Lecturer Prof. Petros Koumoutsakos
   
Class Room HG E5 (Lecture)
HG E33.1, E33.3, E33.5, F26.3, F26.5, G26.3 (Exercise)
   
Class Times Thursdays, 13.15 – 15.00 (Lecture)
Tuesdays,  13.15 – 14.00 (Exercise)
   
Assistance
 		 1- Dr. Philippe Chatelain, CAB H83.1, pchatela_AT_inf.ethz.ch
2- Babak Hejazialhosseini, CAB F84, babak_DOT_hejazi_AT_inf.ethz.ch
3- Rajesh Ramaswamy, CAB G39.2, rajeshr_AT_inf.ethz.ch
4- Wim van Rees, CAB F84, wvanrees_AT_inf.ethz.ch
5- Roman Schaerer, romascha_AT_student.ethz.ch
6- Dr. Ding Yi, CAB F84, yi_DOT_ding_AT_mat.ethz.ch
Who is your TA?
   
Grading Homework : 25% – Final Exam : 75%
Final Exam Date: 28/05/2009, Duration: 2 hours. You will need your laptop and access to your solutions of the Homework. Only material distributed in this class (class notes, handouts, homework solutions, podcasts) is allowed during the exam. Honor Code of conduct is in effect.
 

Overview
Numerical Quadrature: Methods of numerical integration, Euler-Mac Laurin summation. Numerical Differentiation: numerical derivatives, algorithmic differentiation, Ordinary and Partial differential equations: discretization, error analysis, multistep methods, adaptive methods.

The course aims to introduce fundamental concepts for the numerical solution of ordinary and partial differential equations. Emphasis on the computer implementation of numerical methods. Exercises will reflect actual problems from science and engineering.

Material

CLASS 1 (19/02/2009) :
An introduction: The role of Computational Science in shaping Tomorrow’s World (pdf)
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CLASS 2 (26/02/2009) : 
Numerical integration (pdf)
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CLASS 3 (05/03/2009) : 
 Newton-Cotes Formulas (pdf)
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CLASS 4 (12/03/2009) : 
Gauss quadrature (pdf)
Gauss quadrature points and weights (pdf)

CLASS 5 (19/03/2009) : 
Gauss quadrature, ODEs, Initial Value Problems
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CLASS 6 (26/03/2009) : 
Numerical solution of ODEs (pdf)
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CLASS 7 (02/04/2009) : 
Numerical stability (pdf)
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CLASS 8 (09/04/2009) : 
Runge-Kutta schemes (pdf)
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CLASS 9 (23/04/2009) : 
Partial Differential Equations: the diffusion equation (pdf)
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CLASS 10 (30/04/2009) : 
von Neumann stability analysis (pdf)
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CLASS 11 (07/04/2009) : 
PDE stability analysis: modified wavenumbwers (pdf)
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CLASS 12 (14/04/2009) : 
Implicit time advancement and multi-dimensions (pdf)


Exercises
HW 1 (24/2/2009) : Interpolation 
Notes, Problem set, Solution

HW 2 (3/3/2009) : Quadrature 
Problem set, Solution

HW 3 (10/3/2009)
Problem set, Solution

HW 4 (17/3/2009)
Problem set, Solution
 
HW 5 (24/3/2009)
Problem set, Solution

HW 6 (31/3/2009)
Problem set, Solution

HW 7 (7/4/2009)
Problem set, Solution

HW 8 (21/4/2009)
Problem set, Solution

HW 9 (28/4/2009)
Problem set, Solution


HW 10 (5/5/2009)
Problem set, Solution

HW 11 (12/5/2009)
Problem set, Solution

References
Fundamentals of Numerical Analysis, P. Moin (Cambridge University Press)