Introduction to Differential Equations

Tutoring on Introduction to Differential Equations

Learning Objectives:

Understand and apply Concept of Differential Equations

Math Tutoring on Introduction to Differential Equations

A Differential Equation is an equation that contains an unknown function and its derivative.

e.g.  etc.

To solve a Differential Equation, we want to determine an equation that satisfies the Derivative Equation. This will require Integration.

When solving a Differential Equation in the form , it is helpful to rewrite the equation in Differential Form. Then we can integrate both sides of the equation.

Types of Differential Equations:

1.   Ordinary Differential Equations (ODE) – An Ordinary Differential Equation contains only Ordinary Derivative with respect to one Independent Variable.

2.   Partial Differential Equations (PDE) – A Partial Differential Equation contains Partial Derivatives with respect to two or more Independent Variables.

The Order of a Differential Equation (ODE or PDE) – The Order of a Differential Equation is the Order of the highest derivative in the equation.

 

 

 

Linear and Nonlinear Differential Equations:

1.    A Linear Differential Equation can be written in the form:

Note that –

·       The Dependent Variable and all of its derivatives are always to the first power.

·       There are no products of the function y and its derivatives.

·       The coefficients can be zero, constants, or functions of t.

2.    A Nonlinear Differential Equation is a Differential Equation that is NOT linear.

 

 

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Hook Questions:

1.    What is Differential Equations? How to solve it?

2.    What are the Ordinary and Partial Differential Equations?

3.    What is Linear Differential Equation? State some properties of it. 

 

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