Difference Equations: An Introduction with ApplicationsAcademic Press, 2001 - 403페이지 Difference Equations, Second Edition, presents a practical introduction to this important field of solutions for engineering and the physical sciences. Topic coverage includes numerical analysis, numerical methods, differential equations, combinatorics and discrete modeling. A hallmark of this revision is the diverse application to many subfields of mathematics.
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목차
Introduction | 1 |
Section 6 | 6 |
The Difference Calculus | 13 |
2 | 50 |
3 | 89 |
Chapter 3 | 130 |
Discrete Calculus of Variations | 184 |
Chapter 5 | 195 |
The SelfAdjoint Second Order | 229 |
Chapter 10 | 349 |
Appendix | 367 |
Answers to Selected Problems | 373 |
383 | |
396 | |
401 | |
3 | 222 |
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A²y(t approximation Assume asymptotically stable Ay(t Ayo(t Az(t boundary conditions boundary value problem Chapter characteristic equation characteristic roots compute consider converges Corollary defined Definition difference equation differential equations disconjugacy disconjugate eigenfunctions eigenpairs eigenvalues eigenvectors equation y(t Euler-Lagrange equation Example Exercise Find fixed point Floquet multipliers Floquet system formula Green's function Hence homogeneous indefinite sum initial conditions initial value problem interval iteration least period Lemma Let y(t Liapunov function linear equations linearly independent linearly independent solutions matrix method nonlinear nontrivial solution Note obtain order equation oscillatory periodic points polynomials problem ²y(t Proof result Riccati equation satisfies Section sequence Show sin² sint solution of Eq solution of Ly(t solution y(t Sturm-Liouville problem summation t₁ Ty(t u₁ u₁(t unique solution variable vector y(to y₁ y₁(t yo(t z-transform Z(yk zero