| 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](T) 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 |
| QuantumWell | 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. |