Elementary Differential Equations and Boundary Value Problems
This revision of the market-leading book maintains its classic strengths: contemporary approach, flexible chapter construction, clear exposition, and outstanding problems. Like its predecessors, this revision is written from the viewpoint of the applied mathematician, focusing both on the theory and the practical applications of Differential Equations as they apply to engineering and the sciences. Sound and Accurate Exposition of Theory--special attention is made to methods of solution, analysis, and approximation. Use of technology, illustrations, and problem sets help readers develop an intuitive understanding of the material. Historical footnotes trace development of the discipline and identify outstanding individual contributions.
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FIRST ORDER DIFFERENTIAL EQUATIONS
SECOND ORDER LINEAR EQUATIONS
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arbitrary constants assume asymptotically stable boundary conditions boundary value problem Chapter compute consider corresponding critical point cx and c2 defined derivative determine discussed dxjdt dyjdt eigenfunctions eigenvalues eigenvectors Euler method example Figure formula error Fourier series function fundamental set given by Eq heat conduction Hence homogeneous equation indicial equation initial conditions initial value problem integral interval Laplace transform linear system linearly independent linearly independent solutions mathematical matrix motion nonhomogeneous nonlinear obtain order equations order linear equation ordinary differential equations partial differential equations particular solution point x0 polynomial positive regular singular point result roots satisfying the initial second order linear second solution Section series solution set of solutions Show side of Eq solution of Eq Sturm-Liouville problem Substituting Suppose Taylor series temperature term Theorem trajectories unstable variable vectors velocity yp(x yx and y2 zero