Fall 2008 // Doug Jones MWF 10:10 – 11:00 am AC 112 Lecture #1 – Introduction & Sect. 1.1...

Ordinary Differential Equations(ODE)

MAP 2302 – 64054 Fall 2008 // Doug Jones

MWF 10:10 – 11:00 am AC 112Lecture #1 – Introduction & Sect. 1.1

8/20/2008FirstLecture_DifferentialEquations_Fall08.ppt 1

• We have a Web Page: http://faculty.tcc.fl.edu/scma/jonesd

• We have email: [email protected](You need to check your “mymail.tcc.fl.edu” account at least twice a day, morning & evening.)

• We have BlackBoard: http://blackboard.tcc.fl.eduwhere you will find your grades. You can also get to the ODE Web Page through BlackBoard.


How This Course Works.

http://faculty.tcc.fl.edu/scma/jonesd

mailto:[email protected]

http://blackboard.tcc.fl.edu/

We have class – in more ways than one!◦ Class = Maturity, style, and character.◦ Class Periods. You need to attend!

We must have commitment! – I’ll talk about this all semester!


PRELIMINARY:

Look at the Table of Integrals on the inside back cover of your textbook.

Are you able to either derive or verify integrals #1 – #24? If not all, how many can you do?


Let’s Do Some ODE!

Definitions

Classifications

Verifications

Types of Solutions


Section 1.1 – Overview

Definition: Differential Equation (Short Version) “A differential equation is an equation with derivatives in it.”

Definition: Solution (Short Version) “A solution to a differential equation is a function, which when substituted into the differential equation yields an identity.”


Section 1.1 – Definitions

Type◦ Ordinary Differential Equations (ODE’s)◦ Partial Differential Equations (PDE’s)

Order◦ n-th Order means Highest Order Derivative in the

equation is “n.” Linearity

◦ Linear Differential Equation◦ Non-Linear Differential Equation


Section 1.1 – Classifications

• There is a “right way,” and there are many “wrong ways” to verify that a given function is, indeed, a solution to a given ODE.

• It has been my sad experience that many students do not understand the logic behind a “correct” verification.

• Please refer to “ODE DREAMIN’ CH 1” for examples.


Section 1.1 – Verifications

• Explicit Solutions – p. 5.• Implicit Solutions – p. 5.• Infinite Number of Solutions – p. 6.• Piecewise – Defined Solution – p. 7.• n-Parameter Family of Solutions – p. 8.• Particular Solution – p. 8.• Singular Solution – p. 8.• General Solution (Complete Solution) – p. 8.


Section 1.1 – Types of Solutions

Fall 2008 // Doug Jones MWF 10:10 – 11:00 am AC 112 Lecture #1 – Introduction & Sect. 1.1...

Documents

Transcript of Fall 2008 // Doug Jones MWF 10:10 – 11:00 am AC 112 Lecture #1 – Introduction & Sect. 1.1...