First-order differential equation and integrating factor

Introduction:

In this class, the first order and integrating factor of differential equations will be discussed. 

In mathematics, an integrating factor is a function that is chosen to facilitate the solving of a given equation involving differentials. It is commonly used to solve ordinary differential equations, but is also used within multivariable calculus when multiplying through by an integrating factor allows an inexact differential to be made into an exact differential (which can then be integrated to give a scalar field). This is especially useful in thermodynamics where the temperature becomes the integrating factor that makes entropy an exact differential.

Objectives:

• to generalize the integrating factor method from linear scalar differential equations to a linear system of differential equations
  
• to solve first-order linear differential equation
• to make an exact differential equation
• solving the real-life problem by IF method

Lesson Plan:

• Discussion from a lecture slide
• Problem-solving
• Group Work
• Question and Answering
• Home Work