Frank Y. Wang. Physics with MAPLE. The Computer Algebra Resource for Mathematical Methods in Physics. WILEY- VCH WILEY-VCH Verlag GmbH & Co.
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1 Frank Y. Wang Physics with MAPLE The Computer Algebra Resource for Mathematical Methods in Physics WILEY- VCH WILEY-VCH Verlag GmbH & Co. KGaA
2 k Preface Guide for Users Bibliography XI XVII XIX 1 Introduction Overview Basic Algebra and Solving Equations Calculus Differential Equations Exact Solutions Special Functions Numerical Solutions Vectors and Matrices Summary 36 2 Oscillatory Motion Simple Harmonie Oscillator Damped Oscillation Overdamping Underdamping Critical Damping Sinusoidally Driven Oscillation Phase Space 60 3 Calculus of Variations Euler-Lagrange Equation Mathematical Examples Symmetry Properties Principle of Least Action Systems with Many Degrees of Freedom Force of Constraint 89 Pkysics with Maple : The Computer Algebra Resourcefor Mathematical Methods in Physics. Frank Y. Wang Copyright 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN:
3 4 Integration of Equations of Motion Linearization of Equations Double Pendulum Central-force Problem Kepler Problem Correction Terms Motion of a Symmetrie Top Nonlinear Oscillation and Chaos Summary of Lagrangian Mechanics Orthogonal Functions and Expansions Fourier Series Fourier Integrals Orthogonal Functions in Complete Sets Legendre Polynomials Generating Function and Rodrigues Formula Bessel Functions Summary of Special Functions Electrostatics Coulomb'sLaw Curvilinear Coordinates Spherical Coordinates Cylindrical Coordinates Differential Vector Calculus Electric Potential Cavendish's Apparatus for the Inverse Square Law Multipole Expansion Electric Field and Equipotential Boundary-value Problems Theoryof Potential Method of Images Complex-variable Techniques Laplace Equation in Cartesian Coordinates Laplace Equation in Spherical Coordinates Laplace Equation in Cylindrical Coordinates Summary Magnetostatics Magnetic Forces Biot-Savart Law Vector Potential Force and Torque on Magnetic Dipoles Summary of Electromagnetism in Static Conditions 253
4 i VII 9 Electric Circuits Resistors in Series and in Parallel Kirchhoff's Rules Direct-current Circuits RC Circuit RL Circuit RLC Circuit Lissajous Figures Alternating-current Circuits Impedance Bridges Waves WaveEquation Vibrating String Sinusoidal Waves in Linear Combinations Complex Notation Fourier Integrals Uncertainty Principle Gaussian Wave Packet Two-dimensional Circular Membrane Electromagnetic Waves Electric-dipole Radiation Synchrotron Radiation Physical Optics Light as an Electromagnetic Wave Polarization Mathematics of Interference Interference Double-slit Interference Multiple-slit Interference Diffraction Resolution of Single Slits and Circular Apertures Diffraction Gräting Fourier Transform Spectrometry Fresnel Diffraction Special Relativity Lorentz Transformation Length Contraction and Time Dilation Addition of Velocity Doppler Shift Relativistic Kinematics and Dynamics Transformations of Electromagnetic Fields 373
5 VIII 13 Quantum Phenomena Blackbody Radiation Photoelectric and Compton Effects Wave-Particle Duality Bohr Model ofthehydrogen Atom Dielectrics and Paramagnetism Schrödinger Equation in One Dimension (I): Unbound States Formulation of Quantum Mechanics Zero Potential and Plane Waves Step Potential Step Potential (E > V 0 ) Step Potential (E < V 0 ) Barrier Potential Barrier Potential (E > V 0 ) Barrier Potential (E <V 0 ) Summary of Stationary States Wave Packet Reflectionof Wave Packet Schrödinger Equation in One Dimension (II): Bound States Discrete Spectrum Infinite Potential Well Finite Potential Well Series Solution and Hermite Equation Linear Harmonie Oscillator Homogeneous Field Morse Potential Bound Nonstationary States Two-state System Schrödinger Equation in Three Dimensions Central-force Problem Spherical Harmonics Angular Momentum Coulomb Potential HydrogenAtom Electric Potential Due to the Electron Hybrid Bond Orbitals Infinite Spherical Well Quantum Statistics Statistical Distributions Maxwell-Boltzmann Statistics 512
6 fc IX 17.3 Ideal Böse Gas Low Density and Virial Expansion Bose-Einstein Condensation at Low Temperature Ideal Fermi Gas Low Density and Virial Expansion Specific Heat of a Metal at Low Temperature Relativistic Gases General Relativity Basic Formulation Newtonian Limit Gravitational Redshift Schwarzschild Solution Robertson-Walker Metrie 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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