# Differential Equations

## Video Lectures

Displaying all 30 video lectures.

Lecture 1Play Video |
Fundamental Set of SolutionsFind and test whether or not a set of solutions for an ODE. This video covers the three steps which need to be preformed to determine if the set is a fundamental set of solutions. |

Lecture 2Play Video |
Solving Differential Equations: Two Distinct Real RootsThis is a video in the series for solving systems of ordinary differential equations. The video addresses the process of solving the ODE's when they have real distinct eigenvalues. |

Lecture 3Play Video |
Transforming Systems ODE's and Checking SolutionsThis is the introduction video to systems of Ordinary Differential Equations. The first two examples are about placing the system in matrix form then from matrices back to the system of equations. 4 minutes in the video switches topics and discusses how to check whether a vector is a solution to the system of ODE's. |

Lecture 4Play Video |
Solving ODE's with Complex Eigen ValuesAnother video in the series how to solve a system of Ordinary Differential Equations. This video discusses what to do with complex Eigenvalues and the general solutions that result. |

Lecture 5Play Video |
Solving Systems with Repeated Eigen ValuesAnother video in the series how to solve a system of Ordinary Differential Equations. This video discusses what to do with repeated Eigenvalues and the general solutions that result. |

Lecture 6Play Video |
Test For Stability of the OriginThis video addresses the stability of the origin on a phase portrait of a 2X2 system of ordinary differential equations. Math aside this video kinda has it all; explanation, examples, derivation, and humor. |

Lecture 7Play Video |
Solving Separable DE: Example IThe video moves fast remember you can pause it. This is the first film in a series of two about solving separable DEs. It starts out the same as the second but it engages a different problem. This example entertains differential equations which can be represented as two distinct functions that can be separated algebraically then integrated. |

Lecture 8Play Video |
Solving Separable DE: Example IIThe video moves fast remember you can pause it. This is the second film in a series of two about solving separable DEs. It starts out the same as the first but it engages a different problem. This example entertains differential equations which can be represented as two distinct functions that can be separated algebraically then integrated. |

Lecture 9Play Video |
Solve Separable DEs Using SubstitutionThe video moves fast remember you can pause it. This film is the third video on solving separable differential equations and covers the topic of using a substitution when you are presented with composition of functions in your ordinary differential equation. |

Lecture 10Play Video |
Introduction to Differential EquationsThis is an introduction to differential equations. It provides definitions for: differential equations, ordinary differential equations, partial differential equations, order of a differential equation and linear differential equations. This short flick also gives examples of these definitions. In addition, the video talks about Leibniz and prime notation and differential form. Note: There is a mistake at 5:05. In the notation, it should read (d^3y)/(dx^3). |

Lecture 11Play Video |
Check Homogeneous DE y=vxThis video provides a test to determine if an first order DE is homogeneous to functions which can be separated using the substitution y=vx. |

Lecture 12Play Video |
Solving First Order Homogeneous DE: Separable First Order DE Using y=vx (Part I)This is the first video in a series of 3 about solving first order homogeneous differential equations using the change of variables y=vx. |

Lecture 13Play Video |
Solving First Order Homogeneous DE: Separable First Order DE Using y=vx (Part II)This is the second video in a series of 3 about solving first order homogeneous differential equations using the change of variables y=vx. |

Lecture 14Play Video |
Solving First Order Homogeneous DE: Translation and Substitution (Part III)This is the third video in a series of 3 about solving first order homogeneous differential equations using the change of variables y=vx. This flick discusses transforming a non homogeneous DE into a Homogeneous DE using linear transformations. |

Lecture 15Play Video |
Derivation a General Solution and Integrating Factor for a Linear Differential EquationThis video defines total differential, exact equations and uses clairiots theorem to derive the form of the integrating factor for a First order linear ODE. Then the integrating factor is used to derive the formula for a general solution to a first order linear equation. |

Lecture 16Play Video |
Linear Differental Equations: Example IThis the first example of two on how to solve a linear differential equation using and integrating factor. |

Lecture 17Play Video |
Linear Differential Equations: Example IIThis the second example of two on how to solve a linear differential equation using and integrating factor. |

Lecture 18Play Video |
Using Differential OperatorsA differential operator acts on a function. When dealing with differential operators with constant coefficients then the operators are factor-able and do factor like polynomials. This video gives three examples of using differential operators using various notations one example shows the advantage of factoring. |

Lecture 19Play Video |
Solving Linear DE's with Two Distinct Real RootsOne way to solve homogeneous linear differential equations is by using differential operators and characteristic equations. This video is an example of the process where the roots are distinct. |

Lecture 20Play Video |
Solving Linear DE's with Repeated Real RootsOne way to solve homogeneous linear differential equations is by using differential operators and characteristic equations. This video is an example of the process where the roots repeated and real. |

Lecture 21Play Video |
Solving Linear DE's with Complex RootsOne way to solve homogeneous linear differential equations is by using differential operators and characteristic equations. This video is an example of the process where the roots are complex. |

Lecture 22Play Video |
Fundamental Solution Set for Linear DE'sThree criteria for a fundamental set of solutions to a differential equation must be satisfied. The video lays them out and gives an example of the process. |

Lecture 23Play Video |
Factoring OperatorsWhen dealing with differential operators with constant coefficients then the operators are factorable and do factor like polynomials. This video gives three examples using various notation. |

Lecture 24Play Video |
Annihilator Method IThis is the first example of using the annihilator method for solving non-homogeneous linear differential equations. |

Lecture 25Play Video |
Writing a Differential Equation as a SystemThis video is about writing a differential equation as a system of differential equations. The purpose of this video is to get the differential equation in a friendly form for a computer to handle. After the transformation the computer can approximate a solution using various numerical methods. |

Lecture 26Play Video |
Existence and Uniqueness Linear D.E.'sThe video discusses the existence and uniqueness of solutions of ordinary linear differential equations. The flick starts with a theorem then quickly goes to an example. |

Lecture 27Play Video |
Linear Combination and General Solutions to Linear D.E.'sThe definition of linear combination precedes a theorem on general solutions to linear homogeneous differential equations and both are followed by and example. |

Lecture 28Play Video |
Runge-Kutta MethodThe video is about Runge-Kutta method for approximating solutions of a differential equation using a slope field. The flick derives the formula then uses excel to apply the form. Graphs of the actual solution and the approximation are provided to visualize the error of this method. |

Lecture 29Play Video |
The Wronskian and a Test for IndependenceThe Wronskian is a fun name to say and it is not hard to calculate. The video defines the wronskian and talks about using the wronskian to determine whether a set of functions is linearly independent. Then two examples are presented one dependent and one independent. |

Lecture 30Play Video |
Euler MethodThe video is about Euler method for approximating solutions of a differential equation using a slope field. The flick derives the formula then uses excel to apply the form. Graphs of the actual solution and the approximation are provided to visualize the error of this method. |