Progress Report
As of today, October 6, 2010, I have completed all the problems and notes for Chapters
14.
I have also done the notes for Chapter 5.
I have been doing the notes for the whole
chapter before I do the problems for that chapter, so that’s why I have not yet done the
problems for Chapter 5.
Timeline
The following timeline of events represents a loose structure for the progression
of the course:
•
First Two Weeks:
Ch. 1: “Differential Equations and Their Solutions”
This chapter was really easy.
It provided definitions and terminology which will be necessary to know for the
rest of this course.
1.1 Classification of Differential Equations; Origin & Applications
Stated
the difference between ordinary and partial differential equations as well
as defining Linear ODE
1.2 Solutions
Defines the difference between implicit and explicit
solutions of a function
1.3 Initial, BoundaryValue Problems & Existence of Solutions
Provides
a review on how to solve initial value problems.
It defined the Basic
Existence and Uniqueness Theorem by providing conditions, which if met,
will ensure a differential equation to have a unique solution.
Ch. 2: “FirstOrder Equations for Which Exact Solutions are Obtainable”
This
chapter had sections that were difficult as well as sections that were easy.
This
section provided a review of separable and linear equations, which was covered in
Calculus 2.
So, those sections were easy.
This chapter was difficult at first
because it involved partial derivatives, of which my prior knowledge was not
sufficient to fully understand this chapter.
However, after I gauged an
understanding of partial derivatives, this chapter became fairly easy.
2.1 Exact Differential Equations and Integrating Factors
This was a new
concept and an understanding of partial derivatives was important.
If a
differential equation met the conditions outlined in this section, then the
methods provided in this section could be used to solve that problem.
2.2 Separable Equations and Equations Reducible to This Form
Separable
equations have been solved since Calculus I.
This section also introduced
homogenous equations.
This is when a derivative f(x,y) can be written as
g(y/x).
If this condition is met then the transformation y=vx will
transform the homogenous equation into a separable equation.
2.3 Linear Equations and Bernoulli Equations
We learned how to solve
linear equations in Calculus II.
In this section, Bernoulli Equations were
introduced.
They are the same thing as linear equations except the Q(x)
term is multiplied by a power of y.
2.4 Special Integrating Factors and Transformations
Defines 2 special
integrating factors.
It also talks about two types of transformation.
One of
the criteria is that an x, y, and a constant must be present under dx and dy.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
•
Second Two Weeks:
Ch. 3: “Applications of FirstOrder Equations”
Differential equations have many
physical applications.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '11
 profeessor
 Differential Equations, Derivative, Linear Systems, Linear Differential Equations, Bernoulli Equations

Click to edit the document details