Bøger af Eli Hill

Nonlinear equations are those that do not form a straight line. They may form a bell curve, S-curve, or any other nonlinear shape on a graph. These equations have a variable slope and are more complicated as compared to linear equations. A nonlinear equation has a degree of two or greater than two, but not less than two. As the value of the degree increases, so does the curvature of the graph. In general, nonlinear equations cannot be solved analytically. Two criteria can be taken into account when choosing a method for solving nonlinear equations, namely, method convergence and the cost of calculating of the method. Nonlinear equations are utilized for managing projects and making predictions. Some examples of nonlinear equations include S-curve graphs, regression analysis, and logarithmic scales. Important numerical methods for solving nonlinear equations include first order methods, Newton-Raphson method, and bisection method. This book explores all the important aspects of the numerical methods used for solving nonlinear equations. It is a resource guide for experts as well as students.

An equation whose graph solution does not form a straight line is referred to as a nonlinear equation. The variables of a nonlinear equation are either of a degree greater than one or less than one but never one. In solving a nonlinear equation by iterative method, a trial solution is assumed. Thereafter, the trial solution is substituted into the nonlinear equation to determine the error or mismatch, and the mismatch is used in some systematic manner to generate an improved estimate of the solution. Dynamical system refers to an area of study within mathematics which seeks to understand the geometrical properties of trajectories and long-term behavior. These systems use discrete mappings or ordinary differential equations to describe the evolution of a state variable over time. This book aims to shed light on some of the unexplored aspects of nonlinear equations and dynamical systems. It presents researches and studies performed by experts across the globe. The book will serve as a valuable source of reference for graduate and postgraduate students.

Punia's father used to dive for lobsters in an underwater cave. Then the Shark King came to live there. One day, when Punia was a baby, his father went diving for lobsters and never came back. Now Punia has a plan to trick the Shark King, and to bring lobsters to his village once again.