CS 4642: Introduction to Numerical Methods in
Computational Science and Engineering
(MATH 4640, Numerical Anlaysis I)
Fall 2009, MWF 1:05-1:55 pm, Weber SST III,
Prof. Haesun Park
Basic Information:
- Instructor:
Haesun Park,
Office: Klaus 1306, Phone:404-385-2170, e-mail: hpark@cc.gatech.edu
Office Hours: Fridays 10:00-11:00am
- TA:
TA: Mr. Yanjun Zhao, Office Hour:Mondays 2:30-3:30pm, outside 1305 Klaus,
e-mail:zhao@cc.gatech.edu
- Prerequisites:
Calculus and Linear Algebra, or Permission of the instructor.
(MATH 2403, 2413, or 2602)
- Syllabus
(updated on Aug. 17)
Lecture Notes and Announcements:
Assignments:
(all from the textbook by Mike Heath, 2nd Edition)
- August 17: read Chapter 1
- August 26: read Chapter 2:Section 2.1-2.4
- August 28: HW1 Due Sep. 11 hw1.pdf
- August 31: HW1 questions are typed up for those of you who do not have the second edition of the textbook. hw1_full.pdf
- September 13: The course web page is now moved to t-square and is not maintained at this site any more. The students who have registered for the course should check t-quare often.
Syllabus:
- Evaluation:
5 Homeworks (Written problem solving and programming in MATLAB, Fortran, C, or C++.
You may use other programming languages with the instructors permission) 55%
Exam 1, 10% (Sep. 18, Friday, in class, open books/notes)
Exam 2, 10% (Oct. 14, Wednesday, in class, open books/notes)
Exam 3, 10% (Nov. 16, Monday, in class, open books/notes)
Final Exam, 15% (Dec. 9, Wednesday, 11:30am-2:20pm, Weber SST III, open books/notes)
- Textbook:
Required text book:
Scientific Computing: An Introductory Survey, Second Edition
Michael T. Heath, 2002, ISBM 0-07-239910-4
Supplementary book (you do not need to purchase this book):
Introduction to Scientific Computing, Second Edition,
Charles F. Van Loan, Prentice Hall, 2000
- Overview:
This course introduces students to the basic numerical methods
used in many application areas in computational sciences and engineering.
Students will learn the rationale behind the methods and learn how to choose
and apply them to solve complex problems using computers. The course strives
to be reasonably broad and domain neutral, while achieving depth in some
selected key topics including linear system solvers,
systems of nonlinear equations, optimization techniques, interpolation and
approximation of functions, numerical integration and differentiation, and
numerical handling of ordinary differential equations.
-
Topics:
- Introduction:
Floating point arithmetic, source of errors
- Systems of Linear Equations:
Gaussian elimination, pivoting
Solution of Nonlinear Equations:
Bisection and secant method,
fixed-point iteration, Newton's method
Interpolation:
Lagrange Interpolation, Newton interpolation,
Chebyshev polynomials, Hermite interpolation, Splines, FFT
Numerical Differentiation and Integration:
Trapezoidal rule, Simpson's rule, Newton-Cotes quadrature, Gaussian quadrature,
adaptive quadrature, finite difference, Richardson extrapolation
Optimization:
Existence, Optimization in One Dimension, Unconstrained
and Constrained Optimality Conditions, Newton's method, Steepest Descent,
Conjugate Gradient method
Numerical Solution of Ordinary Differential Equations:
Initial value problems, systems of equations, Euler, Runge-Kutta,
boundary value problems, shooting methods, collocation method