1. Power Series Solution of Differential Equations
1. Power Series
2. Ordinary and Singular Points
3. Power Series Solution about an Ordinary Point
4. Regular and Irregular in Singular Points
5. Power Series Solution about Regular Singular Point (Frobenius Method)
2. Bessel's Equations and Bessel's Funtions
1. Beta and Gamma Functions
2. Bessal's Differential Equation Bessel's Functions
3. Recurrence Relations for Bessel's Function
4. Generating Function for Bessel's Function
5. Orthogonality of Bessel's Functions
6. Integral Form of Bessel's Function
3. Legendre's Equation and Legendre's Functions
1. Legendre's Equation and Legendre's Function
1.1 Another Form of Pn (x)
2.Generating Function for Pn (x)
3. The Recurrence Relations for Pn (x)
4.Laplace's Definite Integral for Pn (x)
5. Rodrigues' Formula
6.Orthogonal Property of Legendre's Polynimials
4. Partial Differential Equations of First Order
1. Partial Differential Equations
2. Origin of First Order Partial Differential Equations
2.1 Formation of Partial Differential Equations by Elimination of Two Arbitary Function
2.2 Formation of Partial Differential Equation by Elimination of Arbitary Function
3. Lagrange's Solution of The Linear Partial Differential Equations
4. Geometrical Interpretation of Lagrange's Linear Equations
5. Integral Surface Passing Through a given Curve
6.Surfaces Orthogonal to given System of Surfaces
5.The Laplace Transforms
1. Definition of Extension of Laplace Transform
2. Linearity Property
3. Laplace Transforms of SOme Elementary Functions
4. Shifting Properties
5. Change of Scale Property
6. Laplace Transform of Derivatives
7. Multipilication by tn
8. Laplace Transform of Integrals
9. Division by t
10. Laplace Transform of Laplace Transform
6. Inverse Laplace Transform
1. Linear Property
2. Shifting Properties
3. Change of Scale Property
4. Inverse Laplace Transform of Derivatives
5. Division by s
6. Inverse Laplace Transform of Integrals
7. Method of Partial Fractions to Evaluate Inverse Laplace Transform
8. The Convolution Property
7. Applications of Laplace Transforms
1. Solution of Ordinary Differential Equations with Constant Coefficients
2. Solution of Ordinary Differential Equations with Variable Coefficients
3. Solution of Simultaneous Ordinary Differential Equations
