Mathematical methods for engineers and technologists:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford (u.a.)
Pergamon Pr.
1961
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 253 S. graph. Darst. |
Internformat
MARC
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Datensatz im Suchindex
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|---|---|
| adam_text | COMMENTS
Page
Preface to the first Edition xi
Preface to the second Edition xii
Glossary xiv
Chapter I« Fourier Series and Fourier Integrals 1
1. Periodic Functions ...... 1
2. Fourier Series for Functions with Period 2 it 2
J. The Complex Form of the Fourier Series of
Functions with Period 2n. . . . . 10
4. Odd and Even Functions 11
5. The Fourier Series for Odd and Even Functions
with Period 2t. 13
6. The Fourier Series of Functions with
Arbitrary Period . . ... 16
7. The Differential Equation for a Vibrating
String, and its Solution by Fourier s Method 21
8. Fourier s Integral 25
9. The Complex Form of the Fourier Integral 30
v
MATHEMATICAL METHODS FOE TECHNOLOGISTS
Chapter I (contd.) Paro
10. The Fourier Integrals of Odd and Even
Functions ........ 32
11. Orthogonal Systems of Functions ... 34
12. Minimal Properties of the Fourier Coeffic¬
ients 41
Chapter IIi The Elements of Vector ^ lysis 44
1. The Basic Concepts of Vector Algebra . 44
2. Vector Functions of a Scalar Variable . 46
3. The Moving Trihedron of a Curve in Three
dimensional Space ...... 48
4. Scalar Fields. The Gradient of a Scalar
Field 50
5. Curvilinear Integrals ..... 52
6. Vector Fields 60
7. Surface Integrals 63
8. Green s Formula ...... 68
9. Gauss s Theorem. The Divergence of a
Vector Field 70
10. Stokes s Theorem ...... 74
11. The Vector Form of Stokes s Theorem. The
Curl of a Vector Field 77
12. Differential Operations of the Second Order 79
13. Hamilton s Notation 81
14. Vector Operators in Curvilinear Co ordinates 82
CONTENTS
Page
Chapter III« The Foundations nf Analytic
Function Theory 91
1. Complex Numbers •..••••91
2. Series with Complex Terms .... 94
3. Power Series 96
4. The Exponential, Hyperbolic and Trigonomet¬
ric Functions of a Complex Variable . . 100
5. Some Many valued Functions of a Complex
Variable 105
6. The Derivative of a Function of a Complex
Variable 108
7. Analytic and Harmonic Functions ... 114
8. The Integral of a Function of a Complex
Variable 116
9. Cauchy s Theorem 120
10. Cauchy s Integral Formula .... 124
11. Cauchy type Integrals ..... 126
12. Higher Derivatives of Analytic Functions . 129
13. Sequences and Series of Analytic Functions 129
14. Taylor s Series 132
15. The Laurent Series 137
16. The Isolated Singularities of an Analytic
Function 139
17. Residues 143
18. The Principle of the Argument .... 151
19. Differentiate Mappings 154
WTHEKATICAL METHODS FOR TECHNOLOGISTS
Chapter III (eontd.) Base
20. The Conformal Mapping of Regions . . 163
Chapter IVs On Some Special Functions 177
1. She Gamma Function ...... 177
2. Bessel Functions 183
3. Seduction Formulae for Bessel Functions . 188
4. Bessel Functions of Index n + j • • 190
5. The Integral Hepresentation of Bessel
Functions with Integral Index ... 192
6. An Asymptotic Formula for Jn(x) for Large x 195
7. The Integral logarithm, Sine and Cosine 200
Chapter Tj The Laplace Transform 206
1. Some Notes on Integrals which are Functions
of a Parameter 206
2. The Laplace Transform 210
3. Some Simple Properties of the Laplace
Transform 213
4. The Convolution of Two Functions . . 216
5. Functions with Rational Transforms . . 219
6. The Application of the Laplace Transform to
the Solution of Differential Equations with
Constant Coefficients, and to Systems of
Such Equations ....... 222
7. The Application of the Laplace Transform to
the Solution of Linear Finite Difference
Equations with Constant Coefficients . 225
CONTENTS
Chapter V (contd.) p
8. Functions with Transforms Regular at
Infinity 252
9. The Transforms of some Special Functions 24O
10. Inversion Formulae ..... 244
11. A Sufficient Condition for an Analytic
Function to be a Laplace Transform . 248
Set by Maureen King
|
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| indexdate | 2024-07-09T15:40:06Z |
| institution | BVB |
| language | English |
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| physical | XII, 253 S. graph. Darst. |
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| publishDate | 1961 |
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| publisher | Pergamon Pr. |
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| spelling | Romanovskij, Pavel I. Verfasser aut Rjady fur'e Mathematical methods for engineers and technologists Oxford (u.a.) Pergamon Pr. 1961 XII, 253 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Infinitesimalrechnung (DE-588)4072798-1 gnd rswk-swf Technische Mathematik (DE-588)4827059-3 gnd rswk-swf Technische Mathematik (DE-588)4827059-3 s Infinitesimalrechnung (DE-588)4072798-1 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001366490&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Romanovskij, Pavel I. Mathematical methods for engineers and technologists Infinitesimalrechnung (DE-588)4072798-1 gnd Technische Mathematik (DE-588)4827059-3 gnd |
| subject_GND | (DE-588)4072798-1 (DE-588)4827059-3 |
| title | Mathematical methods for engineers and technologists |
| title_alt | Rjady fur'e |
| title_auth | Mathematical methods for engineers and technologists |
| title_exact_search | Mathematical methods for engineers and technologists |
| title_full | Mathematical methods for engineers and technologists |
| title_fullStr | Mathematical methods for engineers and technologists |
| title_full_unstemmed | Mathematical methods for engineers and technologists |
| title_short | Mathematical methods for engineers and technologists |
| title_sort | mathematical methods for engineers and technologists |
| topic | Infinitesimalrechnung (DE-588)4072798-1 gnd Technische Mathematik (DE-588)4827059-3 gnd |
| topic_facet | Infinitesimalrechnung Technische Mathematik |
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