Introduction to Numerical Methods in Java

This course is about numerical methods. We are NOT going to discuss ALL the theory related to numerical methods (for example how to solve differential equations). We are just going to consider the concrete implementations and numerical principles.

The first section is about matrix algebra and linear systems: such as matrix multiplication, gaussian elimination and applications of these approaches, such as Google’s PageRank algorithm.

Then we will talk about numerical integration. How to use techniques like trapezoidal rule, Simpson formula and Monte–Carlo method – my personal favourite.

The last chapter is about solving differential equations with Euler’s–method and Runge–Kutta approach. We will consider examples such as the pendulum problem.

Section 1:

numerical methods basics

floating point representation

rounding errors

Section 2:

linear algebra

matrix multiplication

Gauss–elimination

Section 3:

eigenvectors and eigenvalues

Google’s PageRank algorithm

Section 4:

solving non–linear equations

root finding

Newton’s method and bisection method

Section 5:

numerical integration

rectangle method and trapezoidal method

Simpson’s method

Monte–Carlo integration

Section 6:

solving differential–equations

Euler’s method

Runge–Kutta method

Section 7:

interpolation

Lagrange method

Thanks for joining my course, let’s get started!