MCEN  6228-001
 
 NUMERICAL METHODS IN ENGINEERING AND SCIENCE
 
SPRING 2007

OBJECTIVE:  The course is designed to give the understanding and working knowledge of scientific computing. The course involves a fair amount of scientific computation and programming.
TIME: 11:00-12:15 am  TR


LOCATION: ECCR 150


TEXT: Numerical Recipes: The Art of Scientific Computing, by W.H. Press, S.A. Teukolsky, W. T. Vetterling, and B.P. Flannery, 2nd Edition

The book (or online version of it) is recommended and should be used as a reference.  Lectures do not follow the book. Class notes will be most useful.


INSTRUCTOR: Dr. Oleg V. Vasilyev

Office:     Engineering Center ECME 126 
Phone:     (303) 492-4717
E-mail:    Oleg.Vasilyev@Colorado.EDU


WEB PAGE: http://multiscalemodeling.colorado.edu/classes/MCEN6228_S2007/


OFFICE HOURS:  TR 9:15-10:30 a.m. or by appointment. 


GRADING: Homework         45% 
Midterm             20%      (in class) 
Final                   35%      (in class or take home)
GUIDELINES
FOR
HOMEWORK
PREPARATION:
  • The problem should be briefly formulated (describe briefly the general method, approach, etc. used.  Be specific how solution was obtained: Did you write your own code?  Did you use IMSL routines?  What computer was used?
  • Present results in graphical form whenever possible.  When it is appropriate to include raw data (usually never!) or listing, place them in appendices.
  • Give an overview of the problem (what did you learn?).  State any conclusions reached.  Comment on unusual or unexpected behavior.  Discuss the significance (and limitations) of results and state any generalities which are evident after solving problem.
  • It would be helpful if you highlight (underline, box, circle, etc.) bottom line results. 
  • Please trim all output/listing to separate 8-1/2"-11" pages, staple (do not paper clip) pages together, and give very large or small numbers in scientific notation.
COMPUTERS 
& 
COMPUTING:		 This course involves a fair amount of scientific computation and programming.  To really understand the subject and gain a working knowledge of scientific computing, one needs to practice and experience numerical difficulties as well as the power of numerical methods.  You may use the engineering PC cluster, personal computer, or any other computer that you can get your hands on. Although you will write some programs yourself, you will also need some "canned" programs such as IMSL library.   You may also want to use MATLAB to write some programs, execute them and plot your results.  You may also use any other public-domain codes such as GAMS. The use of symbolic programs such as Maple, Mathematica, or Macsyma is highly encouraged, especially in problems requiring extensive algebraic manipulations like multi-dimensional Taylor series expansions, etc.

TOPICS: 
  1. Interpolation (general interpolation problem; Lagrange polynomials; piecewise Lagrange interpolation; splines; parametric interpolation; multidimensional interpolation).
  2. Numerical Differentiation (finite differences from interpolation; finite differences from Taylor series; matrix representation of finite difference schemes; Hermitian methods and Pade approximation).
  3. Numerical Integration (Newton-Cotes formulas; trapezoidal rule; Simpson's rule; error analysis; trapezoidal rule with end-correction; Richardson's extrapolation and Romberg integration; adaptive quadrature; Gauss quadrature; semi-infinite intervals; infinite intervals; singularities).
  4. Numerical Solutions of Ordinary Differential Equations (initial value problems; Runge-Kutta type formulas; multi-step methods; implicit methods; accuracy; stability; model equation; phase and amplitude errors; system of differential equations; stiffness; boundary value problems; shooting; direct methods; non-uniform grids; eigenvalue problems).
  5. Numerical Solution of Partial Differential Equations (Modified wave number and von Neumann stability analysis; modified equation analysis; Alternating Direction Implicit methods; approximate factorization; nonlinear equations; iterative methods for elliptic PDEs; conjugate gradient methods; multigrid method; direct methods; methods of weighted residuals; Galerkin method; finite element method).


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  Last updated 11/10/2006