## Elementary Differential Equations with Boundary Value ProblemsThis accessible, attractive, and interesting book enables readers to first solve those differential equations that have the most frequent and interesting applications. This approach illustrates the standard elementary techniques of solution of differential equations. Precise and clear-cut statements of fundamental existence and uniqueness theorems allow understanding of their role in this subject. A strong numerical approach emphasizes that the effective and reliable use of numerical methods often requires preliminary analysis using standard elementary techniques. The first few sections of most chapters introduce the principle ideas of each topic, with remaining sections devoted to extensions and applications. Topics covered include first-order differential equations, linear equations of higher order, power series methods, Laplace transform methods, linear systems of differential equations, numerical methods, nonlinear systems and phenomena, Fourier series methods, and Eigenvalues and boundary value problems. For those involved in the fields of science, engineering, and mathematics. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

FIRSTORDER DIFFERENTIAL EQUATIONS | 1 |

LINEAR EQUATIONS OF HIGHER ORDER | 40 |

POWER SERIES METHODS | 74 |

Copyright | |

7 other sections not shown

### Common terms and phrases

Actual solution Actual values aicos amplitude of motion Approx approximate values associated eigenvectors asymptotically stable boundary value problem C2sin characteristic equation characteristic roots choose Bn computation conditions X(0 cosh Cosine series desired particular solution differential equation direction with frequency eigenfunction eigenvalue eigenvectors endpoint conditions equation yields equilibrium solution x(t Euler's method Finally follows fosin Fourier series ft/sec function given system gives the linearization Hence implies Improved Euler initial value problem integral Iterative formula linear system matrix mode with frequency natural frequency natural mode oscillation positive root recurrence relation regular singular point satisfy the condition Section separation of variables Sine series sinh solution is given solution is y(x solve stable spiral point substitute transforms trial solution Unstable critical point unstable saddle point velocity xi(t xi{t Xn(x yn+i yo(x