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Progress Report

# Progress Report - Progress Report As of today October 6...

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Progress Report As of today, October 6, 2010, I have completed all the problems and notes for Chapters 1-4. 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-, Boundary-Value 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: “First-Order 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.

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Second Two Weeks: Ch. 3: “Applications of First-Order Equations” Differential equations have many physical applications.
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Progress Report - Progress Report As of today October 6...

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