Ordinary Differential Equations: A First Course
Though ordinary differential equations is taught as a core course to students in mathematics and applied mathematics, detailed coverage of the topics with sufficient examples is unique.
Written by a mathematics professor and intended as a textbook for third- and fourth-year undergraduates, the five chapters of this publication give a precise account of higher order differential equations, power series solutions, special functions, existence and uniqueness of solutions, and systems of linear equations.
Relevant motivation for different concepts in each chapter and discussion of theory and problems-without the omission of steps-sets Ordinary Differential Equations: A First Course apart from other texts on ODEs. Full of distinguishing examples and containing exercises at the end of each chapter, this lucid course book will promote self-study among students.
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aktk analytic arbitrary constants basis of solutions Bessel function continuous function converges Corollary Definition determinant eigenvalues eigenvector eigenvector corresponding equation of order Example following theorem Frobenius series function defined fundamental matrix given equation gives Hence the solution homogeneous linear differential indicial equation inequality initial conditions initial value problem integral equation interval Jp(t Legendre equation Legendre polynomials Let us consider let us find Let us take linear differential equation linearly independent solutions n-th order non-singular matrix Note obtain the solution order equation ordinary differential equation ordinary point particular solution Picard's theorem Pn(t power series solution prove recurrence relation regular singular point rewrite satisfies Lipschitz condition solution matrix solution of L(x solution x(t Substituting successive approximations unique solution uniqueness of solution variation of parameters Wronskian x2 are linearly xi(t xn(t