Analysis and Differential Equations

This book presents advanced methods of integral calculus and the classical theory of the ordinary and partial differential equations. It provides explicit solutions of linear and nonlinear differential equations and implicit solutions with discrete approximations. Differential equations that could not be explicitly solved are discussed with special functions such as Bessel functions. New functions are defined from differential equations. Laguerre, Hermite and Legendre orthonormal polynomials as well as several extensions are also considered.

It is illustrated by examples and graphs of functions, with each chapter containing exercises solved in the last chapter.

Contents:

• Introduction
• Expansions with Orthogonal Polynomials
• Differential and Integral Calculus
• Linear Differential Equations
• Linear Differential Equations in ℝp
• Partial Differential Equations
• Special Functions
• Solutions

Readership: Undergraduate and graduate students in mathematics.
Key Features:

• It is self-contained and accessible to undergraduate and graduate students in mathematics
• A large part is devoted to the integral calculus with detailed solutions
• It presents solutions for homogeneous and inhomogeneous differential equations in physics, geometry and population dynamics