理論物理中的Mathematica

內(nèi)容概要

本書為國外物理名著系列之一，由鮑曼編著。
 本書主要內(nèi)容簡介：Classical Mechanics and Nonlinear
Dynamics Class-tested textbook that shows readers how to solve
physical problems and deal with their underlying theoretical
concepts while using Mathematica~ to derive numeric and symbolic
solutions. Delivers dozens of fully interactive examples for
learning and implementation, constants and formulae can readily be
altered and adapted for the user's purposes. New edition offers
enlarged two-volume format suitable to courses in mechanics and
electrodynamics, while offering dozens of new examples and a more
rewarding interactive learning enwironment.

作者簡介

作者：（美國）鮑曼（G.Baumann）

書籍目錄

Volume I
Preface
1  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
    I.1.5  Graphics
    1.1.6  Programming
2  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
  2.3   Kinematics
    2.3.1  Introduction
    2.3.2  Velocity
    2.3.3  Acceleration
    2.3.4  Kinematic Examples
    2.3.5  Exercises
  2.4   Newtonian Mechanics
    2.4.1  Introduction
    2.4.2  Frame of Reference
    2.4.3  Time
    2.4.4  Mass
    2.4.5  Newton's Laws
    2.4.6  Forces in Nature
    2.4.7  Conservation Laws
    2.4.8  Application of Newton's Second Law
    2.4.9  Exercises
    2.4.10 Packages and Programs
  2.5  Central Forces
    2.5.1  Introduction
    2.5.2  Kepler's Laws
    2.5.3  Central Field Motion
    2.5.4  Two-Particle Collisons and Scattering
    2.5.5  Exercises
    2.5.6  Packages and Programs
  2.6  Calculus of Variations
    2.6.1  Introduction
    2.6.2  The Problem of Variations
    2.6.3  Euler's Equation
    2.6.4  Euler Operator
    2.6.5  Algorithm Used in the Calculus of Variations
    2.6.6  Euler Operator for q Dependent Variables
    2.6.7  Euler Operator for q + p Dimensions
    2.6.8  Variations with Constraints
    2.6.9  Exercises
    2.6.10 Packages and Programs
  2.7  Lagrange Dynamics
    2.7.1  Introduction
    2.7.2  Hamilton's Principle Hisorical Remarks
    2.7.3  Hamilton's Principle
    2.7.4  Symmetries and Conservation Laws
    2.7.5  Exercises
    2.7.6  Packages and Programs
  2.8  Hamiltonian Dynamics
    2.8.1  Introduction
    2.8.2  Legendre Transform
    2.8.3  Hamilton's Equation of Motion
    2.8.4  Hamilton's Equations and the Calculus of Variation
    2.8.5  Liouville's Theorem
    2.8.6  Poisson Brackets
    2.8.7  Manifolds and Classes
    2.8.8  Canonical Transformations
    2.8.9  Generating Functions
    2.8.10 Action Variables
    2.8.11 Exercises
    2.8.12 Packages and Programs
  2.9  Chaotic Systems
    2.9.1  Introduction
    2.9.2  Discrete Mappings and Hamiltonians
    2.9.3  Lyapunov Exponents
    2.9.4  Exercises
  2.10  Rigid Body
    2.10.1 Introduction
    2.10.2 The Inertia Tensor
    2.10.3 The Angular Momentum
    2.10.4 Principal Axes of Inertia
    2.10.5 Steiner's Theorem
    2.10.6 Euler's Equations of Motion
    2.10.7 Force-Free Motion of a Symmetrical Top
    2.10.8 Motion of a Symmetrical Top in a Force Field
    2.10.9 Exercises
    2.10.10 Packages and Programms
3  Nonlinear Dynamics
  3.1  Introduction
  3.2  The Korteweg-de Vries Equation
  3.3  Solution of the Korteweg-de Vries Equation
    3.3.1  The Inverse Scattering Transform
    3.3.2  Soliton Solutions of the Korteweg-de Vries Equation
  3.4  Conservation Laws of the Korteweg--de Vries Equation
    3.4.1  Definition of Conservation Laws
    3.4.2  Derivation of Conservation Laws
  3.5  Numerical Solution of the Korteweg--de Vries Equation
  3.6  Exercises
  3.7  Packages and Programs
    3.7.1  Solution of the KdV Equation
    3.7.2  Conservation Laws for the KdV Equation
    3.7.3  Numerical Solution of the KdV Equation
  References
  Index
Volume II
Preface
4    Electrodynamics
  4.1  Introduction
  4.2  Potential and Electric Field of Discrete Charge
Distributions
  4.3  Boundary Problem of Electrostatics
  4.4  Two Ions in the Penning Trap
    4.4.1  The Center of Mass Motion
    4.4.2  Relative Motion of the Ions
  4.5   Exercises
  4.6   Packages and Programs
    4.6.1  Point Charges
    4.6.2  Boundary Problem
    4.6.3  Penning Trap
5  Quantum Mechanics
  5.1  Introduction
  5.2  The Schr6dinger Equation
  5.3  One-Dimensional Potential
  5.4  The Harmonic Oscillator
  5.5  Anharmonic Oscillator
  5.6  Motion in the Central Force Field
  5.7  Second Virial Coefficient and Its Quantum Corrections
    5.7.1  The SVC and Its Relation to ThermodynamicProperties
    5.7.2  Calculation of the Classical SVC Be(T) for the(2 n - n)
-Potential
    5.7.3  Quantum Mechanical Corrections Bqt(T) andBq2 (T) of the
SVC
    5.7.4  Shape Dependence of the Boyle Temperature
    5.7.5  The High-Temperature Partition Function for Diatomic
Molecules
  5.8  Exercises
  5.9  Packages and Programs
    5.9.1  QuantumWell
    5.9.2  HarmonicOscillator
    5.9.3  AnharmonicOsciilator
    5.9.4  CentralField
6  General Relativity
  6.1  Introduction
  6.2  The Orbits in General Relativity
    6.2.1  Quasielliptic Orbits
    6.2.2  Asymptotic Circles
  6.3  Light Bending in the Gravitational Field
  6.4  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
  6.5  The Schwarzschild Solution
    6.5.1  The Schwarzschild Metric in Eddington-Finkelstein Form
    6.5.2  Dingle's Metric
    6.5.3  Schwarzschild Metric in Kruskal Coordinates
  6.6   The Reissner-Nordstrom Solution for a Charged Mass Point
  6.7   Exercises
  6.8   Packages and Programs
    6.8.1  EulerLagrange Equations
    6.8.2  PerihelionShift
    6.8.3  LightBending
7  Fractals
  7.1  Introduction
  7.2  Measuring a Borderline
    7.2.1  Box Counting
  7.3  The Koch Curve
  7.4  Multifractals
    7.4.1  Multifractals with Common Scaling Factor
  7.5  The Renormlization Group
  7.6  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
  7.7  Exercises
  7.8  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  Program Installation
  A.2  Glossary of Files and Functions
  A.3  Mathematica Functions
References
Index

章節(jié)摘錄

版權(quán)頁：插圖：The study of spectroscopic properties of single ions requires that one or two ions are trapped in a cavity. Nowadays, ions can be successfully separated and stored by means of ion traps. Two techniques are used for trapping ions. The first method uses a dynamic electric field, while the second method uses static electric and magnetic fields. The dynamic trap was originally invented by Paul [4.3]. The static trap is based on the work of Penning [4.4]. Both traps use a combination of electric and magnetic fields to confine ions in a certain volume in space. Two paraboloids connected to a dc-source determine the kind of electric field in which the ions are trapped. The form of the paraboloids in turn determines the field of the trap's interior, Since the motion of the ions in Paul's trap is very complicated, we restrict our study to the Penning trap.

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《理論物理中的Mathematica:電動力學,量子力學,廣義相對論和分形(第2版)(影印版)》為國外物理名著系列之一。

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