ANALYSIS AND DIFFERENTIAL EQUATIONS

Advanced methods of integral calculus and classical theories of ordinary and partial differential equations are explored in this book. It offers explicit solutions for both linear and nonlinear differential equations, alongside implicit solutions using discrete approximations. The text addresses equations that resist explicit solutions, utilizing special functions like Bessel functions. Additionally, it introduces new functions derived from differential equations and examines Laguerre, Hermite, and Legendre orthonormal polynomials, along with various extensions.