Mathematical methods in physics / Samuel D. Lindenbaum.

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Ch. 1. Vector analysis. 1.1. Vector algebra. 1.2. Examples and applications. 1.3. Theory of curves in space -- ch. 2. Tensor analysis. 2.1. nth rank tensor. 2.2. 2nd-rank isotropic (invariant) tensor. 2.3. Contraction. 2.4. Outer product theorem. 2.5. 3rd-rank isotropic (invariant) tensor. 2.6. Examples and applications. 2.7. Geometrical representation of tensors. 2.8. Moment of inertia tensor -- ch. 3. Fields. 3.1. Tensor field. 3.2. Gauss' theorem. 3.3. Stokes' theorem. 3.4. Connectivity of space. 3.5. Helmholtz theorem. 3.6. Equivalent forms of Gauss' and Stokes' theorems. 3.7. Maxwell's equations. 3.8. Curvilinear orthogonal coordinate systems -- ch. 4. Matrix and vector algebra in N-dimensional space. 4.1. Algebra of N-dimensional complex space. 4.2. Matrix algebra. 4.3. Examples of matrices. 4.4. Tensor analysis in N-dimensional space. 4.5. Matrices in N-dimensional space. 4.6. Linear independence and completeness.

Ch. 5. Hilbert space. 5.1. Definitions. 5.2. Weierstrass's theorem. 5.3. Examples of complete orthonormal sets -- ch. 6. Theory of functions of a complex variable. 6.1. Theory of complex variables. 6.2. Analytic functions. 6.3. Applications of analytic functions. 6.4. Integral calculus of complex variables. 6.5. Taylor's theorem. 6.6. Laurent theorem. 6.7. Singularities. 6.8. Liouville theorem. 6.9. Multiple-valued functions. 6.10. Theory of residues. 6.11. Analytic continuation -- ch. 7. Theory of ordinary differential equations. 7.1. Ordinary differential equations in physics. 7.2. Ordinary points and singular points. 7.3. Hermite polynomials. 7.4. Behavior of solutions near singular points. 7.5. Bessel functions -- ch. 8. Theory of partial differential equations. 8.1. Examples of field equations in physics. 8.2. Theory of characteristics -- ch. 9. Heat conduction. 9.1. Fundamental equations. 9.2. Infinite medium. 9.3. Semi-infinite medium.

Ch. 10. The eigenvalue problem. 10.1. Eigenvalues and eigenfunctions. 10.2. Harmonic oscillator/free particle in a sphere. 10.3. The variational principle -- ch. 11. Wave equations. 11.1. Infinite medium. 11.2. Retarded and advanced D-functions. 11.3. Field due to a moving point charge. 11.4. Finite boundary medium. 11.5. Green's function method applied to Schrodinger's equation and to heat conduction.

This new book on Mathematical Methods In Physics is intended to be used for a 2-semester course for first year MA or PhD physics graduate students, or senior undergraduates majoring in physics, engineering or other technically related fields. Emphasis has been placed on physics applications, included where appropriate, to complement basic theories. Applications include moment of inertia in "Tensor Analysis"; Maxwell's equations, magnetostatic, stress tensor, continuity equation and heat flow in "fields"; special and spherical harmonics in "Hilbert Space"; electrostatics, hydrodynamics and Gamma function in "Complex Variable Theory"; vibrating string, vibrating membrane and harmonic oscillator in "Ordinary Differential Equations"; age of the earth and temperature variation of the earth's surface in "Heat Conduction"; and field due to a moving point charge (Lienard-Wiechart potentials) in "Wave Equations". Subject not usually found in standard mathematical physics texts include Theory of Curves in Space in "Vector Analysis", and Retarded and Advanced D-Functions in "Wave Equations". Lastly, problem solving techniques are presented by way of appendices, comprising 75 pages of problems with their solutions. These problems provide applications as well as extensions to the theory. A useful compendium, with such excellent features, will surely make it a key reference text

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