Chapter 4 - Fourier Series -

Fourier Series click here

Odd and Even Function click here

-Exercise

Periodic Function click here , click here

-Exercise

Half Range click here

-Exercise

Formula 4 Fourier Series

Chapter 3 - Sequence and Series -

Sequences and Series

Sequences and Their Limits

Series click here

 -Telescoping series

 -Test for a Divergent series

Integral Test click here

 -P-series

Comparison Tests click here

Ratio and Root Test

 -Ratio Test

 -Root Test

Alternating Series

 -Alternating Series Test

 -Absolute and Conditional Convergence

Power Series click here

 -Power Series in x-a

 -Power Series in x

Representing Functions by Power Series

 -Differentiation and Integration of Power Series

Taylor and Maclaurin Series click here

 

Chapter 2 - Second Order Differential Equation -

Second Order Differential Equation Click here

A.Second Order Homogeneous Equation Click here

B.Second Order Non-homogeneous Equation

    1.Solving second order Non-Homogeneous Equation by undetermined coefficient method.

    2.Solving second order Non-Homogeneous Equation by using    Variation of Parameters method.
       Application. Table of particular integral

       

    3.Laplace Transformation Click here, Table of Laplace Transform.

       Characteristics of Laplace Transform:

        -Theorem 1:Linearity
        -Theorem 2:First shift
        -Theorem 3:Multiply with t^n
       Exercise
       Inverse Laplace Transformation , Partial Fraction.

       Application of Laplace Transform.

        -Solving First Order Linear Differential Equation.
        -Solving Second Order Differential Equation.
       Exercise

         

        

           

Chapter 1 - 1st Order Ordinary Differential Equation -

First Order Differential Equation Click here


First Basic Order

1.Separable Equation
2.Homogeneous Equation

3.Linear Equation
1st ODE Application

Linear equation