What you'll learn:
- Determining the Type and Order of a Differential Equation
- Determining whether a Differential Equation is Linear or Nonlinear
- Understand the Different Types of Solutions of Differential Equations: one-parameter families, two-parameter families, singular solutions, general solutions
- Understand Initial Value Problems and the Interval of Definition
- How to Solve Separable Differential Equations, First Order Linear, Exact, Homogeneous, Bernoulli, and DE's of the form dy/dx = f(Ax + By + C)
- How to Determine if Functions are Linearly Independent or Dependent using the Definition
- How to Prove Functions are Linearly Independent using the Wronskian
- How to Solve Higher Order Linear Homogeneous Differential Equations with Constant Coefficients
- How to Solve DE's with the Method of Undetermined Coefficients(The Superposition Principle)
- How to Solve DE's with Variation of Parameters
- How to Solve Cauchy-Euler Differential Equations
- How to Compute Laplace Transforms with the Definition
- How to Compute Laplace Transforms and Inverse Laplace Transforms with Tables, Partial Fractions, and Trigonometric Identities
- How to use the First Translation Theorem to Compute Laplace Transforms
- How to use the Derivatives of Transforms Theorems
- How to Solve DE's using Laplace Transforms
- Understand what the Unit Step Function is and use it to Find the Laplace Transform of a Piecewise Function
- Understand what the Dirac Delta Function is
- How to use the Second Translation Theorem to compute Laplace Transforms and Inverse Laplace Transforms
- How to Solve DE's that involve the Dirac Delta Function
- How to Find the Minimum Radius of Convergence
- How to Solve DE's using Power Series
This is a complete college level course in DifferentialEquations with TONS of examples.
*** In order to get the most out of the course you should know Calculus ***
Basically just,
1) Watch the videos, and try to follow along. Try to do the problems before Ido them if you can. If you can't, no big deal:)
2) After each section there is short assignment(with solutions).
3) Repeat!
If you finish even 50% of this course you will know ALOT of Differential Equations and more importantly just a lot of really solid mathematics.
Differential Equations is an awesome class not just because of the differential equations but because of all of the other key math techniques you learn in the process. This course covers all the key techniques usually covered in most differential equations courses. After taking this course you should know a lot of differential equations and roughly the equivalent of what is taught in a college level course. The hardest thing about this course is the integration techniques, most of which are learned in Calculus 1 and Calculus 2. I have tried to explain these techniques when they come up so hopefully you can follow along and learn lots of math.
I hope you enjoy watching these videos and working through these problems as much as Ihave:)
