Mathematica for theoretical physics: 1 Classical mechanics and nonlinear dynamics
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2005
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| Ausgabe: | 2. ed., expanded, and updated version of the orig. German version |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVI, 544 S. Ill., graph. Darst. 1 CD-ROM (12 cm) |
| ISBN: | 0387251138 |
Internformat
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| 300 | |a XVI, 544 S. |b Ill., graph. Darst. |e 1 CD-ROM (12 cm) | ||
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Datensatz im Suchindex
| _version_ | 1804139082677223424 |
|---|---|
| adam_text | MATHEMATICA FOR THEORETICAL PHYSICS CLASSICAL MECHANICS AND NONLINEAR
DYNAMICS SECOND EDITION GERD BAUMANN CD-ROM INCLUDED 4^ SPRINGER
CONTENTS CLASSICAL MECHANICS AND NONLINEAR DYNAMICS PREFACE INTRODUCTION
1.1 BASICS 1.1.1 STRUCTURE OF MATHEMATICA 1.1.2 INTERACTIVE USE OF
MATHEMATICA 1.1.3 SYMBOLIC CALCULATIONS 1.1.4 NUMERICAL CALCULATIONS
1.1.5 GRAPHICS 1.1.6 PROGRAMMING CLASSICAL MECHANICS 2.1 INTRODUCTION
2.2 MATHEMATICAL TOOLS 2.2.1 INTRODUCTION 2.2.2 COORDINATES 2.2.3
COORDINATE TRANSFORMATIONS AND MATRICES 2.2.4 SCALARS 2.2.5 VECTORS
2.2.6 TENSORS 2.2.7 VECTOR PRODUCTS 2.2.8 DERIVATIVES 2.2.9 INTEGRALS
2.2.10 EXERCISES VII 1 1 2 4 6 11 13 23 31 31 35 35 36 38 54 57 59 64 69
73 74 XII CONTENTS 2.3 2.4 2.5 2.6 KINEMATICS 2.3.1 2.3.2 2.3.3 2.3.4
2.3.5 INTRODUCTION VELOCITY ACCELERATION KINEMATIC EXAMPLES EXERCISES
NEWTONIAN MECHANICS 2.4.1 2.4.2 2.4.3 2.4.4 2.4.5 2.4.6 2.4.7 2.4.8
2.4.9 2.4.10 CENTRAI 2.5.1 2.5.2 2.5.3 2.5.4 2.5.5 2.5.6 INTRODUCTION
FRAME OF REFERENCE TIME MASS NEWTON S LAWS FORCES IN NATURE CONSERVATION
LAWS APPLICATION OF NEWTON S SECOND LAW EXERCISES PACKAGES AND PROGRAMS
I FORCES INTRODUCTION KEPLER S LAWS CENTRAL FIELD MOTION TWO-PARTICLE
COLLISONS AND SCATTERING EXERCISES PACKAGES AND PROGRAMS CALCULUS OF
VARIATIONS 2.6.1 2.6.2 2.6.3 2.6.4 2.6.5 2.6.6 2.6.7 2.6.8 2.6.9
INTRODUCTION THE PROBLEM OF VARIATIONS EULER S EQUATION EULER OPERATOR
ALGORITHM USED IN THE CALCULUS OF VARIATIONS EULER OPERATOR FOR Q
DEPENDENT VARIABLES EULER OPERATOR FOR Q + P DIMENSIONS VARIATIONS WITH
CONSTRAINTS EXERCISES 2.6.10 PACKAGES AND PROGRAMS 2.7 LAGRANGE DYNAMICS
2.7.1 INTRODUCTION 2.7.2 HAMILTON S PRINCIPLE HISTORICAL REMARKS
CONTENTS XIII 2.7.3 HAMILTON S PRINCIPLE 313 2.7.4 SYMMETRIES AND
CONSERVATION LAWS 341 2.7.5 EXERCISES 351 2.7.6 PACKAGES AND PROGRAMS
351 2.8 HAMILTONIAN DYNAMICS 354 2.8.1 INTRODUCTION 354 2.8.2 LEGENDRE
TRANSFORM 355 2.8.3 HAMILTON S EQUATION OF MOTION 362 2.8.4 HAMILTON S
EQUATIONS AND THE CALCULUS OF VARIATION 366 2.8.5 LIOUVILLE S THEOREM
373 2.8.6 POISSON BRACKETS 377 2.8.7 MANIFOLDS AND CLASSES 384 2.8.8
CANONICAL TRANSFORMATIONS 396 2.8.9 GENERATING FUNCTIONS 398 2.8.10
ACTION VARIABLES 403 2.8.11 EXERCISES 419 2.8.12 PACKAGES AND PROGRAMS
419 2.9 CHAOTIC SYSTEMS 422 2.9.1 INTRODUCTION 422 2.9.2 DISCRETE
MAPPINGS AND HAMILTONIANS 431 2.9.3 LYAPUNOV EXPONENTS 435 2.9.4
EXERCISES 448 2.10 RIGID BODY 449 2.10.1 INTRODUCTION 449 2.10.2 THE
INERTIA TENSOR 450 2.10.3 THE ANGULAR MOMENTUM 453 2.10.4 PRINCIPAL AXES
OF INERTIA 454 2.10.5 STEINER S THEOREM 460 2.10.6 EULER S EQUATIONS OF
MOTION 462 2.10.7 FORCE-FREE MOTION OF A SYMMETRICAL TOP 467 2.10.8
MOTION OF A SYMMETRICAL TOP IN A FORCE FIELD 471 2.10.9 EXERCISES 481
2.10.10 PACKAGES AND PROGRAMMS 481 3 NONLINEAR DYNAMICS 485 3.1
INTRODUCTION 485 3.2 THE KORTEWEG-DE VRIES EQUATION 488 3.3 SOLUTION OF
THE KORTEWEG-DE VRIES EQUATION 492 XIV CONTENTS 3.3.1 THE INVERSE
SCATTERING TRANSFORM 49S 3.3.2 SOLITON SOLUTIONS OF THE KORTEWEG-DE
VRIES EQUATION 49? 3.4 CONSERVATION LAWS OF THE KORTEWEG-DE VRIES
EQUATION 505 3.4.1 DEFINITION OF CONSERVATION LAWS 50T 3.4.2 DERIVATION
OF CONSERVATION LAWS 508 3.5 NUMERICAL SOLUTION OF THE KORTEWEG-DE VRIES
EQUATION 511 3.6 EXERCISES 515 3.7 PACKAGES AND PROGRAMS 516 3.7.1
SOLUTION OF THE KDV EQUATION 516 3.7.2 CONSERVATION LAWS FOR THE KDV
EQUATION 517 3.7.3 NUMERICAL SOLUTION OF THE KDV EQUATION 518 REFERENCES
521 INDEX 529 ELECTRODYNAMICS, QUANTUM MECHANICS, GENERAL RELATIVITY,
AND FRACTALS PREFACE ELECTRODYNAMICS 4.1 4.2 4.3 4.4 4.5 4.6
INTRODUCTION POTENTIAL AND ELECTRIC FIELD OF DISCRETE CHARGE
DISTRIBUTIONS BOUNDARY PROBLEM OF ELECTROSTATICS TWO IONS IN THE PENNING
TRAP 4.4.1 THE CENTER OF MASS MOTION 4.4.2 RELATIVE MOTION OF THE IONS
EXERCISES PACKAGES AND PROGRAMS 4.6.1 POINT CHARGES 4.6.2 BOUNDARY
PROBLEM 4.6.3 PENNING TRAP QUANTUM MECHANICS 5.1 5.2 INTRODUCTION THE
SCHRODINEER EAUATION VII 545 545 548 555 566 569 572 577 578 578 581 582
587 587 590 CONTENTS XV 5.3 5.4 5.5 5.6 5.7 5.8 5.9 ONE-DIMENSIONAL
POTENTIAL THE HARMONIC OSCILLATOR ANHARMONIC OSCILLATOR MOTION IN THE
CENTRAL FORCE FIELD SECOND VIRIAL COEFFICIENT AND ITS QUANTUM
CORRECTIONS 5.7.1 THE SVC AND ITS RELATION TO THERMODYNAMIC PROPERTIES
5.7.2 CALCULATION OF THE CLASSICAL SVC B C (T) FOR THE (2 N - N)
-POTENTIAL 5.7.3 QUANTUM MECHANICAL CORRECTIONS B QI (T) AND 5^(71 OF
THE SVC 5.7.4 SHAPE DEPENDENCE OF THE BOYLE TEMPERATURE 5.7.5 THE
HIGH-TEMPERATURE PARTITION FUNCTION FOR DIATOMIC MOLECULES EXERCISES
PACKAGES AND PROGRAMS 5.9.1 QUANTUMWELL 5.9.2 HARMONICOSCILLATOR 5.9.3
ANHARMONICOSCILLATOR 5.9.4 CENTRALFIELD GENERAL RELATIVITY 6.1 6.2 6.3
6.4 6.5 INTRODUCTION THE ORBITS IN GENERAL RELATIVITY 6.2.1
QUASIELLIPTIC ORBITS 6.2.2 ASYMPTOTIC CIRCLES LIGHT BENDING IN THE
GRAVITATIONAL FIELD EINSTEIN S FIELD EQUATIONS (VACUUM CASE) 6.4.1
EXAMPLES FOR METRIC TENSORS 6.4.2 THE CHRISTOFFEL SYMBOLS 6.4.3 THE
RIEMANN TENSOR 6.4.4 EINSTEIN S FIELD EQUATIONS 6.4.5 THE CARTESIAN
SPACE 6.4.6 CARTESIAN SPACE IN CYLINDRICAL COORDINATES 6.4.7 EUCLIDEAN
SPACE IN POLAR COORDINATES THE SCHWARZSCHILD SOLUTION 595 609 619 631
642 644 646 655 680 684 687 688 688 693 695 698 703 703 707 713 719 720
725 727 731 731 733 734 736 737 739 6.5.1 THE SCHWARZSCHILD METRIC IN
EDDINGTON-FINKELSTEIN FORM 739 XVI CONTENTS 6.5.2 DINGLE S METRIC 7
6.5.3 SCHWARZSCHILD METRIC IN KRUSKAL COORDINATES I 1 6.6 THE
REISSNER-NORDSTROM SOLUTION FOR A CHARGED 6.7 6.8 MASS POINT EXERCISES
PACKAGES AND PROGRAMS 6.8.1 EULERLAGRANGE EQUATIONS 6.8.2
PERIHELIONSHIFT 6.8.3 LIGHTBENDING 7 FRACTALS 7.1 7.2 7.3 7.4 7.5 7.6
7.7 7.8 INTRODUCTION MEASURING A BORDERLINE 7.2.1 BOX COUNTING THE KOCH
CURVE MULTIFRACTALS 7.4.1 MULTIFRACTALS WITH COMMON SCALING FACTOR THE
RENORMLIZATION GROUP FRACTIONAL CALCULUS 7.6.1 HISTORICAL REMARKS ON
FRACTIONAL CALCULUS 7.6.2 THE RIEMANN-LIOUVILLE CALCULUS 7.6.3 MELLIN
TRANSFORMS 7.6.4 FRACTIONAL DIFFERENTIAL EQUATIONS EXERCISES PACKAGES
AND PROGRAMS 7.8.1 TREE GENERATION 7.8.2 KOCH CURVES 7.8.3 MULTIFACTALS
7.8.4 RENORMALIZATION 7.8.5 FRACTIONAL CALCULUS APPENDIX A.1 A.2 A.3
PROGRAM INSTALLATION GLOSSARY OF FILES AND FUNCTIONS MATHEMATICA
FUNCTIONS REFERENCES INDE T 752 759 761 761 762 767 773 773 776 781 790
795 798 801 809 810 813 830 856 883 883 883 886 892 895 897 899 899 900
910 923 931
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| id | DE-604.BV023865131 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:38:26Z |
| institution | BVB |
| isbn | 0387251138 |
| language | English |
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| publishDate | 2005 |
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| publisher | Springer |
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| spelling | Baumann, Gerd 1956- Verfasser (DE-588)142960241 aut Mathematica for theoretical physics 1 Classical mechanics and nonlinear dynamics Gerd Baumann 2. ed., expanded, and updated version of the orig. German version New York [u.a.] Springer 2005 XVI, 544 S. Ill., graph. Darst. 1 CD-ROM (12 cm) txt rdacontent n rdamedia nc rdacarrier (DE-604)BV023818776 1 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017528978&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Baumann, Gerd 1956- Mathematica for theoretical physics |
| title | Mathematica for theoretical physics |
| title_auth | Mathematica for theoretical physics |
| title_exact_search | Mathematica for theoretical physics |
| title_full | Mathematica for theoretical physics 1 Classical mechanics and nonlinear dynamics Gerd Baumann |
| title_fullStr | Mathematica for theoretical physics 1 Classical mechanics and nonlinear dynamics Gerd Baumann |
| title_full_unstemmed | Mathematica for theoretical physics 1 Classical mechanics and nonlinear dynamics Gerd Baumann |
| title_short | Mathematica for theoretical physics |
| title_sort | mathematica for theoretical physics classical mechanics and nonlinear dynamics |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017528978&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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