CASA - 2DE11 - Numerical Mathematics

7/28/2019 CASA - 2DE11 - Numerical Mathematics

1/4

Home Education Courses 2DE11 search

Home About us Research Education Vacancies Meetings Newsletter

Topics

Courses

2DE11

Numerical mathematics

Studiewijzer

Doelen, tijdsbesteding,

leerstof etc.

Relevant links

Matlab-website

OWInfo TU/e

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


2/4

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


3/4

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


4/4

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

CASA - 2DE11 - Numerical Mathematics

Documents

Transcript of CASA - 2DE11 - Numerical Mathematics