# Applied Mathematics 2 Semester 2 (FE First Year) BE Production Engineering University of Mumbai Topics and Syllabus

CBCGS [2016 - current]
CBGS [2012 - 2015]
Old [2000 - 2011]

## Syllabus

100 Beta and Gamma Functions, Differentiation Under Integral Sign and Exact Differential Equation old
101 Beta and Gamma Functions and Its Properties
• Differentiation Under Integral Sign with Constant Limits of Integration
102 Rectification of Plane Curves
103 Differential Equation of First Order and First Degree
• Exact Differential Equations, Equations Reducible to Exact Equations By Integrating Factors
200 Differential Calculus old
201 Linear Differential Eqaution with Constant Coeffiecient
• Complimentary function, particular integrals of differential equation of the type f(D)y = X where X is eax,sin (ax+b), cos (ax+b), xn , eaxV, xV.
202 Linear Differential Equations(Review), Equation Reduciable to Linear Form, Bernoulli’S Equation
203 Cauchy’S Homogeneous Linear Differential Equation and Legendre’S Differential Equation, Method of Variation of Parameters
204 Simple Application of Differential Equation of First Order and Second Order to Electrical and Mechanical Engineering Problem
• no formulation of differential equation.
300 Numerical Solution of Ordinary Differential Equations of First Order and First Degree and Multiple Integrals old
301 Multiple Integrals‐Double Integration
• Definition
• Evaluation of Double Integrals
• Change of order of integration
• Evaluation of double integrals by changing the order of integration and changing to polar form (Examples on change of variables by using Jacobians only).
302 Taylor’S Series Method,Euler’S Method,Modified Euler Method,Runga‐Kutta Fourth Order Formula
• SciLab programming is to be taught during lecture hours.
400 Multiple Integrals with Application and Numerical Integration old
401 Triple Integration
• Definition and evaluation (Cartesian, cylindrical  and spherical polar coordinates).
402 Application to Double Integrals to Compute Area, Mass, Volume. Application of Triple Integral to Compute Volume
403 Numerical Integration
• Different type of operators such as shift, forward, backward difference and their relation.
• Interpolation, Newton  interpolation, Newton‐ Cotes formula(with proof).
• 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.
500 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)

600 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 𝑒𝑎𝑥, sin(ax+b), cos (ax+b), 𝑥𝑛, 𝑒𝑎𝑥V, xV.
2.2. Cauchy’s homogeneous linear differential equation and Legendre’s differential equation, Method of variation of parameters

700 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.

800 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.

900 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.

1000 Triple Integration and Applications of Multiple Integrals

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.