Differential Equations Examples

Math 243 - Fall 2025

• Examples
• Notes
• Schedule & Syllabus

Graphics

1. Slope fields (Python, Sage, Octave)
2. Direction fields for planar systems (phase planes) (Python, Octave)
3. Direction field for $\mathbf{x}' = A\mathbf{x}$. (Python)
4. Direction field with a solution curve. (Python)
5. Contour plots and direction fields. (Python)
6. Stream plots. (Python)

Numerical Methods

1. Euler’s method (Python)
2. Euler’s method for systems (Python)

Linear Algebra

1. Finding (exact) eigenvalues and eigenvectors (Octave, Python)
2. Symbolic matrix exponentials (Python, Octave)
3. Numerical matrix exponentials (Octave, Python)
4. Solving $A \mathbf{x} = \mathbf{b}$ numerically (Octave, Python)
5. Solving $A \mathbf{x} = \mathbf{b}$ symbolically (Python, Octave)

Algebra and Calculus

1. Partial fraction decomposition (Python)