ORDINARY DIFFERENTIAL EQUATIONS (2ND EDITION) - WALTER LEIGHTON

"Ordinary Differential Equations" by Walter Leighton is a textbook that provides a comprehensive introduction to the theory and applications of ordinary differential equations. Here's a summary of the content typically covered in such a textbook:

Fundamentals of Differential Equations: The book begins with an overview of basic concepts such as order, linearity, and solutions to ordinary differential equations (ODEs). It covers terminology, notation, and classification of ODEs based on various criteria.

First-Order Differential Equations: The text explores methods for solving first-order ODEs, including separable equations, exact equations, integrating factors, and linear equations. It also introduces concepts such as existence and uniqueness of solutions and direction fields.

Higher-Order Differential Equations: Leighton delves into the theory and techniques for solving higher-order ODEs, including linear equations with constant coefficients, undetermined coefficients, variation of parameters, and systems of first-order equations.

Laplace Transforms: The book introduces Laplace transforms as a powerful tool for solving linear ODEs with discontinuous or nonhomogeneous terms. It covers the definition of Laplace transforms, properties, inversion formulas, and applications to differential equations.

Series Solutions: Leighton explores methods for finding series solutions to ODEs, including power series solutions, Frobenius method for second-order equations with regular singular points, and Bessel's equation.

Applications: Throughout the text, Leighton provides examples and applications of ODEs in various fields such as physics, engineering, biology, and economics. Topics may include population dynamics, mechanical vibrations, electrical circuits, and fluid flow.

Numerical Methods: The book may also include an introduction to numerical methods for solving ODEs, such as Euler's method, Runge-Kutta methods, and finite difference methods.

Overall, "Ordinary Differential Equations" by Walter Leighton serves as a comprehensive textbook for students studying differential equations at the undergraduate level. It covers both theoretical concepts and practical applications, providing readers with the tools and knowledge needed to understand and solve ordinary differential equations in various contexts.