MTH401 Midterm Short Notes

MTH401 Short Notes Mid term · Lec 1 to18 · WEBSITE LINK:

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Lecture#1

Ordinary Differential Equations

The term “Ordinary Differential Equations” also known as ODE is an equation that contains only one independent variable and one or more of its derivatives with respect to the variable. In other words, the ODE is represented as the relation having one independent variable x, the real dependent variable y, with some of its derivatives.

y’,y”, ….yn ,…with respect to x.

Linear y=mx+c

Quadratic ax2+bx+c=0

Cubic ax3+bx2+cx+d=0

Types The ordinary differential equation is further classified into three types. They are:

•  Autonomous ODE
•  Linear ODE
•  Non-linear ODE

Autonomous Ordinary Differential Equations

A differential equation which does not depend on the variable, say x is known as an autonomous differential equation.

Linear Ordinary Differential Equations

If differential equations can be written as the linear combinations of the derivatives of y, then they are called linear ordinary differential equations. These can be further classified into two types:

•  Homogeneous linear differential equations
•  Non-homogeneous linear differential equations

Non-linear Ordinary Differential Equations

If the differential equations cannot be written in the form of linear combinations of the derivatives of y, then it is known as a non-linear ordinary differential equation.

Example

Lecture-2:

Elements of the Theory

Applicable to:

• Chemistry
• Physics
• Engineering
• Medicine
• Biology
• Anthropology

Differential Equation involves an unknown function with one or more of its derivatives

Ordinary D.E. a function where the unknown is dependent upon only one independent variable

Examples of Des