Principles and Techniques of Applied Mathematics
Stimulating, thought-provoking study shows how abstract methods of pure mathematics can be used to systematize problem-solving techniques in applied mathematics. Topics include methods for solving integral equations, finding Green’s function for ordinary or partial differential equations, and for finding the spectral representation of ordinary differential operators. Problems. Appendices. Bibliography.
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Convergence and Complete Spaces
Representation of Linear Vector Spaces
39 other sections not shown
5X x 8H adjoint analytic function applied approximate spectrum arbitrary assume boundary conditions bounded Chapter coefficients components consequently consider constant continuous function continuous spectrum converges coordinates corresponding defined definition derivative diagonal matrix differential equation differential operator discontinuity conditions domain dyad eigen eigenvalue eigenvector of rank elements example exists finite formula function u(x Green's function Hint homogeneous equation illustration implies improper eigenfunctions infinite infinity integral equation inverse Jordan canonical form linear combination linear manifold linear vector space linearly independent mathematical method multiple Note null space O.N. basis obtain orthogonal Problem proof prove Theorem quadratic form real numbers result right-hand side scalar product self-adjoint operator set of vectors sinh solve spectral representation subspace Suppose symbolic function testing functions theory transformation vanishes vector space vectors xx zero