University of Mumbai Syllabus For Semester 2 (FE First Year) Applied Mathematics 2: Knowing the Syllabus is very important for the students of Semester 2 (FE First Year). Shaalaa has also provided a list of topics that every student needs to understand.

The University of Mumbai Semester 2 (FE First Year) Applied Mathematics 2 syllabus for the academic year 2022-2023 is based on the Board's guidelines. Students should read the Semester 2 (FE First Year) Applied Mathematics 2 Syllabus to learn about the subject's subjects and subtopics.

Students will discover the unit names, chapters under each unit, and subtopics under each chapter in the University of Mumbai Semester 2 (FE First Year) Applied Mathematics 2 Syllabus pdf 2022-2023. They will also receive a complete practical syllabus for Semester 2 (FE First Year) Applied Mathematics 2 in addition to this.

## University of Mumbai Semester 2 (FE First Year) Applied Mathematics 2 Revised Syllabus

University of Mumbai Semester 2 (FE First Year) Applied Mathematics 2 and their Unit wise marks distribution

### University of Mumbai Semester 2 (FE First Year) Applied Mathematics 2 Course Structure 2022-2023 With Marking Scheme

## Syllabus

### University of Mumbai Semester 2 (FE First Year) Applied Mathematics 2 Syllabus for Beta and Gamma Functions, Differentiation Under Integral Sign and Exact Differential Equation old

- Differentiation Under Integral Sign with Constant Limits of Integration

- Exact Differential Equations, Equations Reducible to Exact Equations By Integrating Factors

### University of Mumbai Semester 2 (FE First Year) Applied Mathematics 2 Syllabus for Differential Calculus old

- Complimentary 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.

- no formulation of differential equation.

### University of Mumbai Semester 2 (FE First Year) Applied Mathematics 2 Syllabus for Numerical Solution of Ordinary Differential Equations of First Order and First Degree and Multiple Integrals old

- 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).

- SciLab programming is to be taught during lecture hours.

### University of Mumbai Semester 2 (FE First Year) Applied Mathematics 2 Syllabus for Multiple Integrals with Application and Numerical Integration old

- Definition and evaluation (Cartesian, cylindrical and spherical polar coordinates).

- 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.

### University of Mumbai Semester 2 (FE First Year) Applied Mathematics 2 Syllabus for Differential Equations of First Order and First Degree

- Exact Differential Equations
- Equations Reducible to Exact Form by Using Integrating Factors
- Linear Differential Equations
- Equation Reducible to Linear Form
- Bernoulli’S Equation
- Simple Application of Differential Equation of First Order and First Degree to Electrical and Mechanical Engineering Problem

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)

### University of Mumbai Semester 2 (FE First Year) Applied Mathematics 2 Syllabus for Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order

- Linear Differential Equation with Constant Coefficient‐ Complementary Function
- Particular Integrals of Differential Equation
- Cauchy’S Homogeneous Linear Differential Equation
- Legendre’S Differential Equation
- Method of Variation of Parameters

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

### University of Mumbai Semester 2 (FE First Year) Applied Mathematics 2 Syllabus for Numerical Solution of Ordinary Differential Equations of First Order and First Degree, Beta and Gamma Function

- Taylor’S Series Method
- Euler’S Method
- Modified Euler Method
- Runga‐Kutta Fourth Order Formula
- Beta and Gamma Functions and Its Properties

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.

### University of Mumbai Semester 2 (FE First Year) Applied Mathematics 2 Syllabus for Differentiation Under Integral Sign, Numerical Integration and Rectification

- Differentiation Under Integral Sign with Constant Limits of Integration
- Numerical Integration‐ by Trapezoidal
- Numerical Integration‐ by Simpson’S 1/3rd
- Numerical Integration‐ by Simpson’S 3/8th Rule
- Rectification of Plane Curves

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.

### University of Mumbai Semester 2 (FE First Year) Applied Mathematics 2 Syllabus for Double Integration

- Double Integration‐Definition
- Evaluation of Double Integrals
- Change the Order of Integration
- Evaluation of Double Integrals by Changing the Order of Integration and Changing to Polar Form

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.

### University of Mumbai Semester 2 (FE First Year) Applied Mathematics 2 Syllabus for Triple Integration and Applications of Multiple Integrals

- Triple Integration Definition and Evaluation
- Application of Double Integrals to Compute Area
- Application of Double Integrals to Compute Mass
- Application of Double Integrals to Compute Volume
- Application of Triple Integral to Compute Volume

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.