# Mathematics III

### Course Description

This Course on Mathematics - III includes Solution of ODE of First Order and First Degree, Linear Differential Equations, Bessel Functions, Laplace Transformation, Applications of Laplace Transformation, One Dimensional Wave Equation, One Dimensional Heat Equation, Euler-Cauchy Theorem, Higher Order Linear Differential Equations, Boundary Value Problems, Fourier Series, Fourier Integrals, Partial Differential Equations, Solution of One Dimensional Wave Equation, Second Order Partial Differential Equations, THree Dimensional Laplace Equation.

### Course Objective

In school mathematics, you are familiar with the natural numbers , , , , which is usually denoted by . You may remember that, after teaching , , , the teacher taught you to add and multiply two numbers. Now you can realize that you need minimum two numbers to add (or multiply). That is why, these operations are called the binary operations. What do you get as an answer, if you add (or multiply) two natural numbers? Whenever you add two natural numbers, you always get the result as a natural number. We can state this property as: Given any two natural numbers and , the sum (addition) of and , denoted by , is again a natural number. Similarly, the multiplication of any two natural numbers is again a natural number. We describe this property of school mathematics in the language of college mathematics as on the set of natural numbers , the binary operations addition and multiplication are closed .