# Applied Mathematics – 2 Chapter wise Video Lectures

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Ganesh Shegar presents – Engineering On Your Finger Tips

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### Differential Equations of First Order and First Degree

1.1 Exact differential Equations, Equations reducible to exact form by using integrating factors. 1.2 Linear differential equations (Review), equation reducible to linear form, Bernoulli’s equation. 1.3: Simple application of differential equation of first order and first degree to electrical and Mechanical Engineering problem (no formulation of differential equation)

### Linear Differential Equations With Constant Coefficients and Variable Coefficients Of Higher Order

2.1. Linear Differential Equation with constant coefficient‐ complementary function, particular integrals of differential equation of the type f(D)y = X where X is 𝑒 𝑎𝑥, sin(ax+b), cos (ax+b), 𝑥 𝑛 , 𝑒 𝑎𝑥V, xV. 2.2. Cauchy’s homogeneous linear differential equation and Legendre’s differential equation, Method of variation of parameters

### Numerical solution of ordinary differential equations

(a)Taylor’s series method (b)Euler’s method (c) Modified Euler method (d) Runga‐Kutta fourth order formula

Rectification

### Double Integration

5.1. Double integration‐definition, Evaluation of Double Integrals. 5.2. Change the order of integration, Evaluation of double integrals by changing the order of integration and changing to polar form.

### Triple Integral

Triple integration definition and evaluation (Cartesian, cylindrical and spherical polar coordinates

### Numerical Integration

2. Numerical integration‐ by (a) Trapezoidal (b) Simpson’s 1/3rd (c) Simpson’s 3/8th rule (all with proof