Numerical Root Finding in Python and MATLAB

Name: Numerical Root Finding in Python and MATLAB
Rating: 4.4 (50 reviews)

A Hands-on Approach

Created byYarpiz Team, Mostapha Kalami Heris

Last updated 1/2020

English

English [Auto],

What you'll learn

Theory of Bisection, Secant and Newton-Raphson Methods
Python Implementation of 3 Root Finding Methods
MATLAB Implementation of 3 Root Finding Methods

Course content

3 sections • 9 lectures • 1h 14m total length

How bisection method works?13:08
Learn how to find roots of equations using the bisection method, and compare it with Newton's method, by implementing from scratch in Python and MATLAB.
Bisection Method in Python14:51
Implement the bisection method in python, define a and b, check f(a) and f(b) signs, iterate with midpoint c, and apply tolerance and max iterations for robust root finding.
Bisection Method in MATLAB7:35
Demonstrate bisection in matlab with a function that accepts a, b, tolerance, and max iterations to find the root of x^2 - x - 1, the golden ratio.

How secant method works?11:20
Explore the secant method by drawing a line through two points and using the zero crossing as the next root estimate. Relate it to bisection and note faster convergence.
Secant Method in Python2:54
Implement the secant method in python by converting a bisection routine, updating c with a*F(b) - b*F(a) over F(b) - F(a), using F values to converge toward root near 1.618.
Secant Method in MATLAB2:12
Demonstrates implementing the secant method in MATLAB by copying and renaming files, updating the update rule, calling the new function to solve an equation, and verifying the result.

How Newton's method works?7:00
Apply Newton's method to locate roots via tangent line approximation, updating x1 from x0 by x1 = x0 - f(x0)/f'(x0); it can converge fast but offers no guarantees.
Newton-Raphson Method in Python8:21
Implement the newton-raphson method in python with numerical derivative via central difference to solve x^2 - x - 1, starting at 2, tolerance 1e-10, max iterations 200.
Newton-Raphson Method in MATLAB7:27
Implement the Newton-Raphson method in matlab to find roots by iterating x = x - f(x)/f'(x), using a starting point, tolerance, and max iterations with convergence checks.

Requirements

Basic Mathematics
Python Programming
MATLAB Programming

Description

This series of video tutorials covers the numerical methods for Root Finding (Solving Algebraic Equations) from theory to implementation. In this course, three methods are reviewed and implemented using Python and MATLAB from scratch.

At first, two interval-based methods, namely Bisection method and Secant method, are reviewed and implemented. Then, a point-based method which is known as Newton's method for root finding, a.k.a. Newton–Raphson method, is reviewed and implemented. This course is instructed by Dr. Mostapha Kalami Heris, who has years of practical work and active teaching in the field of programming, mathematics, control engineering and computational intelligence.

By the end of this course you will be able to know about the fundamental theory of this root finding methods and implementing them using Python and MATLAB programming languages.

Who this course is for:

Engineering Students
Applied Math and Science Students
Anyone interested in numerical methods

Numerical Root Finding in Python and MATLAB

What you'll learn

Explore related topics

Course content

Bisection Method for Root Finding3 lectures • 36min

Secant Method for Root Finding3 lectures • 16min

Newton-Raphson Method for Root Finding3 lectures • 23min

Requirements

Description

Who this course is for: