Course Outline
In this course, we will learn:
- Row operation and Why row operation didn’t change the solution set?
- How to solve a system of linear equations by Gaussian Elimination method or Gauss-Jordan method?
- How to interpret general solution of a linear system? And how to get it through the nullifying column combination.
- What is vector space, subspace, linear combination, linear independence, span, basis, dimension and what not!
- What is linear transformation? How it help to understand vector spaces?
- Four fundamental subspaces
- Eigenvalue and eigenvector of a linear transformation
- Diagonalization, Inner Product, Gram-Schmidt Process
- Fourier Series (Periodic function, Fourier series, Half Range Fourier Sine and Cosine Series), Complex Notation for Fourier Series
- Fourier Transformations, Fourier Sine and Cosine Transformations
For more details check this .
Extra content which I covered in this course:
- Application of Fourier Transfomation to denoising sound wave https://github.com/emonhossainraihan/MAT216_BracU/blob/main/demo.ipynb
- Why $\exp(M)$ give us the solution of a system of ODE: $$ \frac{d}{dt}\begin{bmatrix}x(t)\\y(t)\end{bmatrix}=\exp\left(\begin{bmatrix} a& b\\ c& d \end{bmatrix}\right)\begin{pmatrix}x(0)\\y(0)\end{pmatrix} $$
Lecture notes
Materials
For summer 2024
Discord server: MAT216 Summer-24 .
For spring 2025
Discord server: MAT216 Spring-25 .
If you need formula-tree which I illustrate in the class then check chapter 11+12 of my lecture notes.