Topics covered in a first year course in differential equations. Need to understand basic differentiation and integration from Calculus before starting here.
What a differential equation is and some terminology?
Another separable differential equation example.
Chain rule using partial derivatives (not a proof; more intuition).
More intuitive building blocks for exact equations.
Using an integrating factor to make a differential equation exact.
Another example of using substitution to solve a first order homogeneous differential equations.
Introduction to 2nd order, linear, homogeneous differential equations with constant coefficients.
Let's find the general solution!
Let's use some initial conditions to solve for the particular solution.
Another example with initial conditions!
What happens when the characteristic equations has complex roots?!
What happens when the characteristic equation has complex roots?
Lets do an example with initial conditions!
What happens when the characteristic equation only has 1 repeated root?
An example where we use initial conditions to solve a repeated-roots differential equation.
Using the method of undetermined coefficients to solve nonhomogeneous linear differential equations.
Another example where the nonhomogeneous part is a polynomial.
Using the Laplace Transform to solve an equation we already knew how to solve.
Second part of using the Laplace Transform to solve a differential equation.
A grab bag of things to know about the Laplace Transform.
Solving a non-homogeneous differential equation using the Laplace Transform.
Introduction to the unit step function and its Laplace Transform.
Using our toolkit to take some inverse Laplace Transforms.
Hairy differential equation involving a step function that we use the Laplace Transform to solve
Figuring out the Laplace Transform of the Dirac Delta Function.
Understanding how the product of the Transforms of two functions relates to their convolution.
Using the Convolution Theorem to solve an initial value problem.