Numerical Analysis 2

News.

• 04/16:  Score histogram for MT 2 posted. Average score: 71.4.
• 05/06:  Problem and solution sets for the final posted.
• 05/07:  Score histograms for final and course total posted. Average scores: 65.4 and 74.3 resp. 
• 05/08:  Final Course Grades have been posted on the CU online system.

Instructor

Bengt Fornberg    ECOT 214    fornberg@colorado.edu   

Grading assistants:  Mike Ostroski and Nate Monnig.

Lectures

MWF  9:00-9:50 am,  ECCR 1B51

Office hours

M  10:30-11:30 am, W  10:00-10:50 am, and  F 11-11.50 am.

Important Information.

• Course syllabus
• Homework Assignments (Typically posted each Wednesday, and due the following Wednesday)

Textbook.

Required textbook:   Atkinson, An Introduction to Numerical Analysis 

Select Lecture Notes.

• Gaussian elimination  
• Linear recursion relations  
• Backwards error analysis  
• Reducible vs. irreducible matrices
• Rotation matrices, and Jacobi's method
• Sturm sequence method for eigenvalues of symmetric tridiagonal matrices
• Double shift method for QR algorithm  
• Methods to calculate eigenvectors   Inverse iteration and Newtin's method
• SVD  Matrix factorizations, with focus on SVD (singular value decomposition)
  
• Lagrange's multipliers  Example of fundamental subspaces of a matrix
• Taylor series method for ODEs  Brief summary, also on the Padé enhancement of the method
• Finite difference method  (Scholarpedia article) More extensive version  (Draft for a future book chapter)
• Lehmer's method  Exact test of the root condition for a linear multistep method
• Derivation of RK-methods 
• GBS method  Illustration of its stability domains
• Instability examples  Notes on instability types for FD approximations (From "A Practical Guide to Pseudospectral Methods")
• Examples of energy estimates  Quick illustrations of some energy estimates (not required to know for class)
• Pseudospectral Methods:  Periodic case   and  Non-periodic case    
• Radial Basis Functions  A recent survey-style article on their use for large-scale geoscience calculations
• Conjugate gradients  Illustration of its application to a small 3x3 test problem

Course Total; Scores.

The final course score has been calculated in the same way as for APPM 5600 last semester, i.e. the final Course Total score is calculated as Homeworks 30%, each (of two) Midterms 15% and Final Exam 40%. For the homeworks, the two lowest scores have been disregarded. This led to the score distribution shown in this histogram. The grade 'ctuoffs' and, in parenthesis, the total number of each grade assigned, were as follows:

A  79 (14),  A- 75 (3),  B+ 70 (7),  B  60 (6),  B- (2).

Policies.

Official CU policy information:

• Honor Code
• Disability services
• Accommodations for religious observances
• Expectations of classroom behavior
• Discrimination and Harassment Policy