2009 Fall MATH 224-01
Bulletin Course Description Structured scientific programming in C/C++ and FORTRAN. Floating point arithmetic and interactive graphics for data visualization. Numerical linear algebra, direct and iterative methods for solving linear systems, matrix factorizations, least squares problems and eigenvalue problems. Iterative methods for nonlinear equations and nonlinear systems, Newton's method. Instructor: Staff
(Instructor named in bulletin description above may not be current. For current instructor, see listing below.)
Title SCIENTIFIC COMPUTING Department MATH Course Number 2009 Fall 224 Section Number 01 Primary Instructor Liu,Jian-Guo Prerequisites Prerequisite: Mathematics 103 and 104.
Prerequisites
Mathematics 103 (multivariable calculus) and Mathematics 104 (linear algebra) or equivalents are needed for the mathematical background. Basic experience in programming in C/C++ or FORTRAN is also necessary (at the level of CPS 006 or higher).
Synopsis of course content
An introduction to programming for scientific applications.
Math 224 focuses on efficient computational approaches to solve problems from linear algebra and nonlinear systems.
Topics include solution of linear systems through direct and iterative methods, matrix factorizations and approximations, least square problems,
eigenproblems, nonlinear equations and optimization, interpolation, numerical integration and differentiation, initial value problems for ODEs.
Mathematical background is used to develop stable, reliable, accurate, and efficient numerical algorithms to be implemented in scientific programming language.
Prerequisites:
Mathematics 103 (multivariable calculus) and Mathematics 104 (linear algebra) or equivalents are needed for the mathematical background.
Basic experience in programming in C/C++ or FORTRAN or MATLAB is also necessary (at the level of CPS 006 or higher).
Textbooks
Scientific Computing, An Introductory Survey, 2nd edition, by Michael T. Heath
Other books:
Numerical linear algebra, L.N. Trefethen and D. Bau
Matrix computations, G.H. Golub and C.F. Van Loan
Numerical recipes, by Press et al.
Numerical mathematics, Quarteroni, Sacco, and Saleri
Assignments
Weekly problem sets will include theory, analysis and computational projects.
A written solution and hardcopy of every code, input or output must be submitted for each problem.
An electronic copy of our code must also be submitted to me via e-mail, in a unique zip or tar/gzip file.
Requests for extensions on homework should be done before the due data; unexcused late assignments will be penalized.
You are encouraged to discuss the homework problems with your classmates, but your final submission must be entirely your own independent work
(see the Duke Community Standard).
Exams
Two exams.
Grade to be based on
Weekly assignments and exams.
Additional Information
Students from all areas of science, engineering, economics
and quantitative studies that need advanced level skills in solving larger scale problems are encouraged to enroll.
Math 225 (Spring) continues this material and focuses on problems for integrals and differential equations.
Programming language: C/C++, Matlab; symbolic algebra: Maple; document preparation: LaTeX
