Ordinary Differential Equations and Linear Algebra - Part 1

If you are curious about how we model a phenomena from nature and how we understand its behavior from past to future mathematically, this is the course that will give you answers.

This course provides a comprehensive qualitative and quantitative analysis of ordinary differential equations and linear algebra. This course is divided in two parts to be able to facilitate the learning experience. The first part focuses on 1st order differential equations and linear algebra. The second part is about higher order equations that presents beautiful theory of linearity, as well as the complexity of nonlinearity.

• Introduction to differential equations and their solutions

• Qualitative Analysis via Directional Fields

• Separable Equations

• Theory of 1st order Differential Equations, i.e. Picard's Theorem

• 1st order Linear Differential Equations with two techniques

• Linear Algebra: Matrix Algebra

  Solving systems of linear equations by using Gauss Jordan Elimination

  Invertibility- Determinants

  Subspaces and Vector Spaces

  Linear Independency

  Span

  Basis-Dimension