Numerical Analysis (CS 450)
What  Value 

Class Time/Location  MWF 9:00am9:50am / 1310 DCL 
Class Webpage  http://bit.ly/cs450s14 
Web forum  Piazza 
Homework submission/grades  UIUC Moodle 
Team
What  Role  Value 

Instructor  Andreas Kloeckner  
andreask@illinois.edu  
Office  4318 Siebel  
Office Hours  Mondays and Wednesdays 10:00 am to 11:00 am (after class)  
TA  Kaushik Kalyanaraman  
kalyana1@illinois.edu  
Office  0207 Siebel  
Office Hours  Mondays 12:45 pm to 1:45 pm; Wednesdays 3:00 pm to 4:00 pm  
TA  Sweta Seethamraju  
seetham2@illinois.edu  
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.
 Resource site for the book
 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
24, 2014 · Out: March 13, 2014)  Homework set 5 (Due: April
1821, 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
1416, 2014 · Progress report due: April1621, 2014 · Out: March 18, 2014) Project starter kit Homework solutions (private, same password as slides)
Schedule
Date  Chapter  Topic 

W  Jan 22  1: Intro 
F  Jan 24  Fw/bw error, conditioning, intro floating point 
M  Jan 27  Floating point 
W  Jan 29  2: System of Linear Equations 
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 
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 
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 
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 
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 
W  Mar 19  GaussNewton, LevenbergMarquardt, Constrained opt 
F  Mar 21  7: Interpolation 
M  Mar 24  No class Spring Break 
W  Mar 26  
F  Mar 28  
M  Mar 31  7: Interpolation 
W  Apr 2  8: Numerical Integration and Differentiation 
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 
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 
M  Apr 21  Stiff problems, PredictorCorrector 
W  Apr 23  10: Boundary Value Problems for ODEs 
F  Apr 25  Intro BVPs, Existence, Uniqueness, Conditioning, Shooting Method 
M  Apr 28  11: Partial Differential Equations 
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 
W  May 14  Final exam at 1:304:30 PM 
Grading
What  Value 

Homework/Quizzes  30% 
Exam #1  20 % 
Exam #2  20 % 
Final Exam  30 % 
Probable grading scale:
Grade  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. In addition, the grading policy is set up so that you can mess up on the homework quite badly without a drastic impact on your grade. The homework is intended as a learning experience, so making mistakes is OK. [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 SciPy lectures
 The Numpy MedKit by Stéfan van der Walt
 The Numpy User Guide by Travis Oliphant
 Numpy/Scipy documentation
 More in this reddit thread
 Spyder (a Python IDE, like Matlab) is installed in the virtual machine. (Applications Menu > Development > Spyder)
 An introduction to Numpy and SciPy
 100 Numpy exercises