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AER336: SCIENTIFIC COMPUTING (Winter 2014)
Instructor: Professor C. P. T. Groth
University of TorontoInstitute for Aerospace Studies (UTIAS)
Phone: 416{667{7715
E-mail: [email protected]
Course Description
This course provides a rst introduction to numerical methods for
scientic computation whichare relevant to engineering problems.
Topics addressed include interpolation, integration, linearsystems,
least-squares tting, nonlinear equations and optimization, initial
value problems, partialdierential equations, and relaxation
methods. The tutorials and assignments make extensive useof MATLAB.
Assignments also require knowledge of FORTRAN, C, or C++.
Textbook: Introduction to Scientic Computing (recommended)by C.
F. Van Loan2nd Edition, Prentice-Hall, 2000
Lectures: Tuesdays, 9-11 am, GB 119Thursdays, 4-6 pm, BA
1240
Tutorials: Tuesdays & Thursdays, GB 119 & BA
1240Teaching Assistant: Jenmy Zhang, Phone: (416) 667-7701,E-mail:
[email protected]
Assignments: Assignment #1, Due: January 23, 2014.Assignment #2,
Due: February 6, 2014.Assignment #3, Due: February 25,
2014.Assignment #4, Due: March 11, 2014.Assignment #5, Due: March
25, 2014.Assignment #6, Due: April 8, 2014.
Marks: 2.0% for ve mini assignments18.0% for the six assignments
(listed above)15.0% for term test #1, Date: March 4, 201415.0% for
term test #2, Date: April 1, 201450.0% for nal exam, Date: April,
2014.
All tests and exams are type X (\open book") andpermit use of
type 1 calculators.
Web Site: See University of Toronto Portal Site:
https://portal.utoronto.ca
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Outline
1. Introduction
{ Information and Outline
{ What is Scientic Computing?
{ Learning to Use MATLAB
2. Polynomial Interpolation
{ Global Polynomial Interpolation
Vandermonde Approach Lagrange Polynomials
{ Piecewise Polynomial Interpolation
Linear, Quadratic, and Cubic Splines3. Numerical Integration
{ Newton-Cotes Rules
Trapezoidal Method Simpson's Method
{ Composite Rules and Adaptive Quadrature
{ Spline Quadrature
{ Gauss Quadrature
4. Linear Systems of Equations
{ LU Decomposition
Pivoting Thomas Algorithm for Tridiagonal Systems
{ Iterative Methods
Jacobi and Gauss-Seidel Methods5. Least Squares Fitting
{ Linear Regression
{ Normal Equations
{ QR Factorization
6. Nonlinear Equations and Optimization
{ Roots of Scalar Nonlinear Equations
Bisection Method
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Newton's Method Secant Method
{ Systems of Nonlinear Equations
{ Minimizing Univariate Functions
Golden Section Search Newton's Method
{ Minimizing Multivariate Functions
Method of Steepest Descent Newton's Method
7. Numerical Dierentiation
{ Finite-Dierence Methods
Forward, Backward, and Central Dierence Methods{ Taylor
Tables
8. Numerical Solution of Ordinary Dierential Equations
{ Initial and Boundary Value Problems
{ Systems of ODEs and Higher-Order ODEs
{ Time Marching Methods
Linear Multistep Methods (LMMs) Explicit and Implicit Euler
Methods Trapezoidal Method Adams-Bashforth and Adams-Moulton
Methods
Predictor-Corrector Methods Heun's (MacCormack's) Method
Burstein Method
Runge-Kutta Methods9. Numerical Solution of Partial Dierential
Equations
{ Model Equations
Linear Convection (Advection) Equation Linear Diusion
Equation
{ Semi-Discrete Approach and Reduction of PDEs to ODEs
10. Numerical Analysis of Time Marching Methods
{ Representative Linear First-Order ODE
Analytic Solution{ Ordinary Dierence Equations
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Converting Time Marching Methods to Ordinary Dierence Equations
Solution of Ordinary Dierence Equations
{ Accuracy and Stability of Time Marching Methods
11. Relaxation Methods
{ Classical Relaxation Methods
Point-Jacobi Gauss-Seidel Successive Overrelaxation (SOR)
{ Ordinary Dierence Equation Approach to Classical Relaxation
Methods
References
Textbook: Introduction to Scientic Computing, 2nd Edition, by C.
F. Van Loan, Prentice-Hall, 2000.
Useful Reference: Fundamentals of Computational Fluid Dynamics,
by H. Lomax, T. H.Pulliam, and D. W. Zingg, Springer, 2001.
Analysis of Numerical Methods, by E. Isaacson and H. B. Keller,
Dover, 1966. Numerical Methods for Scientists and Engineers, by R.
W. Hamming, Dover, 1973. An Introduction to Numerical Computations,
by S. Yakowitz and F. Szidarovszky, MacmillanPublishing, 1989.
Numerical Methods for Engineers and Scientists, by J. D. Homan,
McGraw-Hill, 1992. Numerical Recipes in FORTRAN, The Art of
Scientic Computing, Second Edition, W. H.Press, S. A Teukolsky, W.
T. Vetterling, and B. P. Flannery, Cambridge University
Press,1992.
Scientic Computing and Dierential Equations, by G. H. Golub and
J. M. Ortega, AcademicPress, 1992.
Numerical Methods for Engineers, by B. M. Ayyub, Prentice Hall,
1996. Numerical Methods for Engineers, With Programming and
Software Applications, by S. C.Chapra and R. P. Canale,
McGraw-Hill, 1998.
Numerical Methods, Second Edition, by J. D. Faires and R. L.
Burden, Brooks/Cole Publish-ing, 1998.
Numerical Analysis, 7th Edition, by R. L. Burden and J. D.
Faires, Brooks/Cole Publishing,2000.
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