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Chapter 1 Notes - 1st Day

# Chapter 1 Notes - 1st Day - Differential Equations...

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Differential Equations – Definitions and Terminology An equation containing the derivatives of one or more dependent variables with respect to one or more independent variables is said to be a differential equation. Examples: Differential equations are classified by: 1) Type a. Ordinary Differential Equations b. Partial Differential Equations 2) Order – The order of a differential equation is the order of the highest derivative in the equation. Note: Don’t confuse the order of a derivative with the power to which the derivative is raised. 3) Linearity An n th -order ordinary differential equation is linear if and only if: a) The dependent variable and all its derivatives are to the 1 st degree. b) Each coefficient depends at most on the independent variable x . Examples of linear differential equations Examples of nonlinear differential equations Of course, what we will be concerned with in this course is finding solutions to differential equations.

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Chapter 1 Notes - 1st Day - Differential Equations...

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