MARC Record from marc_columbia

LEADER: 19217cam a2200649 i 4500
001 15329330
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008 190227s2018 vaua ob 001 0 eng d
035 $a(OCoLC)on1088554810
035 $a(NNC)15329330
040 $aKNOVL$beng$erda$epn$cKNOVL$dDKU$dVLB$dOCLCQ$dOCLCO
020 $a9781523120314$q(electronic bk.)
020 $a1523120312$q(electronic bk.)
020 $z9781683920984
020 $z1683920988
035 $a(OCoLC)1088554810
050 4 $aQC20$b.C53 2018eb
082 04 $a530.15$223
049 $aZCUA
100 1 $aClaycomb, J. R.,$eauthor.
245 10 $aMathematical methods for physics :$busing MATLAB & Maple /$cJames R. Claycomb.
264 1 $aDulles, Virginia :$bMercury Learning & Information,$c[2018]
264 4 $c©2018
300 $a1 online resource (xx, 820 pages)
300 $a1 online resource (1 CD-ROM (4 3/4 in.)
336 $atext$btxt$2rdacontent
337 $acomputer$bc$2rdamedia
338 $aonline resource$bcr$2rdacarrier
504 $aIncludes bibliographical references and index.
505 0 $aMachine generated contents note: 1.1. Algebra -- 1.1.1. Systems of Equations -- 1.1.2.Completing the Square -- 1.1.3.Common Denominator -- 1.1.4. Partial Fractions Decomposition -- 1.1.5. Inverse Functions -- 1.1.6. Exponential and Logarithmic Equations -- 1.1.7. Logarithms of Powers, Products and Ratios -- 1.1.8. Radioactive Decay -- 1.1.9. Transcendental Equations -- 1.1.10. Even and Odd Functions -- 1.1.11. Examples in Maple -- 1.2. Trigonometry -- 1.2.1. Polar Coordinates -- 1.2.2.Common Identities -- 1.2.3. Law of Cosines -- 1.2.4. Systems of Equations -- 1.2.5. Transcendental Equations -- 1.3.Complex Numbers -- 1.3.1.Complex Roots -- 1.3.2.Complex Arithmetic -- 1.3.3.Complex Conjugate -- 1.3.4. Euler's Formula -- 1.3.5.Complex Plane -- 1.3.6. Polar Form of Complex Numbers -- 1.3.7. Powers of Complex Numbers -- 1.3.8. Hyperbolic Functions -- 1.4. Elements of Calculus -- 1.4.1. Derivatives -- 1.4.2. Prime and Dot Notation -- 1.4.3. Chain Rule for Derivatives
505 0 $aNote continued: 1.4.4. Product Rule for Derivatives -- 1.4.5. Quotient Rule for Derivatives -- 1.4.6. Indefinite Integrals -- 1.4.7. Definite Integrals -- 1.4.8.Common Integrals and Derivatives -- 1.4.9. Derivatives of Trigonometric and Hyperbolic Functions -- 1.4.10. Euler's Formula -- 1.4.11. Integrals of Trigonometric and Hyperbolic Functions -- 1.4.12. Improper Integrals -- 1.4.13. Integrals of Even and Odd Functions -- 1.5. MATLAB Examples -- 1.5.1. Functional Calculator -- 1.6. Exercises -- 2.1. Vectors and Scalars in Physics -- 2.1.1. Vector Addition and Unit Vectors -- 2.1.2. Scalar Product of Vectors -- 2.1.3. Vector Cross Product -- 2.1.4. Triple Vector Products -- 2.1.5. The Position Vector -- 2.1.6. Expressing Vectors in Different Coordinate Systems -- 2.2. Matrices in Physics -- 2.2.1. Matrix Dimension -- 2.2.2. Matrix Addition and Subtraction -- 2.2.3. Matrix Integration and Differentiation -- 2.2.4. Matrix Multiplication and Commutation -- 2.2.5. Direct Product
505 0 $aNote continued: 2.2.6. Identity Matrix -- 2.2.7. Transpose of a Matrix -- 2.2.8. Symmetric and Antisymmetric Matrices -- 2.2.9. Diagonal Matrix -- 2.2.10. Tridiagonal Matrix -- 2.2.11. Orthogonal Matrices -- 2.2.12.Complex Conjugate of a Matrix -- 2.2.13. Matrix Adjoint (Hermitian Conjugate) -- 2.2.14. Unitary Matrix -- 2.2.15. Partitioned Matrix -- 2.2.16. Matrix Trace -- 2.2.17. Matrix Exponentiation -- 2.3. Matrix Determinant and Inverse -- 2.3.1. Matrix Inverse -- 2.3.2. Singular Matrices -- 2.3.3. Systems of Equations -- 2.4. Eigenvalues and Eigenvectors -- 2.4.1. Matrix Diagonalization -- 2.5. Rotation Matrices -- 2.5.1. Rotations in Two Dimensions -- 2.5.2. Rotations in Three Dimensions -- 2.5.3. Infinitesimal Rotations -- 2.6. MATLAB Examples -- 2.7. Exercises -- 3.1. Single-Variable Calculus -- 3.1.1. Critical Points -- 3.1.2. Integration with Substitution -- 3.1.3. Work-Energy Theorem -- 3.1.4. Integration by Parts -- 3.1.5. Integration with Partial Fractions
505 0 $aNote continued: 3.1.6. Integration by Trig Substitution -- 3.1.7. Differentiating Across the Integral Sign -- 3.1.8. Integrals of Logarithmic Functions -- 3.2. Multivariable Calculus -- 3.2.1. Partial Derivatives -- 3.2.2. Critical Points -- 3.2.3. Double Integrals -- 3.2.4. Triple Integrals -- 3.2.5. Orthogonal Coordinate Systems -- 3.2.6. Cartesian Coordinates -- 3.2.7. Cylindrical Coordinates -- 3.2.8. Spherical Coordinates -- 3.2.9. Line, Volume, and Surface Elements -- 3.3. Gaussian Integrals -- 3.3.1. Error Functions -- 3.4. Series and Approximations -- 3.4.1. Geometric Series -- 3.4.2. Taylor Series -- 3.4.3. Maclaurin Series -- 3.4.4. Index Labels -- 3.4.5. Convergence of Series -- 3.4.6. Ratio Test -- 3.4.7. Integral Test -- 3.4.8. Binomial Theorem -- 3.4.9. Binomial Approximations -- 3.5. Special Integrals -- 3.5.1. Integral Functions -- 3.5.2. Elliptic Integrals -- 3.5.3. Gamma Functions -- 3.5.4. Riemann Zeta Function -- 3.5.5. Writing Integrals in Dimensionless Form
505 0 $aNote continued: 3.5.6. Black-Body Radiation -- 3.6. MATLAB Examples -- 3.7. Exercises -- 4.1. Vector and Scalar Fields -- 4.1.1. Scalar Fields -- 4.1.2. Vector Fields -- 4.1.3. Field Lines -- 4.2. Gradient of Scalar Fields -- 4.2.1. Gradient in Cartesian Coordinates -- 4.2.2. Unit Normal -- 4.2.3. Gradient in Curvilinear Coordinates -- 4.2.4. Cylindrical Coordinates -- 4.2.5. Spherical Coordinates -- 4.2.6. Scalar Field from the Gradient -- 4.3. Divergence of Vector Fields -- 4.3.1. Flux through a Surface -- 4.3.2. Divergence of a Vector Field -- 4.3.3. Gradient in Curvilinear Coordinates -- 4.3.4. Cylindrical Coordinates -- 4.3.5. Spherical Coordinates -- 4.4. Curl of Vector Fields -- 4.4.1. Line Integral -- 4.4.2. Curl of a Vector Field -- 4.4.3. Curl in Cartesian Coordinates -- 4.4.4. Curl in Curvilinear Coordinates -- 4.4.5. Cylindrical Coordinates -- 4.4.6. Spherical Coordinates -- 4.4.7. Vector Potential -- 4.5. Laplacian of Scalar and Vector Fields
505 0 $aNote continued: 4.5.1. Laplacian in Curvilinear Coordinates -- 4.5.2. Cylindrical Coordinates -- 4.5.3. Spherical Coordinates -- 4.5.4. The Vector Laplacian -- 4.6. Vector Identities -- 4.6.1. First Derivatives -- 4.6.2. First Derivatives of Products -- 4.6.3. Second Derivatives -- 4.6.4. Vector Laplacian -- 4.7. Integral Theorems -- 4.7.1. Gradient Theorem -- 4.7.2. Divergence Theorem -- 4.7.3. Cartesian Coordinates -- 4.7.4. Cylindrical Coordinates -- 4.7.5. Stokes's Curl Theorem -- 4.7.6. Navier-Stokes Equation -- 4.8. MATLAB Examples -- 4.9. Exercises -- 5.1. Classification of Differential Equations -- 5.1.1. Order -- 5.1.2. Degree -- 5.1.3. Solution by Direct Integration -- 5.1.4. Exact Differential Equations -- 5.1.5. Sturm-Liouville Form -- 5.2. First Order Differential Equations -- 5.2.1. Homogeneous Equations -- 5.2.2. Inhomogeneous Equations -- 5.3. Linear, Homogeneous with Constant Coefficients -- 5.3.1. Damped Harmonic Oscillator -- 5.3.2. Undamped Motion
505 0 $aNote continued: 5.3.3. Overdamped Motion -- 5.3.4. Underdamped Motion -- 5.3.5. Critically Damped Oscillator -- 5.3.6. Higher Order Differential Equations -- 5.4. Linear Independence -- 5.4.1. Wronskian Determinant -- 5.5. Inhomogeneous with Constant Coefficients -- 5.6. Power Series Solutions to Differential Solutions -- 5.6.1. Standard Form -- 5.6.2. Airy's Differential Equation -- 5.6.3. Hermite's Differential Equation -- 5.6.4. Singular Points -- 5.6.5. Bessel's Differential Equation -- 5.6.6. Legendre's Differential Equation -- 5.7. Systems of Differential Equations -- 5.7.1. Homogeneous Systems -- 5.7.2. Inhomogeneous Systems -- 5.7.3. Solution Vectors -- 5.7.4. Test for Linear Independence -- 5.7.5. General Solution of Homogeneous Systems -- 5.7.7. Charged Particle in Electric and Magnetic Fields -- 5.8. Phase Space -- 5.8.1. Phase Plots -- 5.8.2. Noncrossing Property -- 5.8.3. Autonomous Systems -- 5.8.4. Phase Space Volume -- 5.9. Nonlinear Differential Equations
505 0 $aNote continued: 5.9.1. Predator-Prey System -- 5.9.2. Fixed Points -- 5.9.3. Linearization -- 5.9.4. Simple Pendulum -- 5.9.5. Numerical Solution -- 5.10. MATLAB Examples -- 5.11. Exercises -- 6.1. Dirac Delta Function -- 6.1.1. Representations of the Delta Function -- 6.1.2. Delta Function in Higher Dimensions -- 6.1.3. Delta Function in Spherical Coordinates -- 6.1.4. Poisson's Equation -- 6.1.5. Differential Form of Gauss's Law -- 6.1.6. Heaviside Step Function -- 6.2. Orthogonal Functions -- 6.2.1. Expansions in Orthogonal Functions -- 6.2.2.Completeness Relation -- 6.3. Legendre Polynomials -- 6.3.1. Associated Legendre Polynomials -- 6.3.2. Rodrigues' Formulas -- 6.3.3. Generating Functions -- 6.3.4. Orthogonality Relations -- 6.3.5. Spherical Harmonics -- 6.4. Laguerre Polynomials -- 6.4.1. Rodrigues' Formula -- 6.4.2. Generating Function -- 6.4.3. Orthogonality Relations -- 6.5. Hermite Polynomials -- 6.5.1. Rodrigues' Formula -- 6.5.2. Generating Function
505 0 $aNote continued: 6.5.4. Orthogonality -- 6.6. Bessel Functions -- 6.6.1. Modified Bessel Functions -- 6.6.2. Generating Function -- 6.6.3. Spherical Bessel Functions -- 6.6.4. Rayleigh Formulas -- 6.6.5. Generating Functions -- 6.6.6. Useful Relations -- 6.7. MATLAB Examples -- 6.8. Exercises -- 7.1. Fourier Series -- 7.1.1. Fourier Cosine Series -- 7.1.2. Fourier Sine Series -- 7.1.3. Fourier Exponential Series -- 7.2. Fourier Transforms -- 7.2.1. Power Spectrum -- 7.2.2. Spatial Transforms -- 7.3. Laplace Transforms -- 7.3.1. Properties of the Laplace Transform -- 7.3.2. Inverse Laplace Transform -- 7.3.3. Properties of Inverse Laplace Transforms -- 7.3.4. Table of Laplace Transforms -- 7.3.5. Solving Differential Equations -- 7.4. MATLAB Examples -- 7.5. Exercises -- 8.1. Types of Partial Differential Equations -- 8.1.1. First Order PDEs -- 8.1.2. Second Order PDEs -- 8.1.3. Laplace's Equation -- 8.1.4. Poisson's Equation -- 8.1.5. Diffusion Equation -- 8.1.6. Wave Equation
505 0 $aNote continued: 8.1.7. Helmholtz Equation -- 8.1.8. Klein-Gordon Equation -- 8.2. The Heat Equation -- 8.2.1. Transient Heat Flow -- 8.2.2. Steady State Heat Flow -- 8.2.3. Laplace Transform Solution -- 8.3. Separation of Variables -- 8.3.1. The Heat Equation -- 8.3.2. Laplace's Equation in Cartesian Coordinates -- 8.3.3. Laplace's Equation in Cylindrical Coordinates -- 8.3.4. Wave Equation -- 8.3.5. Helmholtz Equation in Cylindrical Coordinates -- 8.3.6. Helmholtz Equation in Spherical Coordinates -- 8.4. MATLAB Examples -- 8.5. Exercises -- 9.1. Cauchy-Riemann Equations -- 9.1. Laplace's Equation -- 9.2. Integral Theorems -- 9.2.1. Cauchy's Integral Theorem -- 9.2.2. Cauchy's Integral Formula -- 9.2.3. Laurent Series Expansion -- 9.2.4. Types of Singularities -- 9.2.5. Residues -- 9.2.6. Residue Theorem -- 9.2.7. Improper Integrals -- 9.2.8. Fourier Transform Integrals -- 9.3. Conformal Mapping -- 9.3.1. Poisson's Integral Formulas
505 0 $aNote continued: 9.3.2. Schwarz-Christoffel Transformation -- 9.3.3. Conformal Mapping -- 9.3.4. Mappings on the Riemann Sphere -- 9.4. MATLAB Examples -- 9.5. Exercises -- 10.1. Velocity-Dependent Resistive Forces -- 10.1.1. Drag Force Proportional to the Velocity -- 10.1.2. Drag Force on a Falling Body -- 10.2. Variable Mass Dynamics -- 10.2.1. Rocket Motion -- 10.3. Lagrangian Dynamics -- 10.3.1. Calculus of Variations -- 10.3.2. Lagrange's Equations of Motion -- 10.3.3. Lagrange's Equations with Constraints -- 10.4. Hamiltonian Mechanics -- 10.4.1. Legendre Transformation -- 10.4.2. Hamilton's Equations of Motion -- 10.4.3. Poisson Brackets -- 10.5. Orbital and Periodic Motion -- 10.5.1. Kepler Problem -- 10.5.2. Periodic Motion -- 10.5.3. Small Oscillations -- 10.6. Chaotic Dynamics -- 10.6.1. Strange Attractors -- 10.6.2. Lorenz Model -- 10.6.3. Jerk Systems -- 10.6.4. Time Delay Coordinates -- 10.6.5. Lyapunov Exponents -- 10.6.6. Poincare Sections -- 10.7. Fractals
505 0 $aNote continued: 10.7.1. Cantor Set -- 10.7.2. Koch Snowflake -- 10.7.3. Mandelbrot Set -- 10.7.4. Fractal Dimension -- 10.7.5. Chaotic Maps -- 10.8. MATLAB Examples -- 10.9. Exercises -- 11.1. Electrostatics in 1D -- 11.1.1. Integral and Differential Forms of Gauss's Law -- 11.1.2. Laplace's Equation in 1D -- 11.1.3. Poisson's Equation in 1D -- 11.2. Laplace's Equation in Cartesian Coordinates -- 11.2.1.3D Cartesian Coordinates -- 11.2.2. Method of Images -- 11.3. Laplace's Equation in Cylindrical Coordinates -- 11.3.1. Potentials with Planar Symmetry -- 11.3.2. Potentials in 3D Cylindrical Coordinates -- 11.4. Laplace's Equation in Spherical Coordinates -- 11.4.1. Axially Symmetric Potentials -- 11.4.2.3D Spherical Coordinates -- 11.5. Multipole Expansion of Potential -- 11.5.1. Axially Symmetric Potentials -- 11.5.2. Off-Axis Trick -- 11.5.3. Asymmetric Potentials -- 11.6. Electricity and Magnetism -- 11.6.1.Comparison of Electrostatics and Magnetostatics
505 0 $aNote continued: 11.6.2. Electrostatic Examples -- 11.6.3. Magnetostatic Examples -- 11.6.4. Static Electric and Magnetic Fields in Matter -- 11.6.5. Examples: Electrostatic Fields in Matter -- 11.6.6. Examples: Magnetic Fields in Matter -- 11.7. Scalar Electric and Magnetic Potentials -- 11.8. Time-Dependent Fields -- 11.8.1. The Ampere-Maxwell Equation -- 11.8.2. Maxwell's Equations -- 11.8.3. Self-Inductance -- 11.8.4. Mutual Inductance -- 11.8.5. Maxwell's Wave Equations -- 11.8.6. Maxwell's Equations in Matter -- 11.8.7. Time Harmonic Maxwell's Equations -- 11.8.8. Magnetic Monopoles -- 11.9. Radiation -- 11.9.1. Poynting Vector -- 11.9.2. Inhomogeneous Wave Equations -- 11.9.3. Gauge Transformation -- 11.9.4. Radiation Potential Formulation -- 11.9.5. The Hertz Dipole Antenna -- 11.10. MATLAB Examples -- 11.11. Exercises -- 12.1. Schrodinger Equation -- 12.1.1. Time-Dependent Schrodinger Equation -- 12.1.2. Time-Independent Schrodinger Equation
505 0 $aNote continued: 12.1.3. Operators, Expectation Values and Uncertainty -- 12.1.4. Probability Current Density -- 12.2. Bound States I -- 12.2.1. Particle in a Box -- 12.2.2. Semi-Infinite Square Well -- 12.2.3. Square Well with a Step -- 12.3. Bound States II -- 12.3.1. Delta Function Potential -- 12.3.2. Quantum Bouncer -- 12.3.3. Harmonic Oscillator -- 12.3.4. Operator Notation -- 12.3.5. Excited States of the Harmonic Oscillator -- 12.4. Schrodinger Equation in Higher Dimensions -- 12.4.1. Particle in a 3D Box -- 12.4.2. Schrodinger Equation in Spherical Coordinates -- 12.4.3. Radial Equation -- 12.4.4. Hydrogen Radial Wavefunctions -- 12.5. Approximation Methods -- 12.5.1. WKB Approximation -- 12.5.2. Time-Independent Perturbation Theory -- 12.5.3. Degenerate Perturbation Theory -- 12.5.4. Stark Effect -- 12.6. MATLAB Examples -- 12.7. Exercises -- 13.1. Microcanonical Ensemble -- 13.1.1. Number of Microstates and the Entropy -- 13.2. Canonical Ensemble
505 0 $aNote continued: 13.2.1. Boltzmann Factor and Partition Function -- 13.2.2. Average Energy -- 13.2.3. Free Energy and Entropy -- 13.2.4. Specific Heat -- 13.2.5. Rigid Rotator -- 13.2.6. Harmonic Oscillator -- 13.2.7.Composite Systems -- 13.2.8. Stretching a Rubber Band -- 13.3. Continuous Energy Distributions -- 13.3.1. Partition Function and Average Energy -- 13.3.2. Particle in a Box -- 13.3.3. Maxwell-Boltzmann Distribution -- 13.3.4. Relativistic Gas -- 13.4. Grand Canonical Ensemble -- 13.4.1. Gibbs Factor -- 13.4.2. Average Energy and Particle Number -- 13.4.3. Single Species -- 13.4.4. Grand Potential -- 13.4.5.Comparison of Canonical and Grand Canonical Ensembles -- 13.4.6. Bose-Einstein Statistics -- 13.4.7. Black-Body Radiation -- 13.4.8. Debye Theory of Specific Heat -- 13.4.9. Fermi-Dirac Statistics -- 13.5. MATLAB Examples -- 13.6. Exercises -- 14.1. Kinematics -- 14.1.1. Postulates of Special Relativity -- 14.1.2. Time Dilatation -- 14.1.3. Length Contraction
505 0 $aNote continued: 14.1.4. Relativistic Doppler Effect -- 14.1.5. Galilean Transformation -- 14.1.6. Lorentz Transformations -- 14.1.7. Relativistic Addition of Velocities -- 14.1.8. Velocity Addition Approximation -- 14.1.9.4-Vector Notation -- 14.2. Energy and Momentum -- 14.2.1. Newton's Second Law -- 14.2.2. Mass Energy and Kinetic Energy -- 14.2.3. Low Velocity Approximation -- 14.2.4. Energy Momentum Relation -- 14.2.5.Completely Inelastic Collisions -- 14.2.6. Particle Decay -- 14.2.7. Energy Units -- 14.3. Electromagnetics in Relativity -- 14.3.1. Relativistic Transformation of Fields -- 14.3.2. Covariant Formulation of Maxwell's Equations -- 14.3.3. Homogeneous Maxwell Equations -- 14.3.4. Lorentz Force Equation -- 14.4. Relativistic Lagrangian Formulation -- 14.4.1. Lagrangian of a Free Particle -- 14.4.2. Relativistic 1D Harmonic Oscillator -- 14.4.3. Charged Particle in Electric and Magnetic Fields -- 14.5. MATLAB Examples -- 14.6. Exercises
505 0 $aNote continued: 15.1. The Equivalence Principle -- 15.1.1. Classical Approximation to Gravitational Redshift -- 15.1.2. Photon Emitted from a Spherical Star -- 15.1.3. Gravitational Time Dilation -- 15.1.4.Comparison of Time Dilation Factors -- 15.2. Tensor Calculus -- 15.2.1. Tensor Notation -- 15.2.2. Line Element and Spacetime Interval -- 15.2.3. Raising and Lowering Indices -- 15.2.4. Metric Tensor in Spherical Coordinates -- 15.2.5. Dot Product -- 15.2.6. Cross Product -- 15.2.7. Transformation Properties of Tensors -- 15.2.8. Quotient Rule for Tensors -- 15.2.9. Covariant Derivatives -- 15.3. Einstein's Equations -- 15.3.1. Geodesic Equations of Motion -- 15.3.2. Alternative Lagrangian -- 15.3.3. Riemann Curvature Tensor -- 15.3.4. Ricci Tensor -- 15.3.5. Ricci Scalar -- 15.3.6. Einstein Tensor -- 15.3.7. Einstein's Field Equations -- 15.3.8. Friedman Cosmology -- 15.3.9. Killing Vectors -- 15.4. MATLAB Examples -- 15.5. Exercises -- 16.1. Early Models -- 16.1.1.de Broglie waves
505 0 $aNote continued: 16.1.2. Klein-Gordon Equation -- 16.1.3. Probability Current Density -- 16.1.4. Lagrangian Formulation of the Klein-Gordon Equation -- 16.2. Dirac Equation -- 16.2.1. Derivation of a First Order Equation -- 16.2.2. Probability Current -- 16.2.3. Gamma Matrices -- 16.2.4. Positive and Negative Energies -- 16.2.5. Lagrangian Formulation of the Dirac Equation -- 16.3. Solutions to the Dirac Equation -- 16.3.1. Plane Wave Solutions -- 16.3.2. Nonplane Wave Solutions -- 16.3.3. Nonrelativistic Limit -- 16.3.4. Dirac Equation in an Electromagnetic Field -- 16.4. MATLAB Examples -- 16.5. Exercises.
588 0 $aPrint version record.
650 0 $aMathematical physics.
650 6 $aPhysique mathématique.
650 7 $aMathematical physics.$2fast$0(OCoLC)fst01012104
655 4 $aElectronic books.
776 08 $iPrint version:$aClaycomb, J.R.$tMathematical methods for physics.$dDulles, Virginia : Mercury Learning & Information, [2018]$z9781683920984$w(OCoLC)1033527720
856 40 $uhttp://www.columbia.edu/cgi-bin/cul/resolve?clio15329330$zACADEMIC - General Engineering & Project Administration
852 8 $blweb$hEBOOKS