Module 1 NLE

Overview

Subtitle description: The world is full of complex systems and phenomena that we as humans are always trying to better understand. Many of these phenomena do not follow a linear relationship (e.g., y = mx +b), but rather have some non-linearity that engineers and scientist try to describe through mathematical expressions or equations.

A standard non-linear equation is the quadratic equation (y = ax2 +bx +c) which has an analytical solution of the form:

$$x+1\over\sqrt{1-x^2}\label{ref1}$$

This form is also known as finding the roots of an equation (y = 0), and non-linear equations solvers are also called rootfinding methods. Many engineering problems that have a non-linear equation do not have an analytical solution, and thus need to be approximated through some numerical method. Numerical non-linear equation solvers have been developed for countless programming languages and with today’s technology are usually easy to solve. However, it is important to understand how these solvers operate, for the cases where the answers to not match some physical reality, or the solver fails to find any solution.

This module focuses on numerous rootfinding methods and discusses their complexity and efficiency of use./p>

Learning Objectives

At the end of this module, you will be able to:

  • NLE|LO|01: Identify a non-linear equation
  • NLE|LO|02: Bind the root
  • NLE|LO|03: Solve NLE with simple methods
  • NLE|LO|04: Solve NLE with more advanced methods
  • NLE|LO|05: Solve NLE with an open method