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MATH24 Lecture 1

# MATH24 Lecture 1 - MATH24 Differential Equations...

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MATH24 Differential Equations

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Definitions An differential equation is an equation involving an unknown function and its derivatives. The following are differential equations involving the unknown function y. 3 5 + = x dx dy 1 2 2 2 2 = + dx dy dx y d e y ( 29 0 5 sin 4 2 2 3 3 = + + xy dx y d x dx y d x dx dy y dx dy y dx y d 5 3 2 3 7 3 2 2 = + + 0 4 2 2 2 2 = - x y t y (1.1) (1.2) (1.3) (1.4) (1.5) t E i C dt di R dt i d L ϖ ϖ cos 1 2 2 = + + (1.6) ( 29 0 2 2 2 = - + xydy dx y x (1.7)
Definitions A differential equation is an ordinary differential equation (ODE) if the unknown function depends on only one independent variable. If the unknown function depends on two or more independent variables, the differential equation is a partial differential equation (PDE). Equations (1.1) through (1.4) are examples of ordinary differential equations, since the unknown function y depends solely on the variable x. Equation (1.5) is a partial differential equation, since y depends on both the independent variables t and x.

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Definitions In equation 1.6 i is the dependent variable, t the independent variable, and L, R, C, E, and ω are called parameters . Since the equation 1.7 may be written as or we may consider either variable to be dependent, the other being the independent one.
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MATH24 Lecture 1 - MATH24 Differential Equations...

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