Bernd Schröder

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Videos on topics in differential equations

The videos below are my first step towards remote delivery of a differential equations course. Video presentations will be integrated seamlessly with my differential equations book. Presentations are sorted by topic.

For now, however, it should be noted that the videos were shot basically without re-takes in 4-8 hour sessions. Thus some of them will not be as good as they could be and some are slated to be re-shot. Once all needed videos have been created, I can go back and refine the production. The names should be self-explanatory.

The videos were produced with tegrity. For best performance, they should be downloaded and then run with Internet Explorer as the default browser. The slides were produced with the LaTeX beamer package.

 

Introduction.

This is an overview of the course and of my philosophy for the course, the text and the videos. There is some popping on the sound. I may need to re-shoot this one. 

Video.                 Slides.             

 

Modeling.

Derivation of the differential equation for a spring-mass-system.
Video.                 Slides.
Note: This was the first video I shot. The microphone pops a bit, which was fixed for the other videos. Video is a candidate to be re-shot.
Derivation of the differential equation for an LRC circuit.
Video.                 Slides.
Derivation of the differential equations for a multi-loop circuit, Kirchhoff's laws.
Video.                 Slides.
Derivation of the equation for an oscillating string.
Video.                 Slides.  
Derivation of the heat equation.
Video.                 Slides.

First order differential equations.

General solution of separable differential equations.
Video.                  Slides.
Solution of an initial value problem for a separable differential equation. (Reviews integration by substitution and integration by parts.)
Video.                  Slides.
Linear first order differential equations.
Video.                  Slides.
Bernoulli equations.
Video.                  Slides.
Homogeneous first order equations.
Video.                  Slides.
Exact differential equations.
Video.                  Slides.
How to recognize types of first order equations and how to review them. (I misspeak twice, possible candidate for re-shoot.)
Video.                  Slides. 

Second order constant coefficient differential equations.

Solution of linear homogeneous second order differential equations with constant coefficients.
Video.                  Slides.
The method of undetermined coefficients.
Video.                  Slides.
The method of undetermined coefficients when the forcing function solves the homogeneous equation. There is some popping on the sound. I may need to re-shoot this one.
Video.                 Slides.  
The formula for Variation of Parameters. (Solves some rather nasty integrals. Typo on one slide, candidate to be re-shot.)
Video.                  Slides. 
Theory of linear differential equations. There is some popping on the sound. I may need to re-shoot this one.
Video.                 Slides. 

 

 

Laplace transforms.

Solving initial value problems with Laplace transforms.
Video.                  Slides.
An initial value problem that involves damped trigonometric functions.
Video.                  Slides.
Step functions and Laplace transforms.
Video.                  Slides.
Delta functions and Laplace transforms. (Typo in one of the exponentials. May be re-shot.)
Video.                  Slides.

Separation of variables.

Solving the equation for the oscillating string.
Video.                 Slides.  
Deriving the Legendre equation. This presentation plus the presentation on Legendre polynomials (see under series solutions below) provide most of the mathematics for the quantum mechanical description of the hydrogen atom.
Video.                 Slides.  
Deriving the Bessel equation.
Video.                 Slides.  
Eigenvalues of the Laplace operator.
Video.                 Slides.  

 

Series solutions.

Taylor polynomials (summary).
Video.                 Slides. 
Power series (summary).
Video.                 Slides. 
Series solutions about ordinary points.
Video.                  Slides.
Legendre polynomials. This presentation plus the presentation on deriving the Legendre equation (see separation of variables above) provide most of the mathematics for the quantum mechanical description of the hydrogen atom.
Video.                 Slides.
Radius of convergence of power series solutions.
Video.                 Slides.  
Method of Frobenius.
Video.                  Slides.
Method of Frobenius: An example in which we only get one solution. (Also an example of a specific Bessel equation.) There is some popping on the sound. I may need to re-shoot this one.
Video.                 Slides. 
Bessel equations.
Video.                 Slides. 
Reduction of order. This topic fits here, because the fact that the method of Frobenius sometimes gives only one solution motivates reduction of order. There is some popping on the sound. I may need to re-shoot this one.
Video.                 Slides.  

 

Systems of linear differential equations.

Matrix multiplication.
Video.                 Slides.