Methods of Applied MathematicsThis 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. |
Contents
Matrices and Linear Equations | 1 |
Calculus of Variations and Applications | 119 |
Integral Equations | 222 |
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Common terms and phrases
arbitrary associated augmented matrix c₁ C₂ calculation calculus of variations characteristic functions characteristic numbers characteristic value coefficient matrix column components considered constant constraint converges coordinates corresponding characteristic vectors deduce defined denote determined differential equation dx dy e₁ end conditions equation y(x equivalent Euler equation expressed follows form y(x Fredholm equation function y(x given Green's function hence Hermitian homogeneous integral equation interval involved iterative kernel K(x left-hand member linear combination linearly independent method multiple natural boundary conditions nonsingular notation notice obtained orthogonal matrix positive definite possesses prescribed procedure quadratic form reduced relation relevant result of Problem right-hand member satisfies the equation scalar product Section set of equations sin² square matrix stationary function Suppose symmetric matrix takes the form transformation u₁ u₂ unit vectors vanish variables variational problem verify x₁ y₁ zero ду
