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Introduction to Numerical Methods with 245 Solved Problems

Introduction to Numerical Methods with 245 Solved Problems

Andrzej Miękina, Roman Z. Morawski

E-book

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.

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 186

6. 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

  • Titel: Introduction to Numerical Methods with 245 Solved Problems
  • Autor: Andrzej Miękina, Roman Z. Morawski
  • ISBN: 978-83-8156-743-5, 9788381567435
  • Veröffentlichungsdatum: 2025-02-24
  • Format: E-book
  • Artikelkennung: e_49fj
  • Verleger: Oficyna Wydawnicza Politechniki Warszawskiej