Theoretical Physics: Applications of Vectors, Matrices, Tensors and Quaternions

Cover......Page __sk_0000.djvu
Copyright......Page __sk_0002.djvu
Contents......Page __sk_0007.djvu
Preface......Page __sk_0005.djvu
1.1 Elementary Properties of Vectors......Page __sk_0013.djvu
1.2 Scalar Product......Page __sk_0016.djvu
1.3 Vector Product......Page __sk_0017.djvu
1.5 Geometrical Applications......Page __sk_0018.djvu
1.6 Linear Dependence and Representation of Vectors......Page __sk_0021.djvu
1.7 The Schmidt Orthonormalization Process......Page __sk_0024.djvu
Examples......Page __sk_0025.djvu
Problems......Page __sk_0029.djvu
2.1 Groups, Rings, Fields......Page __sk_0031.djvu
2.2 Solvability and Number Concept Extension......Page __sk_0032.djvu
2.3 Vector Spaces......Page __sk_0035.djvu
Examples......Page __sk_0036.djvu
Problems......Page __sk_0040.djvu
3.1 Matrices......Page __sk_0041.djvu
3.2 Inverse Matrix......Page __sk_0045.djvu
3.3 Theorem of Alternatives......Page __sk_0050.djvu
3.4 Excess Variables and Excess Equations......Page __sk_0052.djvu
3.5 Dyadic and Tensor Operators......Page __sk_0053.djvu
3.6 Vector Transforms; Unitary and Hermitian Matrices......Page __sk_0058.djvu
3.8 Diagonalization of Hermitian Matrices......Page __sk_0060.djvu
3.9 Principal Axis Transformation......Page __sk_0063.djvu
3.10 Degeneracy......Page __sk_0064.djvu
Examples......Page __sk_0066.djvu
Problems......Page __sk_0070.djvu
4.1 Distance and Angle in Function Space......Page __sk_0072.djvu
4.2 Fundamental Inequalities......Page __sk_0075.djvu
4.3 Orthonormal Sets of Functions......Page __sk_0076.djvu
4.4 Integral Equations: Fredholm Approach......Page __sk_0077.djvu
4.5 Integral Equations: Hilbert-Schmidt Approach......Page __sk_0082.djvu
4.6 Unitary Integral Transforms......Page __sk_0086.djvu
4.7 Coupled Oscillators......Page __sk_0088.djvu
4.8 Normal Coordinates......Page __sk_0090.djvu
4.9 Unitary Transformations of Eigenvectors......Page __sk_0091.djvu
4.10 Hilbert Space......Page __sk_0093.djvu
Examples......Page __sk_0094.djvu
Problems......Page __sk_0096.djvu
5.1 Differentiation and Integration of Vectors......Page __sk_0098.djvu
5.2 Differential Geometry of Space Curves and Surfaces......Page __sk_0101.djvu
5.3 Gradient......Page __sk_0110.djvu
5.4 Divergence and Laplacian......Page __sk_0113.djvu
5.5 Curl......Page __sk_0119.djvu
5.6 Vector Fields and Helmholtz's Theorem......Page __sk_0123.djvu
5.7 Multiple Integration and Jacobian......Page __sk_0125.djvu
5.8 Vectorial Differential Equations......Page __sk_0127.djvu
5.9 Vectorial Variational Calculus and Hamilton's Principle......Page __sk_0130.djvu
5.10 Fermat's Principle and Mechanical Optical Analogy......Page __sk_0133.djvu
5.11 Dirichlet's Principle......Page __sk_0134.djvu
Examples......Page __sk_0135.djvu
Problems......Page __sk_0142.djvu
6.1 Contravariant and Covariant Vectors......Page __sk_0147.djvu
6.2 Tensors, Symmetrants and Alternants......Page __sk_0150.djvu
6.3 Metric Tensors......Page __sk_0152.djvu
6.4 Relative Tensors, Pseudotensors and Pseudoscalars......Page __sk_0154.djvu
6.6 Covariant Differentiation......Page __sk_0158.djvu
6.7 Riemann-Christoffel, Ricci and Einstein Tensors......Page __sk_0160.djvu
6.8 Curvilinear Coordinate Systems......Page __sk_0161.djvu
Examples......Page __sk_0173.djvu
Problems......Page __sk_0176.djvu
7.1 Scalar Fourier Series and Transforms......Page __sk_0178.djvu
7.2 Vectorial Fourier Series and Transforms......Page __sk_0186.djvu
7.3 The Cauchy-Poisson Theorem and Lattice Sums......Page __sk_0190.djvu
7.4 Wave Mechanics......Page __sk_0194.djvu
7.5 Ehrenfest's Theorem......Page __sk_0197.djvu
7.6 Schrödinger's Equation......Page __sk_0198.djvu
7.7 Potential Well......Page __sk_0200.djvu
7.8 Self-Adjoint Differential Eigenvalue Problems......Page __sk_0202.djvu
7.9 Wave-Particle Dualism......Page __sk_0205.djvu
7.10 Bandwidth-Duration Principle......Page __sk_0206.djvu
7.11 Uncertainty Principle......Page __sk_0208.djvu
7.12 Operator Symbolism and Commutators......Page __sk_0211.djvu
7.13 Hydrogen Atom......Page __sk_0213.djvu
7.14 Harmonic Oscillator......Page __sk_0216.djvu
7.15 Equivalence of Matricial and Differential Formulations......Page __sk_0218.djvu
7.16 Heisenberg and Schrödinger Interpretations......Page __sk_0221.djvu
7.17 Boson and Ferrnion Annihilators and Creators......Page __sk_0224.djvu
7.18 Transmission Barrier......Page __sk_0226.djvu
7.19 Scattering Amplitude and Cross-Sections......Page __sk_0228.djvu
7.20 Green's Functions for Sturm-Liouville Problems......Page __sk_0230.djvu
7.21 Green's Functions as Kernels......Page __sk_0235.djvu
7.22 Reciprocity and Vectorial Operators......Page __sk_0236.djvu
7.23 Green's Functions: Wave, Helmholtz and Laplace Equations......Page __sk_0238.djvu
7.24 The Kirchhoff-Born Approximation......Page __sk_0240.djvu
7.25 Optical Theorem......Page __sk_0242.djvu
Examples......Page __sk_0243.djvu
Problems......Page __sk_0256.djvu
8.1 Space-Time and Minkowskian Metric......Page __sk_0259.djvu
8.2 The Lorentz Transformation......Page __sk_0261.djvu
8.3 Relativistic Paradoxes and the Null Cone......Page __sk_0264.djvu
8.4 4-Vectors and the Relativistic Energy Relation......Page __sk_0265.djvu
8.5 Relativistic Electromagnetics......Page __sk_0269.djvu
8.6 The Klein-Gordon Equation......Page __sk_0272.djvu
8.7 Clifford Algebra and Hypercomplex Vectors......Page __sk_0273.djvu
8.8 The Dirac Equation, Hole Theory and Spinors......Page __sk_0277.djvu
8.9 An Alternative Derivation of Relativistic Mechanics......Page __sk_0282.djvu
Examples......Page __sk_0286.djvu
Problems......Page __sk_0288.djvu
9.1 Commutativity and Conical Rotations......Page __sk_0289.djvu
9.2 Quaternion Maxwell Equations......Page __sk_0291.djvu
9.3 Quaternion Form of Wave-Particle Dualism......Page __sk_0292.djvu
Problems......Page __sk_0294.djvu
10.1 Mechanics of a Mass Point......Page __sk_0295.djvu
10.2 Orbits Under Central Forces......Page __sk_0298.djvu
10.3 The Two-Body Problem and Keplerian Orbits......Page __sk_0299.djvu
10.4 Inertial Systems and Pseudoforces......Page __sk_0301.djvu
10.5 Multiparticulate Systems and Virial Theorem......Page __sk_0303.djvu
10.6 Rigid Body Motions......Page __sk_0305.djvu
10.7 The Hamilton-Jacobi Equation......Page __sk_0306.djvu
10.8 Elastodynamics......Page __sk_0307.djvu
10.9 Elastostatics......Page __sk_0312.djvu
10.10 Viscous Fluids......Page __sk_0314.djvu
10.12 Equation of Mass Conservation......Page __sk_0317.djvu
10.13 Irrotational Flows......Page __sk_0318.djvu
10.14 Vortices......Page __sk_0319.djvu
10.15 General Flow of Fluids......Page __sk_0321.djvu
10.16 Hydrostatics......Page __sk_0322.djvu
10.17 Acoustics......Page __sk_0323.djvu
10.18 Maxwell's Equations......Page __sk_0325.djvu
10.19 Electrostatics......Page __sk_0327.djvu
10.20 Magnetostatics......Page __sk_0329.djvu
10.21 Stationary Electrokinetics......Page __sk_0330.djvu
10.22 Retarded Potentials and the Hertz Vector......Page __sk_0331.djvu
10.23 Hertzian Dipole Field......Page __sk_0333.djvu
10.24 The Poynting Vector and Energy Flow......Page __sk_0334.djvu
10.25 Electromagnetic Waves in Plasma......Page __sk_0335.djvu
10.26 Magnetic Pressure, Convection and Diffusion......Page __sk_0342.djvu
10.27 Hydromagnetic Waves......Page __sk_0343.djvu
10.28 Diffusion......Page __sk_0344.djvu
10.29 The Boltzmann Transport Equation......Page __sk_0346.djvu
Bibliography......Page __sk_0348.djvu
List Of Symbols......Page __sk_0351.djvu
Vector Formulas......Page __sk_0363.djvu
Index......Page __sk_0365.djvu