Cover -- Title page -- Copyright page -- Dedication -- 1 Introduction -- 2 Problem Solving -- 2.1 Analysis -- 2.2 Test-Taking Techniques -- 3 Scientific Programming -- 3.1 Language Fundamentals -- 4 Elementary Mathematics -- 4.1 Algebra -- 4.2 Geometry -- 4.3 Exponential, Logarithmic Functions, and Trigonometry -- 4.4 Analytic Geometry -- 5 Vectors and Matrices -- 5.1 Matrices and Matrix Products -- 5.2 Equation Systems -- 5.3 Traces and Determinants -- 5.4 Vectors and Inner Products -- 5.5 Cross and Outer Products -- 5.6 Vector Identities -- 5.7 Rotations and Orthogonal Matrices -- 5.8 Groups and Matrix Generators -- 5.9 Eigenvalues and Eigenvectors -- 5.10 Similarity Transformations -- 6 Calculus of a Single Variable -- 6.1 Derivatives -- 6.2 Integrals -- 6.3 Series -- 7 Calculus of Several Variables -- 7.1 Partial Derivatives -- 7.2 Multidimensional Taylor Series and Extrema -- 7.3 Multiple Integration -- 7.4 Volumes and Surfaces of Revolution -- 7.5 Change of Variables and Jacobians -- 8 Calculus of Vector Functions -- 8.1 Generalized Coordinates -- 8.2 Vector Differential Operators -- 8.3 Vector Differential Identities -- 8.4 Gauss's and Stokes' Laws and Green's Identities -- 8.5 Lagrange Multipliers -- 9 Probability Theory and Statistics -- 9.1 Random Variables, Probability Density, and Distributions -- 9.2 Mean, Variance, and Standard Deviation -- 9.3 Variable Transformations -- 9.4 Moments and Moment-Generating Function -- 9.5 Multivariate Probability Distributions, Covariance, and Correlation -- 9.6 Gaussian, Binomial, and Poisson Distributions -- 9.7 Least Squares Regression -- 9.8 Error Propagation -- 9.9 Numerical Models -- 10 Complex Analysis -- 10.1 Functions of a Complex Variable -- 10.2 Derivatives, Analyticity, and the Cauchy-Riemann Relations -- 10.3 Conformal Mapping -- 10.4 Cauchy's Theorem and Taylor and Laurent Series.

10.5 Residue Theorem -- 10.6 Dispersion Relations -- 10.7 Method of Steepest Decent -- 11 Differential Equations -- 11.1 Linearity, Superposition, and Initial and Boundary Values -- 11.2 Numerical Solutions -- 11.3 First-Order Differential Equations -- 11.4 Wronskian -- 11.5 Factorization -- 11.6 Method of Undetermined Coefficients -- 11.7 Variation of Parameters -- 11.8 Reduction of Order -- 11.9 Series Solution and Method of Frobenius -- 11.10 Systems of Equations, Eigenvalues, and Eigenvectors -- 12 Transform Theory -- 12.1 Eigenfunctions and Eigenvectors -- 12.2 Sturm-Liouville Theory -- 12.3 Fourier Series -- 12.4 Fourier Transforms -- 12.5 Delta Functions -- 12.6 Green's Functions -- 12.7 Laplace Transforms -- 12.8 z-Transforms -- 13 Partial Differential Equations and Special Functions -- 13.1 Separation of Variables and Rectangular Coordinates -- 13.2 Legendre Polynomials -- 13.3 Spherical Harmonics -- 13.4 Bessel Functions -- 13.5 Spherical Bessel Functions -- 14 Integral Equations and the Calculus of Variations -- 14.1 Volterra and Fredholm Equations -- 14.2 Calculus of Variations the Euler-Lagrange Equation -- 15 Particle Mechanics -- 15.1 Newton's Laws -- 15.2 Forces -- 15.3 Numerical Methods -- 15.4 Work and Energy -- 15.5 Lagrange Equations -- 15.6 Three-Dimensional Particle Motion -- 15.7 Impulse -- 15.8 Oscillatory Motion -- 15.9 Rotational Motion About a Fixed Axis -- 15.10 Torque and Angular Momentum -- 15.11 Motion in Accelerating Reference Systems -- 15.12 Gravitational Forces and Fields -- 15.13 Celestial Mechanics -- 15.14 Dynamics of Systems of Particles -- 15.15 Two-Particle Collisions and Scattering -- 15.16 Mechanics of Rigid Bodies -- 15.17 Hamilton's Equation and Kinematics -- 16 Fluid Mechanics -- 16.1 Continuity Equation -- 16.2 Euler's Equation -- 16.3 Bernoulli's Equation -- 17 Special Relativity.

17.1 Four-Vectors and Lorentz Transformation -- 17.2 Length Contraction, Time Dilation, and Simultaneity -- 17.3 Covariant Notation -- 17.4 Casuality and Minkowski Diagrams -- 17.5 Velocity Addition and Doppler Shift -- 17.6 Energy and Momentum -- 18 Electromagnetism -- 18.1 Maxwell's Equations -- 18.2 Gauss's Law -- 18.3 Electric Potential -- 18.4 Current and Resistivity -- 18.5 Dipoles and Polarization -- 18.6 Boundary Conditions and Green's Functions -- 18.7 Multipole Expansion -- 18.8 Relativistic Formulation of Electromagnetism, Gauge Transformations, and Magnetic Fields -- 18.9 Magnetostatics -- 18.10 Magnetic Dipoles -- 18.11 Magnetization -- 18.12 Induction and Faraday's Law -- 18.13 Circuit Theory and Kirchoff's Laws -- 18.14 Conservation Laws and the Stress Tensor -- 18.15 Lienard-Wiechert Potentials -- 18.16 Radiation from Moving Charges -- 19 Wave Motion -- 19.1 Wave Equation -- 19.2 Propagation of Waves -- 19.3 Planar Electromagnetic Waves -- 19.4 Polarization -- 19.5 Superposition and Interference -- 19.6 Multipole Expansion for Radiating Fields -- 19.7 Phase and Group Velocity -- 19.8 Minimum Time Principle and Ray Optics -- 19.9 Refraction and Snell's Law -- 19.10 Lenses -- 19.11 Mechanical Reflection -- 19.12 Doppler Effect and Shock Waves -- 19.13 Waves in Periodic Media -- 19.14 Conducting Media -- 19.15 Dielectric Media -- 19.16 Reflection and Transmission -- 19.17 Diffraction -- 19.18 Waveguides and Cavities -- 20 Quantum Mechanics -- 20.1 Fundamental Principles -- 20.2 Particle-Wave Duality -- 20.3 Interference of Quantum Waves -- 20.4 Schrödinger Equation -- 20.5 Particle Flux and Reflection -- 20.6 Wave Packet Propagation -- 20.7 Numerical Solutions -- 20.8 Quantum Mechanical Operators -- 20.9 Heisenberg Uncertainty Relation -- 20.10 Hilbert Space Representation -- 20.11 Square Well and Delta Function Potentials.

20.12 WKB Method -- 20.13 Harmonic Oscillators -- 20.14 Heisenberg Representation -- 20.15 Translation Operators -- 20.16 Perturbation Theory -- 20.17 Adiabatic Theorem -- 21 Atomic Physics -- 21.1 Properties of Fermions -- 21.2 Bohr Model -- 21.3 Atomic Spectra and X-Rays -- 21.4 Atomic Units -- 21.5 Angular Momentum -- 21.6 Spin -- 21.7 Interaction of Spins -- 21.8 Hydrogenic Atoms -- 21.9 Atomic Structure -- 21.10 Spin-Orbit Coupling -- 21.11 Atoms in Static Electric and Magnetic Fields -- 21.12 Helium Atom and the Molecule -- 21.13 Interaction of Atoms with Radiation -- 21.14 Selection Rules -- 21.15 Scattering Theory -- 22 Nuclear and Particle Physics -- 22.1 Nuclear Properties -- 22.2 Radioactive Decay -- 22.3 Nuclear Reactions -- 22.4 Fission and Fusion -- 22.5 Fundamental Properties of Elementary Particles -- 23 Thermodynamics and Statistical Mechanics -- 23.1 Entropy -- 23.2 Ensembles -- 23.3 Statistics -- 23.4 Partition Functions -- 23.5 Density of States -- 23.6 Temperature and Energy -- 23.7 Phonons and Photons -- 23.8 The Laws of Thermodynamics -- 23.9 The Legendre Transformation and Thermodynamic Quantities -- 23.10 Expansion of Gases -- 23.11 Heat engines and the Carnot Cycle -- 23.12 Thermodynamic Fluctuations -- 23.13 Phase Transformations -- 23.14 The Chemical Potential and Chemical Reactions -- 23.15 The Fermi Gas -- 23.16 Bose-Einstein Condensation -- 23.17 Physical Kinetics and Transport Theory -- 24 Condensed Matter Physics -- 24.1 Crystal Structure -- 24.2 X-Ray Diffraction -- 24.3 Thermal Properties -- 24.4 Electron Theory of Metals -- 24.5 Superconductors -- 24.6 Semiconductors -- 25 Laboratory Methods -- 25.1 Interaction of Particles with Matter -- 25.2 Radiation Detection and Counting Statistics -- 25.3 Lasers -- Index -- End User License Agreement.