Legendre’S Differential Equation

Beta and Gamma Functions, Differentiation Under Integral Sign and Exact Differential Equation old

Differential Calculus old

Numerical Solution of Ordinary Differential Equations of First Order and First Degree and Multiple Integrals old

Multiple Integrals with Application and Numerical Integration old

Differential Equations of First Order and First Degree

• Exact Differential Equations
• Equations Reducible to Exact Form by Using Integrating Factors
• Linear Differential Equations
• Equation Reducible to Linear Form
• Bernoulli’S Equation
• Simple Application of Differential Equation of First Order and First Degree to Electrical and Mechanical Engineering Problem

Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order

• Linear Differential Equation with Constant Coefficient‐ Complementary Function
• Particular Integrals of Differential Equation
• Cauchy’S Homogeneous Linear Differential Equation
• Legendre’S Differential Equation
• Method of Variation of Parameters

Numerical Solution of Ordinary Differential Equations of First Order and First Degree, Beta and Gamma Function

• Taylor’S Series Method
• Euler’S Method
• Modified Euler Method
• Runga‐Kutta Fourth Order Formula
• Beta and Gamma Functions and Its Properties

Differentiation Under Integral Sign, Numerical Integration and Rectification

• Differentiation Under Integral Sign with Constant Limits of Integration
• Numerical Integration‐ by Trapezoidal
• Numerical Integration‐ by Simpson’S 1/3rd
• Numerical Integration‐ by Simpson’S 3/8th Rule
• Rectification of Plane Curves

Double Integration

• Double Integration‐Definition
• Evaluation of Double Integrals
• Change the Order of Integration
• Evaluation of Double Integrals by Changing the Order of Integration and Changing to Polar Form

Triple Integration and Applications of Multiple Integrals

• Triple Integration Definition and Evaluation
• Application of Double Integrals to Compute Area
• Application of Double Integrals to Compute Mass
• Application of Double Integrals to Compute Volume
• Application of Triple Integral to Compute Volume