Elementary Differential Equations

Livro digital

Título:
Elementary Differential Equations

Autor:
William F. Trench

Categoria:
Matemática & Lógica > Cálculo e Análise

Pessoa doadora:
Raffaello D. N.

Sinopse:
Elementary Differential Equations opens with the practical question of how changing quantities become equations, then moves through first-order techniques, numerical methods, applications, and the standard families of linear equations. Its table of contents shows a deliberately staged path: Chapter 1 introduces models and direction fields, Chapter 2 covers linear, separable, exact, and transformed nonlinear equations, and Chapter 3 shifts to Euler, improved Euler, and Runge-Kutta methods before the book expands into higher-order and system-level problems. The structure is broader than the title alone suggests. After the foundations, the book separates technique from application in a way that keeps growth/decay, cooling and mixing, mechanics, springs, circuits, and central-force motion in their own chapters. Later chapters move into power-series and Frobenius methods, Laplace transforms, higher-order equations, and linear systems, so the reader sees both classical solution methods and the algebraic machinery behind them. The author’s preface also signals a strong emphasis on worked examples, exercises, and technology-supported computation. This is a compact but thorough undergraduate text for readers who already know calculus and want a systematic route through differential equations. Its value lies in the balance between intuition, method, and applications, plus the unusually wide coverage of techniques that connect introductory ODEs to numerical computation, special-function series, and systems. The result is a practical course text that can serve both as a first encounter and as a reference for later study.