Numerical Analysis (CS 450)
Class Time/Location 
MWF 9:00am9:50am / 1310 DCL 
Class Webpage 

Web forum 

Homework submission/grades 
Contents
Team

Instructor 

Office 
4318 Siebel 

Office Hours 
Mondays and Wednesdays 10:00 am to 11:00 am (after class) 


TA 
Kaushik Kalyanaraman 
Office 
0207 Siebel 

Office Hours 
Mondays 12:45 pm to 1:45 pm; Wednesdays 3:00 pm to 4:00 pm 


TA 
Sweta Seethamraju 
Office 
0207 Siebel 

Office Hours 
Mondays and Tuesdays 2:00 pm to 3:00 pm 
Textbook/Material
Scientific Computing: An Introductory Survey by Michael T. Heath. Second Edition. Published by McGrawHill.
Jonathan Richard Shewchuk. An Introduction to the Conjugate Gradient Method Without the Agonizing Pain, August 1994.
Updates/Calendar
 January 22, 2014 (Wedensday)
 Class starts at 9am. See you then, bright and early!
Class Material
Notes (Chapter 4end, public, uploaded after each class)
Full Slides (Chapter 112, public, from book resource site)
Class Slides (Chapter 14. Passwordprotected because of the use of copyrighted slides by Heath, user name and password will be/were announced in class on Jan 24.)
Code (public)
Worksheets (public)
Worksheet solutions (private, same password as slides)
Practice exam for midterm 1 (private, same password as slides)
Study guide for the final (private, same password as slides)
Class recordings (no promises about quality or usability)
Homework
Homework set 1 (Due: February 12, 2014 · Out: January 29, 2014)
Homework set 2 (Due: February 26, 2014 · Out: February 13, 2014) Data file 'Price_of_Gasoline.txt'
Homework set 3 (Due: March 12, 2014 · Out: February 27, 2014)
Homework set 4 (Due: April 2 4, 2014 · Out: March 13, 2014)
Homework set 5 (Due: April 18 21, 2014 · Out: April 6, 2014)
Homework set 6 (Due: May 7, 2014 · Out: April 24, 2014)
Project for 4 credit hours (Grad students only · Due: May 14 16, 2014 · Progress report due: April 16 21, 2014 · Out: March 18, 2014) Project starter kit
Homework solutions (private, same password as slides)
Schedule
Date 
Chapter 
Topic 

W 
Jan 22 
1: Intro 
Introduction, fw/bw error 
F 
Jan 24 
Fw/bw error, conditioning, intro floating point 

M 
Jan 27 
Floating point 

W 
Jan 29 
2: System of Linear Equations 
Cancellation, Intro LA 
F 
Jan 31 
LA conditioning, Intro Gaussian el. 

M 
Feb 3 
Gaussian el, preconditioning, pivoting 

W 
Feb 5 
LA cost, ShermanMorrison 

F 
Feb 7 
3: Linear least squares 
BLAS, Intro least squares 
M 
Feb 10 
Normal equations 

W 
Feb 12 
QR, QR via GramSchmidt 

F 
Feb 14 
Householder, Givens, Rankdeficiency 

M 
Feb 17 
4: Eigenvalues and singular values 
SVD, Intro eigenvalues, Sensitivity 
W 
Feb 19 
Transforms, Schur form, Power iteration 

F 
Feb 21 
Rayleigh quotient it, Intro QR it. 

M 
Feb 24 
QR iteration 

W 
Feb 26 
5: Nonlinear equations 
Krylov space methods, Intro root finding 
F 
Feb 28 
Contractive mappings, convergence rates, sensitivity of root finding 

M 
Mar 3 
Stopping criteria, Bisection, Fixed point iteration, Newton 

W 
Mar 5 
Exam 1 Chapters 14, inclass. 

F 
Mar 7 
6: Optimization 
Secant method, Newton and Secantupdating methods in nD, Intro Optimization 
M 
Mar 10 
Existence/uniqueness of minimizers, sensitivity of opt. 

W 
Mar 12 
Discussion of exam 1, Golden Section Search, Newton for Optimization 

F 
Mar 14 
No class Engineering Open House 

M 
Mar 17 
6: Optimiziation 
Steepest descent, Newton, NelderMead 
W 
Mar 19 
GaussNewton, LevenbergMarquardt, Constrained opt 

F 
Mar 21 
7: Interpolation 
Constrained opt, Intro Interpolation 
M 
Mar 24 
No class Spring Break 

W 
Mar 26 

F 
Mar 28 

M 
Mar 31 
7: Interpolation 
Lagrange basis, Orthogonal polynomials 
W 
Apr 2 
8: Numerical Integration and Differentiation 
Interp. error, Piecewise interp., Intro Quadrature 
F 
Apr 4 
NewtonCotes, accuracy and stability of quadrature 

M 
Apr 7 
Composite and Gaussian quadrature 

W 
Apr 9 
9: Initial Value Problems for ODEs 
Numerical differentiation, Richardson extrapolation, Intro IVPs 
F 
Apr 11 
IVP terminology, stability, examples 

M 
Apr 14 
Euler's method, accuracy, stability 

W 
Apr 16 
Exam 2 Chapters 58, inclass. 

F 
Apr 18 
9: Initial Value Problems for ODEs 
Exam 2 discussion, implicit methods, backward Euler 
M 
Apr 21 
Stiff problems, PredictorCorrector 

W 
Apr 23 
10: Boundary Value Problems for ODEs 
RungeKutta, Stability regions 
F 
Apr 25 
Intro BVPs, Existence, Uniqueness, Conditioning, Shooting Method 

M 
Apr 28 
11: Partial Differential Equations 
Shooting, Sparse Matrices, Finite Difference Method, Intro FEM 
W 
Apr 30 
FEM/Galerkin, sparse linear algebra 

F 
May 2 
Stationary methods, Jacobi, GaussSeidel, SOR, Conjugate Gradients 

M 
May 5 
PDEs: consistency, stability, time integration 

W 
May 7 
Review 
(see study guide posted above) 
W 
May 14 
Final exam at 1:304:30 PM 
Grading
Homework/Quizzes 
30% 
Exam #1 
20 % 
Exam #2 
20 % 
Final Exam 
30 % 
Probable grading scale:

graduate 
undergraduate 
A 
[90, 100) 
[85, 100) 
B 
[80, 90) 
[72, 85) 
C 
[70, 80) 
[60, 72) 
D 
[60, 70) 
[50, 60) 
Late Work policy: Work submitted after the deadline will count for half of its original worth. This offer is good for up to one week after the original deadline. After that, no late work will be accepted.
[Added to clarify on 2/13] You get exactly one submission per homework set. In particular, this means that:
 No regrading of work already graded. If, between the posted solution and your graded work, you still have questions, feel free to raise those on Piazza or during the TA's office hours.
 We do not accept partial submissions unless you have a very good reason. (e.g. we won't let you submit problem 1 and 2 before and 3,4,5 after the deadline.) If you modify your submission after the deadline but before it's graded, your entire submission will be counted as late.
[End addition]
Makeup exam policy: Makeup exams must be requested at least one week before the original or makeup date, whichever is sooner.
Taking the class for 4 credits: Grad students may take CS450 for four credit hours. To this end, an individual project will be assigned around the beginning of March. An initial draft of the report on the project will be due on April 16. The final version of the report (along with all further deliverables, such as code) is due on the day of the final, May 14. The project will count as an extra homework set with double weight.
 Please let me (Andreas) know as soon as you can if you need special accommodations (extra time etc.) on exams. Thanks!
Computing
We will be using Python with the libraries numpy, scipy and matplotlib for inclass work and assignments. No other languages are permitted. Python has a very gentle learning curve, so you should feel at home even if you've never done any work in Python.
Virtual Machine Image
See ComputeVirtualMachineImages to obtain a virtual machine image that you can use to follow the computational exercises in the class and do your homework.
Previous editions of this class
Python Help
Numpy Help
The Numpy MedKit by Stéfan van der Walt
The Numpy User Guide by Travis Oliphant
Spyder (a Python IDE, like Matlab) is installed in the virtual machine. (Applications Menu > Development > Spyder)