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Subject:	Mathematics
Topic:	Differential Calculus
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Name:	Math By Fives (MathByFives)
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Differential Equations

Video Lectures

Displaying all 30 video lectures.

Lecture 1 Play Video	Fundamental Set of Solutions Find 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 2 Play Video	Solving Differential Equations: Two Distinct Real Roots This 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 3 Play Video	Transforming Systems ODE's and Checking Solutions This 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 4 Play Video	Solving ODE's with Complex Eigen Values Another 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 5 Play Video	Solving Systems with Repeated Eigen Values Another 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 6 Play Video	Test For Stability of the Origin This 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 7 Play Video	Solving Separable DE: Example I The 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 8 Play Video	Solving Separable DE: Example II The 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 9 Play Video	Solve Separable DEs Using Substitution The 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 10 Play Video	Introduction to Differential Equations This 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 11 Play Video	Check Homogeneous DE y=vx This 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 12 Play 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 13 Play 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 14 Play 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 15 Play Video	Derivation a General Solution and Integrating Factor for a Linear Differential Equation This 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 16 Play Video	Linear Differental Equations: Example I This the first example of two on how to solve a linear differential equation using and integrating factor.
Lecture 17 Play Video	Linear Differential Equations: Example II This the second example of two on how to solve a linear differential equation using and integrating factor.
Lecture 18 Play Video	Using Differential Operators A 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 19 Play Video	Solving Linear DE's with Two Distinct Real Roots One 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 20 Play Video	Solving Linear DE's with Repeated Real Roots One 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 21 Play Video	Solving Linear DE's with Complex Roots One 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 22 Play Video	Fundamental Solution Set for Linear DE's Three 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 23 Play Video	Factoring Operators When 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 24 Play Video	Annihilator Method I This is the first example of using the annihilator method for solving non-homogeneous linear differential equations.
Lecture 25 Play Video	Writing a Differential Equation as a System This 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 26 Play Video	Existence and Uniqueness Linear D.E.'s The 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 27 Play Video	Linear Combination and General Solutions to Linear D.E.'s The definition of linear combination precedes a theorem on general solutions to linear homogeneous differential equations and both are followed by and example.
Lecture 28 Play Video	Runge-Kutta Method The 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 29 Play Video	The Wronskian and a Test for Independence The 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 30 Play Video	Euler Method The 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.