Lecture 9: Root finding
Contents
Lecture 9: Root finding#
Root finding means finding a solution to equations. For example you might be asked something like:
Find values of \(x\) that satisfy \(x^2 - 1 = 0\).
This case can be solved analytically, it will be true if \(x^2 = 1\), and there are two cases where \(x^2 = 1\), either \(x=1\) or \(x=-1\). \(x=-1\), or \(x=1\) would then be the two roots (or solutions) of this equation.
In this week we will explore why root finding is often solved using computational techniques, explore two common methods for root finding, and walk through how to implement them and apply them to example problems.
Weekly tasks#
- What is root finding and why do it on a computer?
- Continuous functions
- Continuous functions - SOLUTIONS
- Bolzano’s Theorem
- Bolzano’s Theorem - SOLUTIONS
- Writing a root finding algorithm using the bisection method
- Writing a root finding algorithm using the bisection method - SOLUTIONS
- Newton’s Method
- Newton’s Method - SOLUTIONS