Operational methods for linear systems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Reading, Mass. [u.a.]
Addison-Wesley
1962
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| Series: | Addison-Wesley series in mathematics
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 577 S. graph. Darst. |
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| 100 | 1 | |a Kaplan, Wilfred |d 1915- |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Operational methods for linear systems |c by Wilfred Kaplan |
| 264 | 1 | |a Reading, Mass. [u.a.] |b Addison-Wesley |c 1962 | |
| 300 | |a XI, 577 S. |b graph. Darst. | ||
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| 490 | 0 | |a Addison-Wesley series in mathematics | |
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Record in the Search Index
| _version_ | 1804116358978338816 |
|---|---|
| adam_text | CONTENTS
Chapter 1. Linear Differential Equations
1 1 Existence theorem for linear differential equations 1
1 2 Solution of the homogeneous equation with constant coefficients . 2
1 3 Linear differential equations with constant
coefficients; nonhomogeneous case 5
1 4 Simultaneous linear differential equations 8
1 5 Simultaneous linear equations with constant coefficients ... 11
1 6 Integrodifferential equations 17
1 7 Complex functions of a real variable 22
1 8 Differentiation and integration of complex valued functions of t . 26
1 9 Complex solutions of linear differential equations 32
1 10 Forced vibrations 38
1 11 The LRC circuit 42
1 12 Response to unit function and other discontinuous inputs ... 44
1 13 Impulse function and other generalized functions 49
1 14 Application of generalized functions to linear differential equations 56
Chapter 2. Basic Concepts of Systems Analysis
2 1 Operators 64
2 2 Linear Operators 66
2 3 Operators associated with linear differential equations .... 70
2 4 Operators associated with simultaneous linear differential equations 73
2 5 Superposition principle and interchange of operations .... 79
2 6 Translation and stationary systems 83
2 7 Duhamel s integral 87
2 8 Weighting function, impulse response, convolution 89
2 9 Characteristic function, transfer function, frequency response
function 94
2 10 Stability 103
Chapter 3. Analytic Functions of a Complex Variable
3 1 Functions of a complex variable. Limits and continuity . . . 108
3 2 Derivatives and differentials 109
3 3 Integrals 112
vii
Viii CONTENTS
3 4 Analytic functions. Cauchy Riemann equations 115
3 5 The functions log z, a2, za, sin 1 z, cos^1 z 121
3 6 Integrals of analytic functions. Cauchy integral theorem . . . 125
3 7 Cauchy s integral formula 129
3 8 Power series as analytic functions 132
3 9 Power series expansion of general analytic function . . . . 135
3 10 Power series in positive and negative powers, Laurent expansion . 139
3 11 Isolated singularities of an analytic function. Zeros and poles . 142
3 12 The complex number oo 146
3 13 Residues 150
3 14 Residue at infinity 154
3 15 Logarithmic residues; argument principle 156
3 16 Partial fraction expansion of rational functions 158
Chapter 4. Fourier Series and Finite Fourier Transform
4 1 Response to a sum of sinusoidal terms 163
4 2 Periodic inputs. Fourier series 164
4 3 Examples of Fourier series 166
4 4 Uniform convergence 169
4 5 Uniqueness theorem for Fourier series 170
4 6 Uniformly convergent Fourier series 173
4 7 Convergence of Fourier series at a point 175
4 8 Convergence in the mean 180
4 9 Differentiation and integration of Fourier series 181
4 10 Change of period 184
4 11 Complex form of Fourier series 185
4 12 Orthogonal functions 187
4 13 Solution of differential equations by Fourier series 189
4 14 The finite Fourier transform 190
4 15 The truncated Laplace transform as an aid to computation of
finite Fourier transforms 192
4 16 Properties of the finite Fourier transform 198
4 17 Convolution 201
4 18 Special convolutions 203
4 19 The inverse finite Fourier transform 208
4 20 Finite Fourier transforms of generalized functions 211
4 21 Application of finite Fourier transforms to linear differential
equations 215
4 22 Proof of Theorem 23 219
4 23 The weighting function 221
4 24 Response to periodic generalized functions 224
CONTENTS ix
4 25 Systems of differential equations 225
4 26 Integrodifferential equations 230
4 27 Systems analysis for periodic inputs 232
Chapter 5. The Fourier Integral and Fourier Transform
5 1 Introduction of the Fourier integral 235
5 2 Basic properties of the Fourier integral 236
5 3 Fourier transforms 238
5 4 Validity of the formulas 240
5 5 Examples of Fourier integrals 241
5 6 Uniform convergence for improper integrals 245
5 7 Preliminary lemmas 245
5 8 Proof of Theorem 2 248
5 9 Uniqueness theorem 252
5 10 Properties of the Fourier transform 252
5 11 Convolution 257
5 12 Special convolutions 263
5 13 The inverse Fourier transform . 270
5 14 Evaluation of inverse Fourier transforms by residues .... 271
5 15 Proof of Theorem 18 276
5 16 Fourier transforms of generalized functions 278
5 17 Application of Fourier transforms to linear differential equations 284
5 18 The weighting function 290
5 19 Response to generalized functions as inputs 292
5 20 Application of Fourier transforms to simultaneous differential
equations . 295
5 21 Applications of Fourier transforms to integrodifferential equations 297
5 22 Systems analysis by Fourier transforms 298
Chapter 6. The LapU.ce Transform
6 1 Introduction of the Laplace transform 301
6 2 Relations between the Laplace transform and the Fourier transform 303
6 3 Examples of Laplace transforms 303
6 4 Theory of the Laplace transform 309
6 5 Properties of the Laplace transform 311
6 6 The Laplace transform as an analytic function 316
6 7 Inverse transform 317
6 8 Evaluation of inverse transforms by residues 323
6 9 Laplace transforms analytic at infinity 324
6 10 Expansion in terms of Laguerre polynomials 331
6 11 Initial and final value theorems 336
X CONTENTS
6 12 Convolution 340
6 13 Special convolutions 343
6 14 Laplace transforms of generalized functions 353
6 15 Application of Laplace transforms to differential equations . . 356
6 16 Examples 360
6 17 The equation for forced vibrations 364
6 18 Weighting function. Response to generalized functions . . . 367
6 19 Application of Laplace transforms to simultaneous differential
equations 369
6 20 Application of Laplace transforms to integrodifferential equations 372
6 21 System analysis by means of Laplace transforms 373
6 22 The z transform 375
6 23 Application of the z transform to difference equations .... 385
6 24 Sampled data systems 388
6 25 Hilbert transforms 395
Chapter 7. Stability
7 1 Introduction 403
7 2 Signs of the coefficients 403
7 3 Direct method 404
7 4 Hurwitz Routh criterion 405
7 5 Proof of Hurwitz Routh criterion 408
7 6 Nyquist criterion. Polynomial case 415
7 7 Stability determined from graph of arg F(uo) 417
7 8 Nyquist criterion. Rational function case 419
7 9 Root locus method 422
7 10 Properties of the root locus 427
Chapter 8. Time variant Linear Systems
8 1 The linear differential equation of order n; the Wronskian . . 436
8 2 The generalized weighting function; the kernel function . . . 439
8 3 Green s function; impulse response 442
8 4 Adjoint equation 448
8 5 Solution of linear differential equations by infinite series . . . 453
8 6 Equations with coefficients asymptotic to constants .... 456
8 7 Perturbation method 466
8 8 Equations with coefficients which are piecewise constant . . . 468
8 9 Application of Laplace transforms 470
8 10 Equations with periodic coefficients 472
8 11 Evaluation of characteristic exponents 477
8 12 The equation of second order with periodic coefficients . . . 481
CONTENTS xi
8 13 Matrix formulation of differential equations 490
8 14 Stability theorems 496
8 15 Application of Hermitian matrices 499
8 16 Response to bounded inputs 503
8 17 Operational methods 515
Appendix I. The Operational Calculus of Mikusinski . . . 529
Appendix II. Recapitulation of Principal Tables 541
Appendix III. Glossary of Symbols 565
Index 569
|
| any_adam_object | 1 |
| author | Kaplan, Wilfred 1915- |
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| dewey-full | 517.382 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 517 - [Unassigned] |
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| dewey-search | 517.382 |
| dewey-sort | 3517.382 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| indexdate | 2024-07-09T15:37:15Z |
| institution | BVB |
| language | English |
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| physical | XI, 577 S. graph. Darst. |
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| publishDate | 1962 |
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| series2 | Addison-Wesley series in mathematics |
| spelling | Kaplan, Wilfred 1915- Verfasser aut Operational methods for linear systems by Wilfred Kaplan Reading, Mass. [u.a.] Addison-Wesley 1962 XI, 577 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Addison-Wesley series in mathematics Calculus, Operational Linear systems Laplace-Transformation (DE-588)4034577-4 gnd rswk-swf Fourier-Integral (DE-588)4121290-3 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Z-Transformation (DE-588)4191048-5 gnd rswk-swf Dynamisches System (DE-588)4013396-5 s DE-604 Laplace-Transformation (DE-588)4034577-4 s Fourier-Integral (DE-588)4121290-3 s Z-Transformation (DE-588)4191048-5 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001251736&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kaplan, Wilfred 1915- Operational methods for linear systems Calculus, Operational Linear systems Laplace-Transformation (DE-588)4034577-4 gnd Fourier-Integral (DE-588)4121290-3 gnd Dynamisches System (DE-588)4013396-5 gnd Z-Transformation (DE-588)4191048-5 gnd |
| subject_GND | (DE-588)4034577-4 (DE-588)4121290-3 (DE-588)4013396-5 (DE-588)4191048-5 |
| title | Operational methods for linear systems |
| title_auth | Operational methods for linear systems |
| title_exact_search | Operational methods for linear systems |
| title_full | Operational methods for linear systems by Wilfred Kaplan |
| title_fullStr | Operational methods for linear systems by Wilfred Kaplan |
| title_full_unstemmed | Operational methods for linear systems by Wilfred Kaplan |
| title_short | Operational methods for linear systems |
| title_sort | operational methods for linear systems |
| topic | Calculus, Operational Linear systems Laplace-Transformation (DE-588)4034577-4 gnd Fourier-Integral (DE-588)4121290-3 gnd Dynamisches System (DE-588)4013396-5 gnd Z-Transformation (DE-588)4191048-5 gnd |
| topic_facet | Calculus, Operational Linear systems Laplace-Transformation Fourier-Integral Dynamisches System Z-Transformation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001251736&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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