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.