Physics with MAPLE : The Computer Algebra Resource for Mathematical Methods in Physics


Frank Y. Wang
Bok Engelsk 2008 · Electronic books.
Utgitt
Hoboken : : Wiley, , 2008.
Omfang
1 online resource (627 p.)
Opplysninger
Description based upon print version of record.. - Physics with MapleTM The Computer Algebra Resource for Mathematical Methods in Physics; Contents; Preface; Guide for Users; Bibliography; 1 Introduction; 1.1 Overview; 1.2 Basic Algebra and Solving Equations; 1.3 Calculus; 1.4 Differential Equations; 1.4.1 Exact Solutions; 1.4.2 Special Functions; 1.4.3 Numerical Solutions; 1.5 Vectors and Matrices; 1.6 Summary; 2 Oscillatory Motion; 2.1 Simple Harmonic Oscillator; 2.2 Damped Oscillation; 2.2.1 Overdamping; 2.2.2 Underdamping; 2.2.3 Critical Damping; 2.3 Sinusoidally Driven Oscillation; 2.4 Phase Space; 3 Calculus of Variations. - 10.3 Sinusoidal Waves in Linear Combinations10.3.1 Complex Notation; 10.3.2 Fourier Integrals; 10.3.3 Uncertainty Principle; 10.4 Gaussian Wave Packet; 10.5 Two-dimensional Circular Membrane; 10.6 Electromagnetic Waves; 10.6.1 Electric-dipole Radiation; 10.6.2 Synchrotron Radiation; 11 Physical Optics; 11.1 Lightas an Electromagnetic Wave; 11.1.1 Polarization; 11.2 Mathematics of Interference; 11.3 Interference; 11.3.1 Double-slit Interference; 11.3.2 Multiple-slit Interference; 11.4 Diffraction; 11.4.1 Resolution of Single Slits and Circular Apertures; 11.5 Diffraction Grating. - 11.6 Fourier Transform Spectrometry. - 3.1 Euler-Lagrange Equation3.2 Mathematical Examples; 3.3 Symmetry Properties; 3.4 Principle of Least Action; 3.5 Systems with Many Degrees of Freedom; 3.6 Force of Constraint; 4 Integration of Equations of Motion; 4.1 Linearization of Equations; 4.2 Double Pendulum; 4.3 Central-force Problem; 4.3.1 Kepler Problem; 4.3.2 CorrectionTerms; 4.4 Motion of a SymmetricTop; 4.5 Nonlinear Oscillation and Chaos; 4.6 Summary of Lagrangian Mechanics; 5 Orthogonal Functions and Expansions; 5.1 Fourier Series; 5.2 Fourier Integrals; 5.3 Orthogonal Functions in Complete Sets; 5.4 Legendre Polynomials. - 5.4.1 Generating Function and Rodrigues Formula5.5 Bessel Functions; 5.6 Summary of Special Functions; 6 Electrostatics; 6.1 Coulomb'sLaw; 6.2 Curvilinear Coordinates; 6.2.1 Spherical Coordinates; 6.2.2 Cylindrical Coordinates; 6.3 Differential Vector Calculus; 6.4 Electric Potential; 6.4.1 Cavendish's Apparatus for the Inverse Square Law; 6.4.2 Multipole Expansion; 6.5 Electric Field and Equipotential; 7 Boundary-value Problems; 7.1 Theory of Potential; 7.2 Method of Images; 7.3 Complex-variable Techniques; 7.4 Laplace Equation in Cartesian Coordinates. - 7.5 Laplace Equation in Spherical Coordinates7.6 Laplace Equation in Cylindrical Coordinates; 7.7 Summary; 8 Magnetostatics; 8.1 Magnetic Forces; 8.2 Biot-Savart Law; 8.3 Vector Potential; 8.4 Force and Torque on Magnetic Dipoles; 8.5 Summary of Electromagnetism in Static Conditions; 9 Electric Circuits; 9.1 Resistors in Series and in Parallel; 9.2 Kirchhoff's Rules; 9.3 Direct-current Circuits; 9.3.1 RC Circuit; 9.3.2 RL Circuit; 9.3.3 RLC Circuit; 9.3.4 Lissajous Figures; 9.4 Alternating-current Circuits; 9.4.1 Impedance; 9.4.2 Bridges; 10 Waves; 10.1 Wave Equation; 10.2 Vibrating String. - Written by an experienced physicist who is active in applying computer algebra to relativistic astrophysics and education, this is the resource for mathematical methods in physics using MapleTM and MathematicaTM. Through in-depth problems from core courses in the physics curriculum, the author guides students to apply analytical and numerical techniques in mathematical physics, and present the results in interactive graphics. Around 180 simulating exercises are included to facilitate learning by examples. This book is a must-have for students of physics, electrical and mechanical engineer
Emner
Sjanger
Dewey
ISBN
3527406409. - 9783527406401

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