B.E. (Biomedical Engineering) Applied Mathematics II Syllabus - Mumbai University
This is the First Year Biomedical NEP 2020 syllabus under NEP 2020, in force from the academic year 2024-25. The University still sets the earlier Choice Based papers alongside it for ATKT candidates, so check which scheme your exam form names before you revise.
Loading syllabus...
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 𝑒𝑎𝑥, sin(ax + b) , cos (ax +b), 𝑥𝑚, 𝑒𝑎𝑥𝑉
- 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. (Biomedical 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.