differential equations intro
TRANSCRIPT
Differential EquationsIntroduction, types, order, degree, etc
Definition, Notations
Ordinary DE
• Ordinary Differential Equation is one which relates a function y = f (x) to one independent variable x and its derivative/s. Assuming that y is a function of x, the following are examples of ODE
Partial DE
• A partial differential equation is one which relates a function of two or more variables to its partial derivatives.
LDE and NLDE
• Linear Differential Equation
Exercises
Exercises
Order and Degree
• Order of DE – the highest order of derivative contained in the equation.
• Degree of DE – the degree of the highest order of derivative contained in the equation.
Order and Degree
Solution to DE
• Solution to DE – is a function y = f(x) that satisfies the differential equation.
Solution to DE
Initial Value Problem
• Initial Value Problem – a differential equation which supplies a numerical value for some of its derivative at some point (x, y)
General Solution & Particular Solution
• General Solution – solution to a DE without specific initial conditions.
• Particular Solution – solution to a DE with initial conditions
Exercises