Solving Nonlinear Equations Made Simple

Nonlinear equations do not have to be difficult.

Solving Nonlinear Equations Made Simple provides a clear, step-by-step introduction to some of the most important numerical tools used in mathematics, engineering, and computational science. Beginning with the basic idea of a system of nonlinear equations, Peter I. Kattan explains the Jacobian matrix and shows exactly how it is used in the Newton-Raphson method. The discussion then addresses one of the most troublesome numerical problems: what happens when the Jacobian becomes singular or nearly singular. Through simple equations and carefully worked examples, readers are introduced to modified Newton-Raphson methods, regularization, damping, and the Levenberg-Marquardt method. Written for students, beginners, engineers, and anyone who has struggled with conventional explanations of nonlinear solution methods, this concise guide focuses on understanding the ideas first and the mathematics second.