A copy of the takehome for the end of the semester is here takehome
To help prepare for the all exams including the final you should complete a definitions notebook following the sample definitions outline ( as a Mathematica notebook) for chapter 1 and keep this for future reference. An html version of definitions outline is also available.
You should update this notebook constantly throughout the semester, as you will be allowed to use it on your final exam.
You will be asked to state definitions and theorems on quizzes and tests and will also be asked for examples and, in some cases, counterexamples - All of this type of information should be in your defintions notebook.
I have copies of several other Differential Equations books that you may borrow. Stop by my office and I will loan you one. All of these texts cover the same basic material; there may be some differences in notation and the order of presentation, but some students find it useful to have another resource.
You need to reveiw and become proficient with the use of log and exponential functions
We will use the software Mathematica frequently during the semester. The software is installled on all LSU maintained public-use computers, so there is no need for you to purchase your own copy. If you don't have a copy of Mathematica but wish to view Mathematica files using the Mathematica front end reader, go to http://www.wolfram.com/products/mathreader which is Wolfram's Mathreader site.
If you don't have a copy of Mathematica but are interested in purchasing a student version of Mathematica take a look at http://www.wolfram.com/products/student/mathforstudents.
This is a link to an introduction to entering Mathematica. It contains some basic explanations and examples.
Here's a link to a direction field or slope field(Mathematica) file. It will generate a solution for a DE ( a general solution and some particular solutions) and produce graphs of the particular solutions along with that of the slopefield.
Here is a notebook about first order linear D.E.'s
For information about an integration notebook
Here's a notebook (in Mathematica) which finds some solutions to simple first order D.E.'s and plots a sample of integral curves. First Order D.E.'s This a notebook (in Mathematica) which deals with solutions to D.E.'s, direction fields, isoclines and equilibrium solutions
This a notebook (in Mathematica) which deals with phase diagrams to first order autonomous D.E.'s Phase Diagram Notebook
This a notebook (in Mathematica) which uses Euler's method to approximate solutions to first order D.E.'s. It assumes the D.E. has a closed form solution, which is used to give error estimations. Euler's Method Notebook
A file (notebook) on using Mathematica to perform some Row Operations on matrices.
This is a notebook on second order homogeneous DE's.
This is a notebook on second order non-homogeneous DE's.
This is a notebook on second order DE's with non-zero forcing functions.
This is a notebook for sytems of linear D.E.'s, the constant coefficient, homogeneous case.
This is a portion of a notebook on systems of linear DE's. A 3 x 3 system of DE's requiring a generalized eigenvector in a notebook form
Here is a file on Laplace Transforms useful for switched forcing functions. Laplace Transforms Notebook
Some notebooks for applications using DE's are given below.
Here's a link to a file for DE's modeling velocity with air resistance.
Here's a link to a file for a logistic DE's modeling population growth .
Here's a link to a file for DE's modeling Newton's Law of Cooling .
Here's a link to a file for DE's modeling mixture problems .
Here's a link to a file for DE's modeling LRC circuits . It is designed primarily for RC circuits where the EMF is either constant or a sinusodial function.
This is a link to a Mathematica notebook that uses manipulators or panels with buttons to investigate simply results for the applications.
Here are some explanations and examples of annuities (in html) or annuities (as a Mathematica notebook)
Here's a link to some old lecture notebooks (Mathematica files) and html files.
Material on applications of DE's as an html document or applications of DE's as a Mathematica notebook.
To find some background material on some of the mathematicians and scientist that contributed to the sutdy of differential equations (and more generally mathematics as a whole) you might start by going to site of biograhpies maintained by Wolfram.
A few facts for a Linera Algebra Review
A copy of the Linear Algebra supplement is available in PDF format. If your computer can't read pdf files, download Acrobat Reader - it's a free download, just do a search for "Acrobat Reader".
A few facts about solutions to systems of equations and matrices
The system AX = B either has no solution, exactly one solution (a unique solution) or free variables (infinitely many solutions)
A square matrix A has an inverse if and only if det(A) is NOT equal to 0.
If AX = B is a square system of equations (same number of variables as unknowns) then there is a unique solution if det(A) is not equal to 0, in which case the inverse of A exist and the solution is X =Inverse(A).B
The system AX = 0 always has X = 0 as a solution. If A is a square matrix, then there is a free variable if det(A) = 0, otherwise there is only one solution, X = 0.
One example of resonance is found in The Tacoma Narrows Bridge where the bridge eventullay collapses.
A file for Jumping off a bridge using DE's to analyze the motion as a Mathematica file or as an html file fo
General information related to ODE may be found at ODE forum, a part of the Math Forum Internet Resource Collection.
A file for Rosche's DE as a Mathematica file or as an html file
The form and nature of this page will evolve over the course of the semester.