Fall 2008 // Doug Jones MWF 10:10 – 11:00 am AC 112 Lecture #1 – Introduction & Sect. 1.1 8/20/2008 FirstLecture_DifferentialEquations_Fall08.ppt 1.

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Presentation transcript:

Fall 2008 // Doug Jones MWF 10:10 – 11:00 am AC 112 Lecture #1 – Introduction & Sect /20/2008 FirstLecture_DifferentialEquations_Fall08.ppt 1

We have a Web Page: We have (You need to check your “mymail.tcc.fl.edu” account at least twice a day, morning & We have BlackBoard: where you will find your grades. You can also get to the ODE Web Page through BlackBoard. 8/20/2008FirstLecture_DifferentialEquations_Fall08.ppt2

 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! 8/20/2008FirstLecture_DifferentialEquations_Fall08.ppt3

 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? 8/20/2008FirstLecture_DifferentialEquations_Fall08.ppt4

 Definitions  Classifications  Verifications  Types of Solutions 8/20/2008FirstLecture_DifferentialEquations_Fall08.ppt5

 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.” 8/20/2008FirstLecture_DifferentialEquations_Fall08.ppt6

 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 8/20/2008FirstLecture_DifferentialEquations_Fall08.ppt7

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.ODE DREAMIN’ CH 1 8/20/2008FirstLecture_DifferentialEquations_Fall08.ppt8

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. 8/20/2008FirstLecture_DifferentialEquations_Fall08.ppt9