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## Applied Mathematics 2

Students studying First Year Engineering will find this subject very useful. Hundreds of important topics on Applied Mathematics 2 are organized neatly into lessons below.

### Overview

#### Topics Covered

As per Choice Based Grading System

Chap 1. 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 ...

As per Choice Based Grading System

Chap 1. 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)

Chap 2. 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), $x^n, \ e^{ax}$ V, xV.

2.2. Cauchy’s homogeneous linear differential equation and Legendre’s differential equation, Method of variation of parameters.

Chap 3. Numerical solution of ordinary differential equations of first order and first degree, Beta and Gamma Function

3.1. (a)Taylor’s series method (b)Euler’s method(c) Modified Euler method (d) Runga‐Kutta fourth order formula (SciLab programming is to be taught during lecture hours)

3.2 .Beta and Gamma functions and its properties.

Chap 4. Differentiation under Integral sign, Numerical Integration and Rectification

4.1. Differentiation under integral sign with constant limits of integration.

4.2. Numerical integration‐by (a) Trapezoidal (b) Simpson’s 1/3rd (c) Simpson’s 3/8th rule (all with proof). (Scilab programming on (a) (b) (c) (d) is to be taught during lecture hours)

4.3. Rectification of plane curves

Chap 5. 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.

Chap 6. Triple Integration and Applications of Multiple Integral

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

6.2. Application of double integrals to compute Area, Mass, Volume. Application of triple integral to compute volume.