Linear Ordinary Differential EquationsLinear Ordinary Differential Equations, a text for advanced undergraduate or beginning graduate students, presents a thorough development of the main topics in linear differential equations. A rich collection of applications, examples, and exercises illustrates each topic. The authors reinforce students' understanding of calculus, linear algebra, and analysis while introducing the many applications of differential equations in science and engineering. Three recurrent themes run through the book. The methods of linear algebra are applied directly to the analysis of systems with constant or periodic coefficients and serve as a guide in the study of eigenvalues and eigenfunction expansions. The use of power series, beginning with the matrix exponential function leads to the special functions solving classical equations. Techniques from real analysis illuminate the development of series solutions, existence theorems for initial value problems, the asymptotic behavior solutions, and the convergence of eigenfunction expansions. |
Contents
OT57_ch1 | 1 |
OT57_ch2 | 19 |
OT57_ch3 | 49 |
OT57_ch4 | 93 |
OT57_ch5 | 119 |
OT57_ch6 | 163 |
OT57_ch7 | 221 |
OT57_ch8 | 245 |
OT57_ch9 | 281 |
OT57_ch10 | 305 |
OT57_backmatter | 333 |
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LINEAR ORDINARY DIFFERENTIAL EQUATIONS. EARL A. CODDINGTON. ROBERT CARLSON No preview available - 2013 |
Common terms and phrases
A₁ analytic B₁ Bessel equation boundary conditions c₁ Cauchy sequence characteristic polynomial Compute Consider continuous functions convex cos(t defined denote differential equations eigenfunctions eigenvalue eigenvectors equation of order example exercise Find a basis first-order follows form x(t formula given by X(t hence Hint implies indicial polynomial inequality initial value problem inner product interval invertible Jordan canonical form Lemma linear systems linearly independent log(t m₁ matrix Mmn F Mmn(F Mn(C Mn(F multiplicity nonhomogeneous nontrivial solution norm normed vector space polynomial of degree positive integer power series power series representation Proof r₁ regular singular point result satisfying X(0 selfadjoint series converges Show sin(t solution X(t Sp(B Suppose t₁ t²x Theorem vector space Wx(t x₁ x₁(t Xm(t zero