Methods of Mathematical Physics

R. Courant; David Hilbert

doi:10.1002/9783527617210

Abstract

Partial table of contents: THE ALGEBRA OF LINEAR TRANSFORMATIONS AND QUADRATIC FORMS. Transformation to Principal Axes of Quadratic and Hermitian Forms. Minimum-Maximum Property of Eigenvalues. SERIES EXPANSION OF ARBITRARY FUNCTIONS. Orthogonal Systems of Functions. Measure of Independence and Dimension Number. Fourier Series. Legendre Polynomials. LINEAR INTEGRAL EQUATIONS. The Expansion Theorem and Its Applications. Neumann Series and the Reciprocal Kernel. The Fredholm Formulas. THE CALCULUS OF VARIATIONS. Direct Solutions. The Euler Equations. VIBRATION AND EIGENVALUE PROBLEMS. Systems of a Finite Number of Degrees of Freedom. The Vibrating String. The Vibrating Membrane. Green's Function (Influence Function) and Reduction of Differential Equations to Integral Equations. APPLICATION OF THE CALCULUS OF VARIATIONS TO EIGENVALUE PROBLEMS. Completeness and Expansion Theorems. Nodes of Eigenfunctions. SPECIAL FUNCTIONS DEFINED BY EIGENVALUE PROBLEMS. Bessel Functions. Asymptotic Expansions. Additional Bibliography. Index.

Keywords

PhysicsTheoretical physicsStatistical physicsClassical mechanics

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Publication Info

Year: 1989
Type: book
Citations: 8095
Access: Closed

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APA Style

                            
                                    R. Courant, 
                                
                                    David Hilbert
                                
                            (1989). 
                            Methods of Mathematical Physics. 
                            
                            .
                            https://doi.org/10.1002/9783527617210

Identifiers

DOI: 10.1002/9783527617210