Differential Equations
Ordinary differential equations: first- and second-order methods, systems of equations, and Laplace transforms for modeling how quantities change over time.
First-Order ODEs
Classifying an equation, the standard first-order solution methods, and the models they describe.
3 topics planned
Second & Higher-Order ODEs
Homogeneous and nonhomogeneous linear equations, and the vibrating and oscillating systems they model.
4 topics planned
Series Solutions
Solving with power series when no elementary closed form exists.
1 topic planned
Laplace Transforms
Turning an initial value problem into algebra, including discontinuous and impulsive forcing.
1 topic planned
Systems & Numerical Methods
Coupled first-order systems, the phase plane, and numerical schemes when there is no closed form.
2 topics planned