Methods of Mathematical Physics / Edition 1by Richard Courant, D. Hilbert
Pub. Date: 01/15/1953
This classic work is now available in an inexpensive unabridged paperback edition. Since the first volume of this work came out in Germany in 1924, this book has remained standard in the field. Courant and Hilbert's treatment restores the historically deep connections between physical intuition and mathematical development, providing the reader with a unified approach to mathematical physics. The present volumes represent Richard Courant's second and final revision of 1953.
Table of ContentsPartial 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.
LINEAR INTEGRAL EQUATIONS.
The Expansion Theorem and Its Applications.
Neumann Series and the Reciprocal Kernel.
The Fredholm Formulas.
THE CALCULUS OF VARIATIONS.
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.
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