Mathematical analysis for engineers / Bernard Dacorogna, Chiara Tanteri.

Format:

Book

Author/Creator:

Dacorogna, Bernard, 1953-

Contributor:

Tanteri, Chiara.

Standardized Title:

Analyse avancée pour ingénieurs. English

Language:

English

Subjects (All):

Mathematical analysis.

Vector analysis.

Fourier analysis.

Physical Description:

x, 359 pages : illustrations ; 24 cm

Place of Publication:

London : Imperial College Press ; Singapore ; Hackensack, NJ : Distributed by World Scientific Pub. Co., [2012]

Summary:

This book follows an advanced course in analysis (vector analysis, complex analysis and Courier analysis) for engineering students, but can also be useful, as a complement to a more theoretical course, to mathematics and physics students.

The first three parts of the book represent the theoretical aspect and are independent of each other. The fourth part gives detailed solutions to all exorcises that are proposed in the first three parts.

Key Features

Highlights definitions and theorems with mathematical rigor

Discusses some significant examples in detail

Presents several exercises, and all exercises are fully solved at the end of the book Book jacket.

Contents:

I Vector analysis 1

1 Differential operators of mathematical physics 3

1.1 Definitions and theoretical results 3

1.2 Examples 5

1.3 Exercises 7

2 Line integrals 9

2.1 Definitions and theoretical results 9

2.2 Examples 10

2.3 Exercises 11

3 Gradient vector fields 13

3.1 Definitions and theoretical results 13

3.2 Examples 14

3.3 Exercises 18

4 Green theorem 21

4.1 Definitions and theoretical results 21

4.2 Examples 23

4.3 Exercises 24

5 Surface integrals 27

5.1 Definitions and theoretical results 27

5.2 Examples 29

5.3 Exercises 31

6 Divergence theorem 33

6.1 Definitions and theoretical results 33

6.2 Examples 34

6.3 Exercises 37

7 Stokes theorem 39

7.1 Definitions and theoretical results 39

7.2 Examples 41

7.3 Exercises 43

8 Appendix 45

8.1 Some notations and notions of topology 45

8.2 Some notations for functional spaces 49

8.3 Curves 50

8.4 Surfaces 52

8.5 Change of variables 64

II Complex analysis 67

9 Holomorphic functions and Cauchy-Riemann equations 69

9.1 Definitions and theoretical results 69

9.2 Examples 71

9.3 Exercises 74

10 Complex integration 77

10.1 Definitions and theoretical results 77

10.2 Examples 78

10.3 Exercises 79

11 Laurent series 83

11.1 Definitions and theoretical results 83

11.2 Examples 86

11.3 Exercises 88

12 Residue theorem and applications 91

12.1 Part I 91

12.1.1 Definitions and theoretical results 91

12.1.2 Examples 92

12.2 Part II: Evaluation of real integrals 93

12.3 Exercises 97

13 Conformal mapping 101

13.1 Definitions and theoretical results 101

13.2 Examples 102

13.3 Exercises 104

III Fourier analysis 107

14 Fourier series 109

14.1 Definitions and theoretical results 109

14.2 Examples 113

14.3 Exercises 116

15 Fourier transform 121

15.1 Definitions and theoretical results 121

15.2 Examples 123

15.3 Exercises 125

16 Laplace transform 127

16.1 Definitions and theoretical results 127

16.2 Examples 129

16.3 Exercises 132

17 Applications to ordinary differential equations 135

17.1 Cauchy problem 135

17.2 Sturm-Liouville problem 137

17.3 Some other examples solved by Fourier analysis 140

17.4 Exercises 143

18 Applications to partial differential equations 145

18.1 Heat equation 145

18.2 Wave equation 150

18.3 Laplace equation in a rectangle 152

18.4 Laplace equation in a disk 155

18.5 Laplace equation in a simply connected domain 159

18.6 Exercises 162

IV Solutions to the exercises 167

1 Differential operators of mathematical physics 169

2 Line integrals 177

3 Gradient vector fields 181

4 Green theorem 189

5 Surface integrals 199

6 Divergence theorem 203

7 Stokes theorem 219

9 Holomorphic functions and Cauchy-Riemann equations 233

10 Complex integration 239

11 Laurent series 247

12 Residue theorem and applications 263

13 Conformal mapping 277

14 Fourier series 291

15 Fourier transform 303

16 Laplace transform 309

17 Applications to ordinary differential equations 317

18 Applications to partial differential equations 331.

Notes:

Translation of the 3rd French ed.: Analyse avancée pour ingénieurs.

Includes bibliographical references and index.

ISBN:

1848169124

9781848169128

OCLC:

793214096

Publisher Number:

99950365218