MTH361: Numerical Analysis 1
Department of Mathematics, UMass Dartmouth
Fall 2012, Larts Room 218, 8:00 - 9:15 AM
14 Week Tentative Schedule
MTH361 Syllabus
MATLAB codes created "on the fly" in class can be downloaded from
here
Please let me know if you found bugs in the codes
Interpolation
- Week 1 (Sept 6):
- Cardinal functions and polynomial basis.
- Lagrange formulation of an interpolant.
- Interpolation on equally-spaced points and Runge Phenomenon.
- MATLAB code demo in class.
- Week 2 (Sept 11 & Sept 13):
- Chebyshev points and Barycentric Lagrange interpolation formula.
- Ellipse of analyticity and Potential theory.
- Lebesque functions.
- Barycentric Lagrange interpolation weights.
- MATLAB code demo in class.
- Week 3 (Sept 18 & Sept 20):
- Chebyshev polynomials and recurrence relations.
- Chebyshev polynomial interpolant.
- Condition number of Chebyshev matrix.
- MATLAB code demo in class.
Root Finding Methods
- Week 4 (Sept 25 & Sept 27):
- Roots of polynomial interpolants
- Companion matrix
- MATLAB code demo in class.
- Week 5 (Oct 2 & Oct 4):
- Colleague matrix
- Dealing with multiple roots.
- MATLAB code demo in class.
- Week 6 (Oct 9 & Oct 11):
- Bisection and Newton's methods.
- MATLAB code demo in class.
Numerical Derivatives and Differentiation Matrices
- Week 7 (Oct 16 & Oct 18):
- Spatial derivatives with finite difference.
- Computing FD weights through Taylor expansions and Cardinal functions.
- MATLAB code demo in class.
- Week 8 (Oct 23 & Oct 25):
- Use Fornberg's way for FD weights calculation.
- Fornberg's one line Mathematica command.
- MATLAB code demo in class.
- Week 9 (Oct 30 & Nov 1):
- Assembling weights to form differentiation matrices.
- Differentiation matrix on Chebyshev points.
- MATLAB code demo in class.
Numerical Integration and Intro to Pseudospectral Methods for BVPs
- Week 10 (Nov 6 & Nov 8):
- Clenshaw-Curtis quadrature.
- Simple map to deal with interval [a,b].
- Integrating discontinuous functions with interval splitting.
- MATLAB code demo in class.
- Week 11 (Nov 13 & Nov 15):
- Solving 1D BVP on [-1.1] with Pseudospectral Methods.
- Deal with interval [a,b].
- Expose students to use MATLAB parallel computing toolbox for computing
several BVPs independently.
- Week 12 (Nov 20):
- Intro to radial basis function collocation method.
- Chebfun demo.
Error Propagation, Estimation, and Conditioning
- Week 13 (Nov 27 & Nov 29):
- Sources of errors and simple error analysis.
- rounding, chopping, and playing with Maple command called: digits.
- Week 14 (Dec 4 & Dec 6):
- Final Exam Week (Dec 12 - Dec 18):
