Separable differential equations (1W)
Solve separable first-order differential equations by separating the variables and integrating both sides of the equation. Section 2.2 from the book. View lesson →
Differential Equations Lessons
Integrating Factors (1F)
The method of integrating factors helps you solve first order linear differential equations. You have to integrate with respect to t two times in order to solve each problem. Section 2.1. View lesson →
Modeling a tank with dyed water (2M)
A first example of modeling with differential equations. Many problems are similar to the tank problem, where you have to account for how much of something is flowing in and how much is flowing out. Section 2.3. View lesson →
Modeling credit card interest (2W)
More modeling problems. This lesson is a discussion of the credit card interest problem that we did in class. Section 2.3. View lesson →
Autonomous equations (3M)
An autonomous equation is a differential equation that depends only on y and y', and not on t. You can understand these without solving the differential equation by finding the equilibrium solutions. Section 2.5. View lesson →
Euler's Method (3W)
Euler's method uses the tangent line approximation to find an approximate solution for first order differential equations that you cannot solve in other ways. Section 2.7. View lesson →
Linear Homogeneous equations with constant coefficients (4M)
Second order linear homogeneous differential equations, with constant coefficients. They are pretty easy to solve, and you don't have to do any integration. Section 3.1. View lesson →
Complex Roots to the Characteristic Equation (4W)
Although the method from Monday technically works even if the roots to the characteristic equation are not real, there is a way to eliminate the imaginary numbers by using sines and cosines. Section 3.3. View lesson →
Trigonometry review (5W)
Use trigonometry identities to combine sine and cosines into a single term. Some terminology: frequency, amplitude, quasi frequency, etc. Section 3.7. View lesson →
Analyze damped oscillation (5F)
This is a quick lesson discussing how to analyze damped oscillations. Section 3.7. View lesson →
Method of Undetermined Coefficients (6W)
The method of undetermined coefficients lets you solve non-homogeneous linear differential equations. Section 3.5. View lesson →
Undetermined coefficients, part 2 (6F)
How to find the format for the particular solution, and when and how to “bump up” the particular solution. Section 3.5. View lesson →
Forced oscillation and resonance (7M)
An introduction to resonance and forced oscillation. Section 3.8. View lesson →
Using Laplace Transforms (7F)
Using Laplace transforms to solve initial value problems. Section 6.1. View lesson →
Laplace transforms of discontinuous functions (9W)
A start-to-finish example of a differential equation with a discontinuous function. Section 6.4. View lesson →