Ordinary Differential Equations and Linear Algebra - Part 1
Rice University
Study of ordinary differential equations (e.g., solutions to separable and linear first-order equations and to higher-order linear equations with constant coefficients, systems of linear differential equations, the properties of solutions to differential equations) and linear algebra (e.g., vector spaces and solutions to algebraic linear equations, dimension, eigenvalues, and eigenvectors of a matrix), as well as the application of linear algebra to first-order systems of differential equatio...
About this Course
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.
What You'll Learn
- 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
Prerequisites
- This course require single variable calculus, differentiation and integration.
Instructors
Betul Orcan-Ekmekci
Assistant Teaching Professor