Methods of Applied Mathematics
This invaluable book offers engineers and physicists working knowledge of a number of mathematical facts and techniques not commonly treated in courses in advanced calculus, but nevertheless extremely useful when applied to typical problems in many different fields. It deals principally with linear algebraic equations, quadratic and Hermitian forms, operations with vectors and matrices, the calculus of variations, and the formulations and theory of linear integral equations. Annotated problems and exercises accompany each chapter.
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Matrices and Linear Equations
Calculus of Variations and Applications
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applies arbitrary associated augmented matrix calculation calculus of variations characteristic functions characteristic numbers characteristic value coefficient matrix column components considered constant constraint continuous solution converges coordinates corresponding characteristic vectors deduce defined deflection denote determined diagonal elements differential equation dx dy end conditions equivalent Euler equation expressed finite follows Fredholm equation function y(x given Green's function hence Hermitian homogeneous infinite integral equation integrand interval involved iterative kernel K(x left-hand member linear combination linear equations linearly independent modal matrix multiple natural boundary conditions nonsingular normal notation notice obtained orthogonal matrix positice positive definite possesses potential energy preceding prescribed procedure quadratic form quantities reduced relation relevant replaced result of Problem right-hand member satisfies the equation scalar product set of equations square matrix stationary function Suppose symmetric matrix takes the form transformation unit vectors vanish variables variational problem verify zero