be given. Exceptional
cases, such as illness or accidents, will be handled on an individual basis
(instructor must be notified prior to the due dates or tests of the problem and
proof presented - otherwise a score of zero will be given). Students will have one
week from the date an assignment or homework or test is returned to
seek corrections on the grading. After that time, no changes will be
made to scores. All assignments will be due on a specific date and must conform
to the usual programming guidelines discussed in previous CSc courses (e.g.,
proper header, inline documentation, structured/disciplined programming). All
cases of plagiarism or excessive collaboration on assignments or tests will be
treated as academic dishonesty.
The homework will be assigned
from time to time. The source code
listing and output are due at the beginning of the class period on the due date
noted on the assignment. With the
exception of one or more assignments in Matlab, the programs can be done in the
C programming language (you must obtain prior permission of the instructor for
use of other programming languages).
Topics to be covered include*ö:
I.
Introduction Aug 24-Sept 7
A. History
– Mathematics, Scientific Computing
B. Mathematical
Foundations
1.
Data Representation and Conversion Text, Appendix E
2.
Floating Point Numbers Text, Chap. 2
3.
Rounding and Chopping Text, Chap. 2
4.
Errors – Sources, Noise, Propagation,
Uncertainty Text, Chap
2
5.
*Summation Text, Chap. 2
6.
Mean Value Theorems Text,
Appendix A
7.
*Formulae
– Algebra, Geometry, Trig,
Calculus Text, Appendix B
8.
Taylor Series Text, Chap. 1
9.
*Commercial Packages Text, Appendix C
http://www.netlib.org, http://www.aptech.com, http://www.mathwizards.com
http://www.mathsoft.com, http://www.omatrix.com, http://www.vni.com/products/wave
http://rlab.sourceforge.net,
http://www.geo.fmi.fi/prog/tela.html
http://www.mathware.com, http://www.scientek.com/macsyma/mxmain.htm
http://www.scg.uwaterloo.ca,
http://www.wolfram.com, http://www.mupad.de
http://www.uni-koeln.de/REDUCE
öhttp://www.octave.org öhttp://www.scilab.org
10.
Matlab Text, Appendix D
http://www.csc.lsu.edu/~kraft/courses/csc2262.matlab.html
http://www.rpi.edu/~lvovy/Fall2003/node2.html
http://www.cyclismo.org/tutorial/matlab/
http://ise.stanford.edu/Matlab/matlab-primer.pdf
http://www4.ncsu.edu/unity/users/p/pfackler/www/MPRIMER.htm
http://www.math.mtu.edu/~msgocken/intro/intro.html
II. Roots Text, Chap. 3 Sept 9-21
A. Bisection
(Bracketing)
http://math.fullerton.edu/mathews/n2003/Web/BisectionMod/BisectionMod.html
B. *False
Positioning
C. Newton’s
Method (Newton-Raphson)
D. *Bairstow’s
Method
E. Secant
Method
F. Fixed
Point Iteration
G. *Ill-Behaved
Functions
H. *Multiple
Roots
III. Interpolation and Approximation Text,
Chap. 4 Sept
23-Oct Oct 12
http://www.ce.ufl.edu/~kgurl/Classes/Lect3421/NM5_curve_s02.pdf
A. Polynomial
Interpolation
(Lagrangian Polynomials,
Piecewise Linear Interpolation)
B. Fourier
Approximation
C. Spline
Function Interpolation
D. *Best
Approximation (Minimax)
E. Chebyshev
Polynomials
F. *Near-Minimax
Approximation
G. Least-Squares
Approximation
H. *Approximating
Trigonometric Functions (Curve Fitting)
Midterm Exam Oct 14
IV.
Numerical Integration and Differentiation Text,
Chap. 5 Oct
19-Oct 28
A. Trapezoid
Rule - Integration
B. Simpson
Rule - Integration
C. Gaussian
Integration (Gauss-Jordan)
D. *Newton-Cotes
and Romberge Integration
E. Differentiation
V.
Linear Equations Text, Chap. 6 Nov 2-11
A. Systems
of Linear Equations
B. Matrix
Arithmetic
C. Gaussian
Elimination (Gauss-Seidel)
D. LU
Factorization (Decomposition, Matrix Inversion)
E. Iteration
Methods
F. *Least
Squares Data Fitting Text, Chap. 7
G. *Eigenvalue
Problems Text, Chap. 7
H. *Nonlinear
Systems Text, Chap. 7
I.
Newton’s Method
J.
General Newton Method
K. Modified
Newton Method
VI. Ordinary Differential
Equations (ODE) Text,
Chap. 8 Nov
16-23
A. General
Theory of Differential Equations
B. Euler’s
Method
C. Stability
and Implicit Methods
D. Taylor
and Runge-Kutta Methods
E. Multistep
Methods
F. Systems
of Differential Equations
G. *Finite
Difference Method – Two Point Boundary Value Problems
VII. *Partial Differential
Equations (PDE) Text,
Chap. 9 Nov
30-Dec 2
A. Poisson
Equation
B. One-Dimensional
Heat Problem – Discretization
C. One-Dimensional
Wave Equation
VIII. *Optimization
A. One-Dimensional
B. Multidimensional
C. Constrained
Optimization
D. Monte
Carlo Simulation
IX. *Applications Dec 2
Notes: See http://www.csc.lsu.edu/~kraft/courses/csc2262.notes1.html
and http://www.csc.lsu.edu/~kraft/courses/csc2262.notes2.html
*
The asterisk implies optional material as time permits.
öThis symbol implies
free software at the website.