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

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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 2021-2022 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 2021-2022. They will also receive a complete practical syllabus for Semester 2 (FE First Year) Applied Mathematics 2 in addition to this.

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

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 2021-2022 With Marking Scheme

#Unit/TopicWeightage
C  Beta and Gamma Functions, Differentiation Under Integral Sign and Exact Differential Equation old 
101  Beta and Gamma Functions and Its Properties 
102  Rectification of Plane Curves 
103  Differential Equation of First Order and First Degree 
CC  Differential Calculus old 
201  Linear Differential Eqaution with Constant Coeffiecient 
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 
CCC  Numerical Solution of Ordinary Differential Equations of First Order and First Degree and Multiple Integrals old 
301  Multiple Integrals‐Double Integration 
302  Taylor’S Series Method,Euler’S Method,Modified Euler Method,Runga‐Kutta Fourth Order Formula 
CD  Multiple Integrals with Application and Numerical Integration old 
401  Triple Integration 
402  Application to Double Integrals to Compute Area, Mass, Volume. Application of Triple Integral to Compute Volume 
403  Numerical Integration 
D  Differential Equations of First Order and First Degree 
DC  Linear Differential Equations with Constant Coefficients and Variable Coefficients of Higher Order 
DCC  Numerical Solution of Ordinary Differential Equations of First Order and First Degree, Beta and Gamma Function 
DCCC  Differentiation Under Integral Sign, Numerical Integration and Rectification 
CM  Double Integration 
M  Triple Integration and Applications of Multiple Integrals 
 Total -
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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

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

University of Mumbai Semester 2 (FE First Year) Applied Mathematics 2 Syllabus for 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.

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

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.

University of Mumbai Semester 2 (FE First Year) Applied Mathematics 2 Syllabus for 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.

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

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

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

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

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

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

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

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.

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