Solved Problems in Numerical Methods for Students of Electronics and Information Technology

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  • Producent: Oficyna Wydawnicza Politechniki Warszawskiej
  • Autor: Roman Z. Morawski, Andrzej Miękina
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Solved Problems in Numerical Methods for Students of Electronics and Information Technology

rok wydania: 2021
ISBN 978-83-8156-142-6
ilość stron: 208
format: A4
oprawa: miękka

 

Opis
A collection of solved problems in numerical methods, presented in this textbook, is the result of the authors' experience of teaching the undergraduate students of the Faculty of Electronics and Information Technology at Warsaw University of Technology in the period 1985–2020, and in particular – the students following the English-medium programmes of study offered there during last 25 years. It is assumed to be a complementary teaching material with respect to the lecture notes, distributed among the students at the beginning of each semester. It may be useful for students attending any engineering-oriented course of numerical methods.

 

Table od contents
Preface / 7
Notation / 10

1. Accuracy of computation / 11
1.1. Propagation of data errors / 11
1.2. Propagation of rounding errors / 22
1.3. Propagation of data errors and rounding errors / 34
1.4. Engineering applications / 37

2. Solving linear algebraic equations / 46
2.1. Matrix factorisation / 46
2.2. Non-iterative algorithms / 52
2.3. Iterative algorithms / 62

3. Approximation / 66
3.1. Interpolation / 66
3.2. Least-squares approximation / 73
3.3. Other types of approximation / 87
3.4. Engineering applications / 90

4. Solving nonlinear algebraic equations / 93
4.1. Preliminary exercises / 93
4.2. Single-point iterative algorithms / 95
4.3. Multiple-point iterative algorithms / 111
4.4. Accuracy of numerical solutions / 115
4.5. Engineering applications / 121

5. Numerical differentiation / 123
5.1. Accuracy / 123
5.2. Design of differentiation formulae / 130
5.3. Optimisation of differentiation step / 135
5.4. Engineering applications / 138

6. Numerical integration / 140
6.1. Preliminary exercises / 140
6.2. Quadrature-based methods / 144
6.3. Monte-Carlo methods / 160
6.4. Engineering applications / 163

7. Solving ordinary differential equations / 165
7.1. Preliminary exercises / 165
7.2. Single-step methods / 168
7.3. Multi-step methods / 186
7.4. Engineering applications / 198

Index of basic concepts of numerical analysis / 204
Index of MATLAN functions / 206