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2DE11 - Numerical mathematics
Lectures
This course is taught by: dr.ir. M.J.H. [email protected].
InstructionThe instruction hours are taught by: dr. Rik [email protected].
Please note that it is required to hand in reports for all exercises. I
is not possible to finish this course by doing the written exam only
The assignments that have to be handed in should be made in
pairs. There are four assignments that have equal weights, and
make up 25% of the final grade; the final exam makes up the othe
75%.To pass the course, you need to score:
at least 50% of the points for the homework,
at least 50% of the points for the exam,
and (as usual) at least 55% in total.
Matlab
The assignments form an essential part of the course. Some of the
exercises require writing computer programs. It is advised to dothe programming in Matlab. TU/e has a nice Matlab-website. The
parts you should look at are Chapter 1: Basic elements of Matlab
and Chapter 6: Programming in Matlab.
Try to do the following exercises from the website:
Exercises 1.1-1.4, 1.6-1.16, 1.20-1.22, 1.24, 1.28, 1.30
Exercises 6.1, 6.6, 6.7
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You can also visit the website of the creators of Matlab to find a lis
of tutorials. The PDF-file by the University of Dundee offers a nicecompact reference guide.
Finally, there is also the excellent booklet MATLAB Primerby
Kermit Sigmon and Timothy A. Davis, Chapman & Hall/CRC,
London, 2002.
Contents
All topics are covered in class. You are encouraged to attend al
lectures and take notes.
You can also study the following parts of the book Scientific
Computing. An Introductory Survey, Second edition, Michael T
Heath, McGraw-Hill, New York (2002).
Chapter 1: Scientific computing1.1 Introduction
1.1.1 Computational problems
1.1.1 General strategy
1.2 Approximations in scientific computation1.2.1 Sources of approximation
1.2.2 Absolute error and relative error
1.2.3 Data error and computational error
1.2.4 Truncation error and rounding error
1.2.6 Sensitivity and conditioning
1.2.7 Stability and accuracy1.3 Computer arithmetic
1.3.1 Floating-point numbers
1.3.2 Normalization
1.3.3 Properties of floating-point systems1.3.4 Rounding
1.3.5 Machine precision
1.3.8 Floating-point arithmetic
1.3.9 Cancellation
Chapter 7: Interpolation
7.1 Interpolation7.3 Polynomial interpolation
7.3.1 Monomial basis
7.3.2 Lagrange interpolation
7.3.5 Interpolating continuous functions
Chapter 8: Numerical integration and differentiation
8.6 Numerical differentiation
8.6.1 Finite difference approximations
8.7 Richardson extrapolation
8.3 Numerical quadrature
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8.3.1 Newton-Cotes quadrature
8.3.3 Gaussian quadrature
8.3.5 Composite quadrature
Chapter 5: Nonlinear equations
5.1 Nonlinear equations
5.2 Existence and uniqueness
5.3 Sensitivity and conditioning
5.4 Convergence rates and stopping criteria
5.5 Nonlinear equations in one dimension
5.5.1 Interval bisection
5.5.2 Fixed-point iteration
5.5.3 Newton's method
Chapter 2: Systems of linear equations
2.1 Linear systems
2.2 Existence and uniqueness
2.3 Sensitivity and conditioning
2.3.1 Vector norms
2.3.2 Matrix norms
2.3.3 Matrix condition number
2.3.4 Error bounds
2.3.5 Residual
2.4 Solving linear systems2.4.1 Problem transformations
2.4.2 Triangular linear systems
2.4.3 Elimentary elimination matrices
2.4.5 Pivoting
2.4.6 Implementation of Gaussian elimination2.4.7 Complexity of solving linear systems
Chapter 9: Initial value problems for ordinary differential
equations
9.1 Ordinary differential equations
9.2 Existence, uniqueness and conditioning
9.3 Numerical solution of ODEs
9.3.1 Euler's method
9.3.2 Accuracy and stability
9.3.3 Implicit methods
9.3.4 Stiffness
If you would like to practice exercises from the book, here is a
recommended selection:
Chapter 1
Review questions: 1.1, 1.2, 1.3, 1.4, 1.8, 1.18, 1.19, 1.25
Exercises: -
Computer problems: 1.1, 1.4, 1.7, 1.14, 1.17
Chapter 7
Review questions: 7.8, 7.15
Exercises: 7.2, 7.6
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Computer problems: -
Chapter 8
Review questions: 8.12, 8.20, 8.22, 8.27, 8.40
Exercises: -
Computer problems: 8.1a
Chapter 5
Review questions: 5.2, 5.3, 5.9, 5.12
Exercises: 5.2, 5.4, 5.6
Computer problems: 5.2, 5.13, 5.14
Chapter 2
Review questions: 2.3, 2.4, 2.5, 2.11, 2.19, 2.22, 2.41, 2.44,
2.45, 2.48, 2.52, 2.53, 2.55, 2.59
Exercises: 2.2, 2.13, 2.17, 2.21, 2.26, 2.27Computer problems: 2.3, 2.6, 2.17
Chapter 9
Review questions: 9.9, 9.16, 9.19, 9.20, 9.25, 9.37
Exercises: 9.4
Computer problems: 9.1a
Please consult the course description for more information. You
can also check the general information system from the university,
OWinfo TU/e.
Old exams
During the exams you can use a pocket calculator. You may notuse the lectures notes, books or your notebook. To prepare for the
exam, please study some old exams:
25 January 2010 and the answers to the questions
27 October 2009 and the answers to the questions8 January 2009 and the answers to the questions
Last updated by Martijn Anthonissen on 14 June 2011
Centre for Analysis, Scientific Computing and Applications. For questions please refer to the editor.
This page modified: Tue Jun 14 11:31:03 CEST 2011
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