Introduction to Numerical Methods with 245 Solved Problems
- Dodaj recenzję:
- Kod: 6625
- Producent: Oficyna Wydawnicza Politechniki Warszawskiej
- Autor: Andrzej Miękina, Roman Z. Morawski
- Rok wydania: 2025, wydanie II
- ISBN: 978-83-8156-742-8
- Liczba stron: 280
- Oprawa: miękka
- Format: A4
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- Cena netto: 61,90 zł 65,00 zł
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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 1985–2025, and in particular – the students following the English-medium programmes of study offered there during last 30 years. It is composed of seven chapters devoted to basic numerical problems, such as accuracy of computation, approximation of functions, numerical differentiation and integration, solving algebraic and differential equations. Each chapter contains a short general introduction followed by a considerable number of solved numerical problems. The textbook may be useful for students attending any engineering-oriented course of numerical methods.
Table of Contents
Preface / 7
Notation / 10
1. Accuracy of computation / 13
1.0. Introduction to Chapter 1 / 13
1.1. Propagation of data errors / 17
1.2. Propagation of rounding errors / 27
1.3. Propagation of data errors and rounding errors / 40
1.4. Engineering applications / 45
2. Solving linear algebraic equations / 54
2.0. Introduction to Chapter 2 / 54
2.1. Matrix factorisation / 59
2.2. Non-iterative algorithms / 66
2.3. Iterative algorithms / 78
2.4. Engineering applications / 81
3. Approximation / 84
3.0. Introduction to Chapter 3 / 84
3.1. Interpolation / 91
3.2. Least-squares approximation / 101
3.3. Other types of approximation / 117
3.4. Engineering applications / 120
4. Solving nonlinear algebraic equations / 123
4.0. Introduction to Chapter 4 / 123
4.1. Preliminary exercises / 132
4.2. Single-point iterative algorithms / 134
4.3. Multiple-point iterative algorithms / 150
4.4. Accuracy of numerical solutions / 155
4.5. Engineering applications / 164
5. Numerical differentiation / 166
5.0. Introduction to Chapter 5 / 166
5.1. Accuracy / 170
5.2. Design of differentiation formulae / 179
5.3. Optimisation of differentiation step / 184
5.4. Engineering applications / 1866. Numerical integration / 189
6.0. Introduction to Chapter 6 / 189
6.1. Preliminary exercises / 195
6.2. Quadrature-based methods / 199
6.3. Monte-Carlo methods / 219
6.4. Engineering applications / 222
7. Solving ordinary differential equations / 225
7.0. Introduction to Chapter 7 / 225
7.1. Preliminary exercises / 234
7.2. Single-step methods / 237
7.3. Multi-step methods / 258
7.4. Engineering applications / 270
Index of basic concepts of numerical analysis / 276
Index of MATLAN functions / 278
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