week_01_1.2,1.2 - MATH2860U: Chapter 1 1 INTRODUCTION TO...

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MATH2860U: Chapter 1 1 INTRODUCTION TO DIFFERENTIAL EQUATIONS Definitions and Terminology (Section 1.1, pg. 2) Recall: Back in Calculus II, we introduced the concept of a differential equation. Definition: A differential equation is an equation which contains the derivatives of an unknown function (dependent variable) with respect to one or more independent variables. Notation: In order for us to talk about differential equations and figure out how to solve them, it helps to classify them according to a few criteria: type, order, and linearity. Ordinary Differential Equation vs Partial Differential Equation Definition: An ordinary differential equation ( ODE ) is one in which the unknown function depends on a single independent variable. A partial differential equation ( PDE ) is one in which the unknown function depends on more than one independent variables. Order of a Differential Equation Definition: The order of a differential equation (either ODE or PDE) is the order of the highest derivative in the equation.
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MATH2860U: Chapter 1 2 Note: If we write a differential equation in the form ) , , , , , ( ) 1 ( n n n y y y y x f dx y d where f is a real-valued continuous function, then the differential equation is said to be in normal form . Linear vs Nonlinear Differential Equations
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week_01_1.2,1.2 - MATH2860U: Chapter 1 1 INTRODUCTION TO...

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