Announcements
05/06/19 Solution set to the final posted on Canvas. For scores on Final and Course, see below.
Quick Links
Course Information
Text:
An Introduction to Numerical Analysis by K.E. Atkinson, John Wiley & Sons, 2nd ed., 1989, ISBN 9780471624899
Good reading: (first three titles available online through CU Library)
Numerical Linear Algebra by L.N. Trefethen and D. Bau, III, SIAM 1997, ISBN 0898713617
A First Course in the Numerical Analysis of Differential Equations by A. Iserles, Cambridge Univ. Press, 1996, ISBN 0 521 55655 4
A Primer on Radial Basis Functions with Applications to the Geosciences, by B. Fornberg and N. Flyer, SIAM, 2015, ISBN 9781611974027 (especially Chapter 1) Bibliography
Numerical Solution of Partial Differential Equations by K.W. Morton and D.F. Mayers, Cambridge Univ. Press, 1994, ISBN 0 521 42922 6
Lecture Times and Location
Instructor  Room Number  Time 

Bengt Fornberg  ECCR 135  MW 3:00 to 4:15 pm 
Office Hours
Instructor/TA  Room Number  Office Hours 

Bengt Fornberg  ECOT 214  TBA 
Homeworks
HW_01 Due 01/23/19
HW_02 Due 01/30/19
HW_03 Due 02/06/19
HW_04 Due 02/13/19 File with Matlab code for Problem 3 Background to Problem 4 will be given in class next Monday, or can be found in Lecture Notes Overdetermined linear systems
HW_05 Due 02/20/19 Please disregard Problem 2, since this accidentally got duplicated from Homework 4. File with Matlab code for Problem 4
HW_06 Due 02/27/19
HW_07 Due 03/18/19
HW_08 Due 04/03/19
HW_09 Due 04/10/19
HW_10 Due 04/17/19
Final Exam and Course overall
These links show histograms over scores for Final and for Course total. The socre for course total was calculated as follows: The two lowest homework scroes were discarded. Then, homework average, the two midterms, and the final (all scored up to 100 pionts) were multiplied by 0.15, 0.20, 0.20, 0.45, and then added together. The following grade cutoffs were then applied: A 80, A 75, B+ 70, B 65, B 60, C+ 55, C 50.
Lecture notes
 Reducible vs. Irreducible matrices
 Illconditioning of Hilbert matrix when solving linear systems
 Schur's theorem
 Key theorem for normal matrices
 Aitken extrapolation
 Double shift QR method
 Sturm sequence for eigenvalues
 Calculation of eigenvectors
 Rotation matrices
 Proof that the SVD dexomposition exists
 Example of SVD used for image compression
 Overdetermined linear systems
 FD weights (pages 16 from the book "A Primer on Radial Basis Functions with Applications to the Geosciences")
 Padé approximations
 Linear recursion relations
 Lehmer's method for testing the root condition
 Stability domains for some ODE solvers
 BDF formulas
 Taylor method for solving ODEs
 Derivation of RungeKutta methods
 Collection of explicit RK methods
 Reduce linear ODE BVP to two IVP
 Newton's method for 2point BVP
 Energy estimates
 Forward Euler for heat equation  stability condition
 Lax equivalence theorem
 Higher order FD for first derivative
 Instability examples
 Nonlinear instability example
 LaxWendroff for conservation laws
 Box scheme
 Benefits of high order accurate approximations
 ADI  Alternating Direction Implicit
 Compact stencils, Part 1
 Compact stencils, Part 2
 Reverse CuthillMcKee
 Matlab codes for some Fast Poisson Solvers

Radial Basis Function (RBF) presentation (given 2016 at Air Force Inst. of Technology)