Physics with MAPLE: the computer algebra resource for mathematical methods in physics
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Weinheim
WILEY-VCH
2006
|
| Schriftenreihe: | Physics textbook
|
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XX, 605 S. graph. Darst. |
| ISBN: | 9783527406401 3527406409 |
Internformat
MARC
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| 245 | 1 | 0 | |a Physics with MAPLE |b the computer algebra resource for mathematical methods in physics |c Frank Y. Wang |
| 264 | 1 | |a Weinheim |b WILEY-VCH |c 2006 | |
| 300 | |a XX, 605 S. |b graph. Darst. | ||
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Datensatz im Suchindex
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| adam_text | Contents
Preface XI
Guide for Users XVII
Bibliography XIX
1 Introduction 1
1.1 Overview 1
1.2 Basic Algebra and Solving Equations 10
1.3 Calculus 14
1.4 Differential Equations 17
1.4.1 Exact Solutions 18
1.4.2 Special Functions 19
1.4.3 Numerical Solutions 21
1.5 Vectors and Matrices 24
1.6 Summary 36
2 Oscillatory Motion 41
2.1 Simple Harmonie Oscillator 41
2.2 Damped Oscillation 45
2.2.1 Overdamping 46
2.2.2 Underdamping 48
2.2.3 Critical Damping 49
2.3 Sinusoidally Driven Oscillation 50
2.4 Phase Space 60
3 Calculus of Variations 71
3.1 Euler Lagrange Equation 71
3.2 Mathematical Examples 72
3.3 Symmetry Properties 80
3.4 Principle of Least Action 82
3.5 Systems with Many Degrees of Freedom 86
3.6 Force ofConstraint 89
Physics wilh Maple™: The Computer Algebra Resourcefor Mathematical Methods in Physics. Frank Y. Wang
Copyright © 2006 WILEY VCH Verlag GmbH Co. KGaA. Weinheim
ISBN: 3 527^0640 9
VI Contents
4 Integration of Equations of Motion 101
4.1 Linearization of Equations 101
4.2 Double Pendulum 102
4.3 Central force Problem 108
4.3.1 Kepler Problem 109
4.3.2 Correction Terms 117
4.4 Motion of a Symmetrie Top 118
4.5 Nonlinear Oscillation and Chaos 126
4.6 Summary of Lagrangian Mechanics 134
5 Orthogonal Functions and Expansions 139
5.1 Fourier Series 139
5.2 Fourier Integrals 143
5.3 Orthogonal Functions in Complete Sets 146
5.4 Legendre Polynomials 147
5.4.1 Generating Function and Rodrigues Formula 151
5.5 Bessel Functions 152
5.6 Summary of Special Functions 163
6 Electrostatics 169
6.1 Coulomb sLaw 169
6.2 Curvilinear Coordinates 172
6.2.1 Spherical Coordinates 174
6.2.2 Cylindrical Coordinates 178
6.3 Differential Vector Calculus 180
6.4 Electric Potential 181
6.4.1 Cavendish s Apparatus for the Inverse Square Law 186
6.4.2 Multipole Expansion 190
6.5 Electric Field and Equipotential 197
7 Boundary value Problems 205
7.1 Theoryof Potential 205
7.2 Method of Images 206
7.3 Complex variable Techniques 208
7.4 Laplace Equation in Cartesian Coordinates 214
7.5 Laplace Equation in Spherical Coordinates 218
7.6 Laplace Equation in Cylindrical Coordinates 223
7.7 Summary 231
8 Magnetostatics 235
8.1 Magnetic Forces 235
8.2 Biot Savart Law 238
8.3 Vector Potential 244
8.4 Force and Torque on Magnetic Dipoles 250
8.5 Summary of Electromagnetism in Static Conditions 253
Contents VII
9 Electric Circuits 259
9.1 Resistors in Series and in Parallel 259
9.2 Kirchhoff s Rules 261
9.3 Direct current Circuits 263
9.3.1 RC Circuit 264
9.3.2 RL Circuit 265
9.3.3 RLC Circuit 266
9.3.4 Lissajous Figures 269
9.4 Alternating current Circuits 271
9.4.1 Impedance 271
9.4.2 Bridges 277
10 Waves 283
10.1 Wave Equation 283
10.2 Vibrating String 287
10.3 Sinusoidal Waves in Linear Combinations 290
10.3.1 Complex Notation 290
10.3.2 Fourier Integrals 291
10.3.3 Uncertainty Principle 292
10.4 Gaussian Wave Packet 297
10.5 Two dimensional Circular Membrane 301
10.6 Electromagnetic Waves 305
10.6.1 Electric dipole Radiation 306
10.6.2 Synchrotron Radiation 312
11 Physical Optics 321
11.1 Light as an Electromagnetic Wave 321
11.1.1 Polarization 322
11.2 Mathematics of Interference 325
11.3 Interference 328
11.3.1 Double slit Interference 329
11.3.2 Multiple slit Interference 330
11.4 Diffraction 334
11.4.1 Resolution of Single Slits and Circular Apertures 336
11.5 Diffraction Gräting 340
11.6 Fourier Transform Spectrometry 343
11.7 Fresnel Diffraction 346
12 Special Relativity 353
12.1 Lorentz Transformation 353
12.1.1 Length Contraction and Time Dilation 357
12.1.2 Addition of Velocity 361
12.1.3 Doppier Shift 363
12.2 Relativistic Kinematics and Dynamics 367
12.3 Transformations of Electromagnetic Fields 373
VIII Contents
13 Quantum Phenomena 379
13.1 Blackbody Radiation 379
13.2 Photoelectric and Compton Effects 383
13.3 Wave Particle Duality 385
13.4 Bohr Model of the Hydrogen Atom 387
13.5 Dielectrics and Paramagnetism 390
14 Schrödinger Equation in One Dimension (I): Unbound States 401
14.1 Formulation of Quantum Mechanics 401
14.2 Zero Potential and Plane Waves 403
14.3 Step Potential 404
14.3.1 Step Potential (E Vo) 404
14.3.2 Step Potential (E V0) 407
14.4 Barrier Potential 408
14.4.1 Barrier Potential (E Vo) 409
14.4.2 Barrier Potential (E V0) 410
14.5 Summary of Stationary States 411
14.6 Wave Packet 414
14.6.1 Reflectionof Wave Packet 417
15 Schrödinger Equation in One Dimension (II): Bound States 425
15.1 Discrete Spectrum 425
15.2 Infinite Potential Well 426
15.3 Finite Potential Well 428
15.4 Series Solution and Hermite Equation 436
15.5 Linear Harmonie Oscillator 438
15.6 Homogeneous Field 441
15.7 Morse Potential 445
15.8 Bound Nonstationary States 449
15.9 Two state System 450
16 Schrödinger Equation in Three Dimensions 465
16.1 Central force Problem 465
16.2 Spherical Harmonics 466
16.3 Angular Momentan 470
16.4 Coulomb Potential 472
16.5 Hydrogen Atom 474
16.5.1 Electric Potential Due to the Electron 492
16.5.2 Hybrid Bond Orbitals 494
16.6 Infinite Spherical Well 497
17 Quantum Statistics 509
17.1 Statistical Distributions 509
17.2 Maxwell Boltzmann Statistics 512
Contents IX
17.3 Ideal Böse Gas 515
17.3.1 Low Density and Virial Expansion 518
17.3.2 Bose Einstein Condensation at Low Temperature 522
17.4 Ideal Fermi Gas 528
17.4.1 Low Density and Virial Expansion 530
17.4.2 Specific Heat of a Metal at Low Temperature 531
17.5 Relativistic Gases 538
18 General Relativity 545
18.1 Basic Formulation 545
18.2 Newtonian Limit 549
18.2.1 Gravitational Redshift 551
18.3 Schwarzschild Solution 553
18.4 Robertson Walker Metric 563
18.4.1 Evolution of the Universe 565
Appendix
A Physical and Astrophysical Constants 577
B Mathematical Notes 579
B.l Legendre Equation and Series Solutions 579
B.2 Whittaker Function and Hypergeometric Series 583
B.2.1 Harmonie Oscillator 584
B.2.2 Morse Potential 586
B.2.3 Coulomb Potential 587
B.3 Clausius Mossotti Equation 589
B.4 Bose Einstein Integral Function 592
B.5 Embedding Formula 596
Index 599
|
| adam_txt |
Contents
Preface XI
Guide for Users XVII
Bibliography XIX
1 Introduction 1
1.1 Overview 1
1.2 Basic Algebra and Solving Equations 10
1.3 Calculus 14
1.4 Differential Equations 17
1.4.1 Exact Solutions 18
1.4.2 Special Functions 19
1.4.3 Numerical Solutions 21
1.5 Vectors and Matrices 24
1.6 Summary 36
2 Oscillatory Motion 41
2.1 Simple Harmonie Oscillator 41
2.2 Damped Oscillation 45
2.2.1 Overdamping 46
2.2.2 Underdamping 48
2.2.3 Critical Damping 49
2.3 Sinusoidally Driven Oscillation 50
2.4 Phase Space 60
3 Calculus of Variations 71
3.1 Euler Lagrange Equation 71
3.2 Mathematical Examples 72
3.3 Symmetry Properties 80
3.4 Principle of Least Action 82
3.5 Systems with Many Degrees of Freedom 86
3.6 Force ofConstraint 89
Physics wilh Maple™: The Computer Algebra Resourcefor Mathematical Methods in Physics. Frank Y. Wang
Copyright © 2006 WILEY VCH Verlag GmbH Co. KGaA. Weinheim
ISBN: 3 527^0640 9
VI Contents
4 Integration of Equations of Motion 101
4.1 Linearization of Equations 101
4.2 Double Pendulum 102
4.3 Central force Problem 108
4.3.1 Kepler Problem 109
4.3.2 Correction Terms 117
4.4 Motion of a Symmetrie Top 118
4.5 Nonlinear Oscillation and Chaos 126
4.6 Summary of Lagrangian Mechanics 134
5 Orthogonal Functions and Expansions 139
5.1 Fourier Series 139
5.2 Fourier Integrals 143
5.3 Orthogonal Functions in Complete Sets 146
5.4 Legendre Polynomials 147
5.4.1 Generating Function and Rodrigues Formula 151
5.5 Bessel Functions 152
5.6 Summary of Special Functions 163
6 Electrostatics 169
6.1 Coulomb'sLaw 169
6.2 Curvilinear Coordinates 172
6.2.1 Spherical Coordinates 174
6.2.2 Cylindrical Coordinates 178
6.3 Differential Vector Calculus 180
6.4 Electric Potential 181
6.4.1 Cavendish's Apparatus for the Inverse Square Law 186
6.4.2 Multipole Expansion 190
6.5 Electric Field and Equipotential 197
7 Boundary value Problems 205
7.1 Theoryof Potential 205
7.2 Method of Images 206
7.3 Complex variable Techniques 208
7.4 Laplace Equation in Cartesian Coordinates 214
7.5 Laplace Equation in Spherical Coordinates 218
7.6 Laplace Equation in Cylindrical Coordinates 223
7.7 Summary 231
8 Magnetostatics 235
8.1 Magnetic Forces 235
8.2 Biot Savart Law 238
8.3 Vector Potential 244
8.4 Force and Torque on Magnetic Dipoles 250
8.5 Summary of Electromagnetism in Static Conditions 253
Contents VII
9 Electric Circuits 259
9.1 Resistors in Series and in Parallel 259
9.2 Kirchhoff's Rules 261
9.3 Direct current Circuits 263
9.3.1 RC Circuit 264
9.3.2 RL Circuit 265
9.3.3 RLC Circuit 266
9.3.4 Lissajous Figures 269
9.4 Alternating current Circuits 271
9.4.1 Impedance 271
9.4.2 Bridges 277
10 Waves 283
10.1 Wave Equation 283
10.2 Vibrating String 287
10.3 Sinusoidal Waves in Linear Combinations 290
10.3.1 Complex Notation 290
10.3.2 Fourier Integrals 291
10.3.3 Uncertainty Principle 292
10.4 Gaussian Wave Packet 297
10.5 Two dimensional Circular Membrane 301
10.6 Electromagnetic Waves 305
10.6.1 Electric dipole Radiation 306
10.6.2 Synchrotron Radiation 312
11 Physical Optics 321
11.1 Light as an Electromagnetic Wave 321
11.1.1 Polarization 322
11.2 Mathematics of Interference 325
11.3 Interference 328
11.3.1 Double slit Interference 329
11.3.2 Multiple slit Interference 330
11.4 Diffraction 334
11.4.1 Resolution of Single Slits and Circular Apertures 336
11.5 Diffraction Gräting 340
11.6 Fourier Transform Spectrometry 343
11.7 Fresnel Diffraction 346
12 Special Relativity 353
12.1 Lorentz Transformation 353
12.1.1 Length Contraction and Time Dilation 357
12.1.2 Addition of Velocity 361
12.1.3 Doppier Shift 363
12.2 Relativistic Kinematics and Dynamics 367
12.3 Transformations of Electromagnetic Fields 373
VIII Contents
13 Quantum Phenomena 379
13.1 Blackbody Radiation 379
13.2 Photoelectric and Compton Effects 383
13.3 Wave Particle Duality 385
13.4 Bohr Model of the Hydrogen Atom 387
13.5 Dielectrics and Paramagnetism 390
14 Schrödinger Equation in One Dimension (I): Unbound States 401
14.1 Formulation of Quantum Mechanics 401
14.2 Zero Potential and Plane Waves 403
14.3 Step Potential 404
14.3.1 Step Potential (E Vo) 404
14.3.2 Step Potential (E V0) 407
14.4 Barrier Potential 408
14.4.1 Barrier Potential (E Vo) 409
14.4.2 Barrier Potential (E V0) 410
14.5 Summary of Stationary States 411
14.6 Wave Packet 414
14.6.1 Reflectionof Wave Packet 417
15 Schrödinger Equation in One Dimension (II): Bound States 425
15.1 Discrete Spectrum 425
15.2 Infinite Potential Well 426
15.3 Finite Potential Well 428
15.4 Series Solution and Hermite Equation 436
15.5 Linear Harmonie Oscillator 438
15.6 Homogeneous Field 441
15.7 Morse Potential 445
15.8 Bound Nonstationary States 449
15.9 Two state System 450
16 Schrödinger Equation in Three Dimensions 465
16.1 Central force Problem 465
16.2 Spherical Harmonics 466
16.3 Angular Momentan 470
16.4 Coulomb Potential 472
16.5 Hydrogen Atom 474
16.5.1 Electric Potential Due to the Electron 492
16.5.2 Hybrid Bond Orbitals 494
16.6 Infinite Spherical Well 497
17 Quantum Statistics 509
17.1 Statistical Distributions 509
17.2 Maxwell Boltzmann Statistics 512
Contents IX
17.3 Ideal Böse Gas 515
17.3.1 Low Density and Virial Expansion 518
17.3.2 Bose Einstein Condensation at Low Temperature 522
17.4 Ideal Fermi Gas 528
17.4.1 Low Density and Virial Expansion 530
17.4.2 Specific Heat of a Metal at Low Temperature 531
17.5 Relativistic Gases 538
18 General Relativity 545
18.1 Basic Formulation 545
18.2 Newtonian Limit 549
18.2.1 Gravitational Redshift 551
18.3 Schwarzschild Solution 553
18.4 Robertson Walker Metric 563
18.4.1 Evolution of the Universe 565
Appendix
A Physical and Astrophysical Constants 577
B Mathematical Notes 579
B.l Legendre Equation and Series Solutions 579
B.2 Whittaker Function and Hypergeometric Series 583
B.2.1 Harmonie Oscillator 584
B.2.2 Morse Potential 586
B.2.3 Coulomb Potential 587
B.3 Clausius Mossotti Equation 589
B.4 Bose Einstein Integral Function 592
B.5 Embedding Formula 596
Index 599 |
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| author | Wang, Frank Y. |
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| callnumber-sort | QC 220.7 A4 |
| callnumber-subject | QC - Physics |
| classification_rvk | SK 950 ST 601 |
| ctrlnum | (OCoLC)70249765 (DE-599)BVBBV021520682 |
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| dewey-ones | 530 - Physics |
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| dewey-sort | 3530.150285 |
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| discipline | Physik Informatik Mathematik |
| discipline_str_mv | Physik Informatik Mathematik |
| format | Book |
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| genre | (DE-588)4143389-0 Aufgabensammlung gnd-content |
| genre_facet | Aufgabensammlung |
| id | DE-604.BV021520682 |
| illustrated | Illustrated |
| index_date | 2024-07-02T14:22:28Z |
| indexdate | 2024-07-09T20:37:42Z |
| institution | BVB |
| isbn | 9783527406401 3527406409 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014737188 |
| oclc_num | 70249765 |
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| physical | XX, 605 S. graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | WILEY-VCH |
| record_format | marc |
| series2 | Physics textbook |
| spelling | Wang, Frank Y. Verfasser (DE-588)131348418 aut Physics with MAPLE the computer algebra resource for mathematical methods in physics Frank Y. Wang Weinheim WILEY-VCH 2006 XX, 605 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Physics textbook Maple (Computer file) Logique algébrique - Informatique Physique mathématique - Informatique Datenverarbeitung Mathematische Physik Algebraic logic Data processing Mathematical physics Data processing Maple Programm (DE-588)4209397-1 gnd rswk-swf Computerphysik (DE-588)4273564-6 gnd rswk-swf (DE-588)4143389-0 Aufgabensammlung gnd-content Computerphysik (DE-588)4273564-6 s Maple Programm (DE-588)4209397-1 s DE-604 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2686538&prov=M&dok_var=1&dok_ext=htm Inhaltstext HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014737188&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wang, Frank Y. Physics with MAPLE the computer algebra resource for mathematical methods in physics Maple (Computer file) Logique algébrique - Informatique Physique mathématique - Informatique Datenverarbeitung Mathematische Physik Algebraic logic Data processing Mathematical physics Data processing Maple Programm (DE-588)4209397-1 gnd Computerphysik (DE-588)4273564-6 gnd |
| subject_GND | (DE-588)4209397-1 (DE-588)4273564-6 (DE-588)4143389-0 |
| title | Physics with MAPLE the computer algebra resource for mathematical methods in physics |
| title_auth | Physics with MAPLE the computer algebra resource for mathematical methods in physics |
| title_exact_search | Physics with MAPLE the computer algebra resource for mathematical methods in physics |
| title_exact_search_txtP | Physics with MAPLE the computer algebra resource for mathematical methods in physics |
| title_full | Physics with MAPLE the computer algebra resource for mathematical methods in physics Frank Y. Wang |
| title_fullStr | Physics with MAPLE the computer algebra resource for mathematical methods in physics Frank Y. Wang |
| title_full_unstemmed | Physics with MAPLE the computer algebra resource for mathematical methods in physics Frank Y. Wang |
| title_short | Physics with MAPLE |
| title_sort | physics with maple the computer algebra resource for mathematical methods in physics |
| title_sub | the computer algebra resource for mathematical methods in physics |
| topic | Maple (Computer file) Logique algébrique - Informatique Physique mathématique - Informatique Datenverarbeitung Mathematische Physik Algebraic logic Data processing Mathematical physics Data processing Maple Programm (DE-588)4209397-1 gnd Computerphysik (DE-588)4273564-6 gnd |
| topic_facet | Maple (Computer file) Logique algébrique - Informatique Physique mathématique - Informatique Datenverarbeitung Mathematische Physik Algebraic logic Data processing Mathematical physics Data processing Maple Programm Computerphysik Aufgabensammlung |
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