
Mathematica for Theoretical Physics
Classical Mechanics and Nonlinear Dynamics
By: Gerd Baumann
Hardcover | 23 September 2005 | Edition Number 2
At a Glance
564 Pages
Revised
23.9 x 15.6 x 2.1
Hardcover
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Mathematica for Theoretical Physics:
Classical Mechanics and Nonlinear Dynamics
This second edition of Baumann's MathematicaA(R) in Theoretical Physics shows readers how to solve physical problems and deal with their underlying theoretical concepts while using MathematicaA(R) to derive numeric and symbolic solutions. Each example and calculation can be evaluated by the reader, and the reader can change the example calculations and adopt the given code to related or similar problems.
The second edition has been completely revised and expanded into two volumes:
The first volume covers classical mechanics and nonlinear dynamics. Both topics are the basis of a regular mechanics course. The second volume covers electrodynamics, quantum mechanics, relativity, and fractals and fractional calculus.
New examples have been added and the representation has been reworked to provide a more interactive problem-solving presentation. This book can be used as a textbook or as a reference work, by students and researchers alike. A brief glossary of terms and functions is contained in the appendices.
The CD-ROM accompanying each of the two volumes contains MathematicaA(R)
notebooks as well as MathematicaA(R) programs. The notebooks contain the entire text of the corresponding volume and can interface with MathematicaA(R). The examples given in the text can also be interactively used and changed for the readera (TM)s purposes.
The Author, Gerd Baumann, is affiliated with the Mathematical Physics Division of the University of Ulm, Germany, where he is professor. He is the author of Symmetry Analysis of Differential Equations with MathematicaA(R). Dr. Baumann has given numerous invited talks at universities and industry alike. He regularly hosts seminars and lectures on symbolic computing at the University of Ulm and at TECHNISCHE UNIVERSITA"T MAoeNCHEN (TUM), Munich.
Industry Reviews
From the reviews of the second edition:
"The new edition contains a lot of new material and examples ... . It is shown how Mathematica can be used to support (or to replace) many of the usual 'by-hand' calculations and to study the results instantaneously by means of graphical representations. In particular, advantage is taken of many special functions and operations ... which are available in Mathematica. The book contains many sample programs, in written form." (M. Plum, Zentralblatt MATH, Vol. 1095 (21), 2006)
| Classical Mechanics and Nonlinear Dynamics | |
| Preface | p. vii |
| Introduction | p. 1 |
| Basics | p. 1 |
| Structure of Mathematica | p. 2 |
| Interactive Use of Mathematica | p. 4 |
| Symbolic Calculations | p. 6 |
| Numerical Calculations | p. 11 |
| Graphics | p. 13 |
| Programming | p. 23 |
| Classical Mechanics | p. 31 |
| Introduction | p. 31 |
| Mathematical Tools | p. 35 |
| Introduction | p. 35 |
| Coordinates | p. 36 |
| Coordinate Transformations and Matrices | p. 38 |
| Scalars | p. 54 |
| Vectors | p. 57 |
| Tensors | p. 59 |
| Vector Products | p. 64 |
| Derivatives | p. 69 |
| Integrals | p. 73 |
| Exercises | p. 74 |
| Kinematics | p. 76 |
| Introduction | p. 76 |
| Velocity | p. 77 |
| Acceleration | p. 81 |
| Kinematic Examples | p. 82 |
| Exercises | p. 94 |
| Newtonian Mechanics | p. 96 |
| Introduction | p. 96 |
| Frame of Reference | p. 98 |
| Time | p. 100 |
| Mass | p. 101 |
| Newton's Laws | p. 103 |
| Forces in Nature | p. 106 |
| Conservation Laws | p. 111 |
| Application of Newton's Second Law | p. 118 |
| Exercises | p. 188 |
| Packages and Programs | p. 188 |
| Central Forces | p. 201 |
| Introduction | p. 201 |
| Kepler's Laws | p. 202 |
| Central Field Motion | p. 208 |
| Two-Particle Collisons and Scattering | p. 240 |
| Exercises | p. 272 |
| Packages and Programs | p. 273 |
| Calculus of Variations | p. 274 |
| Introduction | p. 274 |
| The Problem of Variations | p. 276 |
| Euler's Equation | p. 281 |
| Euler Operator | p. 283 |
| Algorithm Used in the Calculus of Variations | p. 284 |
| Euler Operator for q Dependent Variables | p. 293 |
| Euler Operator for q + p Dimensions | p. 296 |
| Variations with Constraints | p. 300 |
| Exercises | p. 303 |
| Packages and Programs | p. 303 |
| Lagrange Dynamics | p. 305 |
| Introduction | p. 305 |
| Hamilton's Principle Historical Remarks | p. 306 |
| Hamilton's Principle | p. 313 |
| Symmetries and Conservation Laws | p. 341 |
| Exercises | p. 351 |
| Packages and Programs | p. 351 |
| Hamiltonian Dynamics | p. 354 |
| Introduction | p. 354 |
| Legendre Transform | p. 355 |
| Hamilton's Equation of Motion | p. 362 |
| Hamilton's Equations and the Calculus of Variation | p. 366 |
| Liouville's Theorem | p. 373 |
| Poisson Brackets | p. 377 |
| Manifolds and Classes | p. 384 |
| Canonical Transformations | p. 396 |
| Generating Functions | p. 398 |
| Action Variables | p. 403 |
| Exercises | p. 419 |
| Packages and Programs | p. 419 |
| Chaotic Systems | p. 422 |
| Introduction | p. 422 |
| Discrete Mappings and Hamiltonians | p. 431 |
| Lyapunov Exponents | p. 435 |
| Exercises | p. 448 |
| Rigid Body | p. 449 |
| Introduction | p. 449 |
| The Inertia Tensor | p. 450 |
| The Angular Momentum | p. 453 |
| Principal Axes of Inertia | p. 454 |
| Steiner's Theorem | p. 460 |
| Euler's Equations of Motion | p. 462 |
| Force-Free Motion of a Symmetrical Top | p. 467 |
| Motion of a Symmetrical Top in a Force Field | p. 471 |
| Exercises | p. 481 |
| Packages and Programms | p. 481 |
| Nonlinear Dynamics | p. 485 |
| Introduction | p. 485 |
| The Korteweg-de Vries Equation | p. 488 |
| Solution of the Korteweg-de Vries Equation | p. 492 |
| The Inverse Scattering Transform | p. 492 |
| Soliton Solutions of the Korteweg-de Vries Equation | p. 498 |
| Conservation Laws of the Korteweg-de Vries Equation | p. 505 |
| Definition of Conservation Laws | p. 506 |
| Derivation of Conservation Laws | p. 508 |
| Numerical Solution of the Korteweg-de Vries Equation | p. 511 |
| Exercises | p. 515 |
| Packages and Programs | p. 516 |
| Solution of the KdV Equation | p. 516 |
| Conservation Laws for the KdV Equation | p. 517 |
| Numerical Solution of the KdV Equation | p. 518 |
| References | p. 521 |
| Index | p. 529 |
| Electrodynamics, Quantum Mechanics, General Relativity, and Fractals | |
| Preface | p. vii |
| Electrodynamics | p. 545 |
| Introduction | p. 545 |
| Potential and Electric Field of Discrete Charge Distributions | p. 548 |
| Boundary Problem of Electrostatics | p. 555 |
| Two Ions in the Penning Trap | p. 566 |
| The Center of Mass Motion | p. 569 |
| Relative Motion of the Ions | p. 572 |
| Exercises | p. 577 |
| Packages and Programs | p. 578 |
| Point Charges | p. 578 |
| Boundary Problem | p. 581 |
| Penning Trap | p. 582 |
| Quantum Mechanics | p. 587 |
| Introduction | p. 587 |
| The Schrodinger Equation | p. 590 |
| One-Dimensional Potential | p. 595 |
| The Harmonic Oscillator | p. 609 |
| Anharmonic Oscillator | p. 619 |
| Motion in the Central Force Field | p. 631 |
| Second Virial Coefficient and Its Quantum Corrections | p. 642 |
| The SVC and Its Relation to Thermodynamic Properties | p. 644 |
| Calculation of the Classical SVC B[subscript c] (T) for the (2n - n) -Potential | p. 646 |
| Quantum Mechanical Corrections B[subscript q1] (T) and B[subscript q2] of the SVC | p. 655 |
| Shape Dependence of the Boyle Temperature | p. 680 |
| The High-Temperature Partition Function for Diatomic Molecules | p. 684 |
| Exercises | p. 687 |
| Packages and Programs | p. 688 |
| Quantum Well | p. 688 |
| HarmonicOscillator | p. 693 |
| AnharmonicOscillator | p. 695 |
| CentralField | p. 698 |
| General Relativity | p. 703 |
| Introduction | p. 703 |
| The Orbits in General Relativity | p. 707 |
| Quasielliptic Orbits | p. 713 |
| Asymptotic Circles | p. 719 |
| Light Bending in the Gravitational Field | p. 720 |
| Einstein's Field Equations (Vacuum Case) | p. 725 |
| Examples for Metric Tensors | p. 727 |
| The Christoffel Symbols | p. 731 |
| The Riemann Tensor | p. 731 |
| Einstein's Field Equations | p. 733 |
| The Cartesian Space | p. 734 |
| Cartesian Space in Cylindrical Coordinates | p. 736 |
| Euclidean Space in Polar Coordinates | p. 737 |
| The Schwarzschild Solution | p. 739 |
| The Schwarzschild Metric in Eddington-Finkelstein Form | p. 739 |
| Dingle's Metric | p. 742 |
| Schwarzschild Metric in Kruskal Coordinates | p. 748 |
| The Reissner-Nordstrom Solution for a Charged Mass Point | p. 752 |
| Exercises | p. 759 |
| Packages and Programs | p. 761 |
| EulerLagrange Equations | p. 761 |
| PerihelionShift | p. 762 |
| LightBending | p. 767 |
| Fractals | p. 773 |
| Introduction | p. 773 |
| Measuring a Borderline | p. 776 |
| Box Counting | p. 781 |
| The Koch Curve | p. 790 |
| Multifractals | p. 795 |
| Multifractals with Common Scaling Factor | p. 798 |
| The Renormlization Group | p. 801 |
| Fractional Calculus | p. 809 |
| Historical Remarks on Fractional Calculus | p. 810 |
| The Riemann-Liouville Calculus | p. 813 |
| Mellin Transforms | p. 830 |
| Fractional Differential Equations | p. 856 |
| Exercises | p. 883 |
| Packages and Programs | p. 883 |
| Tree Generation | p. 883 |
| Koch Curves | p. 886 |
| Multifactals | p. 892 |
| Renormalization | p. 895 |
| Fractional Calculus | p. 897 |
| Appendix | p. 899 |
| Program Installation | p. 899 |
| Glossary of Files and Functions | p. 900 |
| Mathematica Functions | p. 910 |
| References | p. 923 |
| Index | p. 931 |
| Table of Contents provided by Ingram. All Rights Reserved. |
ISBN: 9780387016740
ISBN-10: 0387016740
Published: 23rd September 2005
Format: Hardcover
Language: English
Number of Pages: 564
Audience: Professional and Scholarly
Publisher: Springer Nature B.V.
Country of Publication: GB
Edition Number: 2
Edition Type: Revised
Dimensions (cm): 23.9 x 15.6 x 2.1
Weight (kg): 0.98
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