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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arbitrary associated augmented matrix calculation calculus of variations characteristic functions characteristic numbers characteristic value coefficient coefﬁcients coeﬂicients column components considered constant constraint converges coordinates corresponding characteristic vectors deduce deﬁned deﬂection denote determined differential equation dx dy end conditions equation y(x equivalent Euler equation exists expressed ﬁnite ﬁrst ﬁxed follows form y(x Fredholm equation function f function y(x given Green’s function hence Hermitian homogeneous inﬁnite integral equation integrand interval involved iterative left-hand member linear combination linearly independent multiple natural boundary conditions nonsingular nontrivial solution normal notation notice obtained orthogonal matrix positive deﬁnite possesses potential energy prescribed procedure quadratic form quantities reduced relation relevant replaced result of Problem right-hand member satisﬁes satisﬁes the equation satisfy scalar product set of equations speciﬁed square matrix stationary function Suppose symmetric matrix takes the form transformation unit vectors vanish variables variational problem verify zero