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

**Beta and Gamma Function**

**Differentiation under Integral sign**

**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

**Volume of Solid**

**Numerical Integration**

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

**Tracing of curves**

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