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Ordinary Differential Equations (ODE) MAP 2302 – 64054

Ordinary Differential Equations (ODE) MAP 2302 – 64054. Fall 2008 // Doug Jones MWF 10:10 – 11:00 am AC 112 Lecture #1 – Introduction & Sect. 1.1. How This Course Works. We have a Web Page: http://faculty.tcc.fl.edu/scma/jonesd

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Ordinary Differential Equations (ODE) MAP 2302 – 64054

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  1. Ordinary Differential Equations(ODE)MAP 2302 – 64054 Fall 2008 // Doug Jones MWF 10:10 – 11:00 am AC 112 Lecture #1 – Introduction & Sect. 1.1 FirstLecture_DifferentialEquations_Fall08.ppt

  2. How This Course Works. FirstLecture_DifferentialEquations_Fall08.ppt • We have a Web Page:http://faculty.tcc.fl.edu/scma/jonesd • We have email:jonesd@tcc.fl.edu(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.

  3. FirstLecture_DifferentialEquations_Fall08.ppt • 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!

  4. Let’s Do Some ODE! FirstLecture_DifferentialEquations_Fall08.ppt 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?

  5. Section 1.1 – Overview FirstLecture_DifferentialEquations_Fall08.ppt Definitions Classifications Verifications Types of Solutions

  6. Section 1.1 – Definitions FirstLecture_DifferentialEquations_Fall08.ppt 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.”

  7. Section 1.1 – Classifications FirstLecture_DifferentialEquations_Fall08.ppt • 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. Section 1.1 – Verifications FirstLecture_DifferentialEquations_Fall08.ppt • 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.

  9. Section 1.1 – Types of Solutions FirstLecture_DifferentialEquations_Fall08.ppt • 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.

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