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!