## What to Prepare For Sem 2 Applied Maths:

**Double Integration + Area + Mass:**

(Note: Very Important Chapter as 4-5 problems can be asked. It is a major chapter.

You cannot pass Sem 2 Maths by leaving Double Integration chapter in option)

**Topics to be prepared**

**I want to Just Pass: Problems based on**

- Evaluation of Simple Double integration in Cartesian and Polar Co-ordinates.
- Changing the order of integration.
- Evaluation by Changing the order of integration.
- Computing the Area of a region using Double Integration

**I want to get good Marks:**

**I want to Score Maximum:**

- Computing the Mass of a Lamina using Double Integration

**Triple Integration + Volume**

**(Note: A Small Chapter)**

**Topics to be prepared**

**I want to Just Pass: Problems based on**

- Evaluation of Triple integration based on Cartesian coordinates.
- Evaluation of Volume using Triple integration in Cartesian system.

**I want to get good Marks: (As above and plus)**

- Evaluation of Triple integration based on cylindrical and spherical polar coordinates.
- Evaluation of Volume using Triple integration in Polar system.

**Numerical Solutions of D.E.:**

**(Note: Very Easy Chapter. Only a Fool will leave this Chapter)**

**Topics to be prepared**

**I want to Just Pass: Problems based on**

- Runga‐Kutta fourth order formula: Very Important. One problem sure on this Topic.
- Taylor’s series method: Very Important. One problem sure on this Topic.

**I want to get good Marks: (As above and plus)**

- Modified Euler method or Runge-Kutta method of order 2.
- Euler’s method.

**Numerical Integration: **

**(Note: Very Very Very Easy Chapter. Only a Fool will leave this Chapter)**

** ****Topics to be prepared**

**I want to Just Pass: Problems based on**

- Numerical integration by Trapezoidal rule
- Numerical integration by Simpson’s 1/3rd rule
- Numerical integration by Simpson’s 3/8th rule.

**(Very Important. One problem on for sure)**

**Rectification:**

**(Note: A Small Chapter)**

**Topics to be prepared**

**I want to Just Pass:**

- Safely Avoid this chapter.

**I want to get good Marks: Problems based on**

- Rectification of plane curves using cartesian equations.
- Rectification of plane curves in using Polar equations.
- Rectification of plane curves in using Parametric equations.

**Differential Equations of First Order + ****First Degree & Its Applications**

**(Note: Very Important Chapter as 3-4 problems can be asked. It is a major chapter)**

**Topics to be prepared**

**I want to Just Pass: Problems based on**

- Variable Separable Method.
- Homogenous Differential Equations.
- Exact Differential Equations.
- Equations reducible to exact form by using integrating factors. (4 Methods)
- Linear differential equations. (Two Forms)
- Equation reducible to linear form. (Two Forms)

**I want to get good Marks: (As above and plus)**

- Bernoulli’s equation.

**I want to Score Maximum: (As above and plus)**

- Simple application of differential equation of first order and first degree to electrical and Mechanical Engineering problem

**Linear Differential Equations ****Homogenous Differential Equations:**

**(Note: Very Important Chapter as 3-4 problems can be asked. It is a major chapter)**

**Topics to be prepared**

**I want to Just Pass: Problems based on**

- Complementary Function: Very Important. One Compulsory problem sure on this Topic.
- Particular Integrals:
*f*(D) y = X where X is e^{ax}, sin (ax + b), cos (ax + b), x^{n}, e^{ax}V, xV. - Method of Variation Of Parameters: Very Important. One problem sure on this Topic.

**I want to get good Marks: (As above and plus)**

- Cauchy’s Homogeneous Linear Differential Equation.
- Legendre’s Differential Equation.

**(One problem on one of the above topic for sure)**

**Beta & Gamma Functions ****& D.U.I.S.**

**(Note: One problem asked in compulsory question)**

**Topics to be prepared**

**I want to Just Pass:**

- Safely Avoid this chapter.

**I want to get good Marks: Problems based on**

- Definitions of Beta and Gamma functions.
- Properties of Beta and Gamma functions.
- Duplication Formula

**I want to Score Maximum: (As above and plus)**

- Proof of Duplication Formula
- Differentiation under integral sign with constant limits of integration.

** **