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B.E. (Artificial Intelligence and Data Science) Applied Mathematics II Syllabus - Mumbai University

This is the FY BE AI and DS syllabus under NEP 2020, in force from the academic year 2024-25. The third and fourth years of this degree are still taught on the earlier CBCS REV-2019 'C' Scheme, because the University has published no NEP syllabus for Semesters V to VIII of any engineering branch.

Applied Mathematics-II.pdf
Semester 2 · FY BE AI and DS · NEP 2020

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Syllabus for Applied Mathematics-II

Semester 2 · FY BE AI and DS · NEP 2020

Module 01 3 2 hours

  • 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 02 3 1 hours

  • 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), x m , 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 03 2 2 hours

  • 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 04 2 1 2 hours

  • 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 05 2 2 hours

  • 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 06 3 1 hours

  • 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, 9thEd.
  • 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. (Artificial Intelligence and Data Science), item 7.7 (R-A), under NEP 2020, in force from the academic year 2024-25. Wording, module numbering and hours are as printed in that syllabus.

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.

PDF B.E. Artificial Intelligence and Data Science - First Year, Semester I and II - NEP 2020 - Item 7.7 (R-A) NEP 2020, Semesters I and II, in force from 2024-25 Read full PDF Read
PDF B.E. Artificial Intelligence and Data Science - Second Year, Semester III and IV - NEP 2020 - Item 6.20 (N) NEP 2020, Semesters III and IV, in force from 2025-26 Read full PDF Read
PDF B.E. Artificial Intelligence and Data Science - Third Year, Semester V and VI - CBCS REV-2019 C Scheme - Item 6.42 (R) CBCS REV-2019 'C' Scheme, Semesters V and VI, in force from 2022-23 Read full PDF Read
PDF B.E. Artificial Intelligence and Data Science - Fourth Year, Semester VII and VIII - CBCS REV-2019 C Scheme - Item 6.12 (N) CBCS REV-2019 'C' Scheme, Semesters VII and VIII, in force from 2023-24 Read full PDF Read
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