B.E. (Computer Engineering) Applied Mathematics II Syllabus - Mumbai University 2026
The University has moved this degree onto NEP 2020 one year at a time. The first and second years are NEP 2020 syllabi; the third and fourth years are still examined on the REV-2019 'C' Scheme, which is what the University sets for them this year.
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Syllabus for Applied Mathematics-II
Module 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. # Self learning topics: Simple application of differential equation of first order and first degree to electrical and Mechanical Engineering problem
Module 2: Linear Differential Equations With Constant 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), 𝑥𝑚 , 𝑒 𝑎𝑥 𝑉
- 2.2 Method of variation of parameters. # Self learning topics: Cauchy’s homogeneous linear differential equation and Legendre’s differential equation, Applications of Higher order differential equation.
Module 3: Beta and Gamma Function, Differentiation under Integral sign
- 3.1 Beta and Gamma functions and its properties.
- 3.2 Differentiation under integral sign with constant limits of integration. # Self learning topics: Rectification of curves.(Cartesian, Polar and Parametric)
Module 4: Multiple Integration- I
- Pre-requisite: Tracing of curves
- 4.1 Double integration‐ definition, Evaluation of Double Integrals.(Cartesian & Polar)
- 4.2 Change the order of integration.(No Evaluation)
- 4.3 Evaluation of double integrals by changing to polar coordinates
Module 5: Multiple Integration- II
- 5.1 Triple integration definition and evaluation (Cartesian, cylindrical and spherical polar coordinates).
- 5.2 Application of double integrals to compute Area, Mass. # Self learning topics: Application of triple integrals to compute Volume.
Module 6: Numerical solution of ordinary differential equations of first order and first degree, and , Numerical Integration
- 6.1 Numerical solution of ordinary differential equation using (a) Euler’s method (b) Modified Euler method, (c) Runge‐ Kutta fourth order method
- 6.2 Numerical integration‐ by (a) Trapezoidal (b) Simpson’s 1/3rd (c) Simpson’s 3/8th rule (all without proof)
References
- 1 Higher Engineering Mathematics, Dr.B.S.Grewal, Khanna Publication
- 2 Advanced Engineering Mathematics, Erwin Kreyszig, Wiley EasternLimited, 9th Ed.
- 3 Engineering Mathematics by Srimanta Pal and SubodhBhunia, Oxford University Press
- 4 Applied Numerical Methods with MATLAB for Engineers and Scientists by Steven Chapra, McGraw Hill
- 5 Elementary Linear Algebra with Application by Howard Anton and Christ Rorres. 6th edition. John Wiley & Sons,INC.
Reproduced from the University of Mumbai syllabus for B.E. (Computer Engineering) under NEP 2020, in force from the academic year 2024-25. Wording is as printed in that syllabus. Module numbering is as printed there too.
The complete syllabus
This subject is cut from the University circular for its year. Open a document here if you want the whole thing rather than a single subject.