Abell M. Differential Equations with Mathematica 5ed 2022

Textbook in PDF format

Differential Equations with Mathematica, Fifth Edition uses the fundamental concepts of the popular platform to solve (analytically, numerically, and/or graphically) differential equations of interest to students, instructors, and scientists.
Mathematica’s diversity makes it particularly well suited to performing calculations encountered when solving many ordinary and partial differential equations. In some cases, Mathematica’s built-in functions can immediately solve a differential equation by providing an explicit, implicit, or numerical solution. In other cases, Mathematica can be used to perform the calculations encountered when solving a differential equation.
Because one goal of elementary differential equations courses is to introduce students to basic methods and algorithms so that they gain proficiency in them, nearly every topic covered this book introduces basic commands, also including typical examples of their application. A study of differential equations relies on concepts from calculus and linear algebra, so this text also includes discussions of relevant commands useful in those areas. In many cases, seeing a solution graphically is most meaningful, so the book relies heavily on Mathematica’s outstanding graphics capabilities.
Introduction to differential equations
First-order ordinary differential equations
Applications of first-order equations
Higher-order linear differential equations
Applications of higher-order differential equations
Systems of ordinary differential equations
Applications of systems of ordinary differential equations
Laplace transform methods
Eigenvalue problems and Fourier series
Partial differential equations