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B.E. (Artificial Intelligence and Data Science) Applied Mathematics I Syllabus - Mumbai University 2026

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-I.pdf
Semester 1 · FY BE AI and DS · NEP 2020

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Syllabus for Applied Mathematics-I

Semester 1 · FY BE AI and DS · NEP 2020

Module 01: Complex Numbers 2 2 hours

  • Pre-requisite: Review of Complex Numbers‐ Algebra of Complex Numbers, Cartesian, polar and exponential form of complex number, Statement of D’Moivre’s Theorem.
  • 1.1 Expansion of sinnθ, cosnθ in terms of sines and cosines of multiples of θ and Expansion of sinnθ, cosnθ in powers of sinθ, cosθ.
  • 1.2 Powers and Roots of a complex number. # Self-learning topic: Basic of Complex Number.

Module 02: Hyperbolic Functions & Logarithms of Complex Numbers 3 1 hours

  • 2.1 Circular functions of complex number and Hyperbolic functions. Inverse Circular and Inverse Hyperbolic Functions. Separation of real and imaginary parts of all types of Functions. (Simple Examples)
  • 2.2 Logarithm of Complex Number (Simple Examples) # Self-learning topic: Applications of complex numbers in Electrical circuits.

Module 03: Partial Differentiation 3 2 hours

  • 3.1 Partial Differentiation: Function of two and three variables, Partial derivatives of first and higher order. Differentiation of composite function.
  • 3.2 Euler’s Theorem on Homogeneous functions with two independent variables (with proof). Deductions from Euler’s Theorem. (without proof). # Self-learning topics: Total differentials, implicit functions, Euler’s Theorem on Homogeneous functions with three independent variables.

Module 04: Applications of Partial Differentiation and Successive Differentiation. 1 3 hours

  • 4.1 Maxima and Minima of a function of two independent variables,
  • 4.2 Successive differentiation: nth derivative of standard functions. Leibnitz’s Theorem (without proof) and simple examples. # Self-learning topics: Jacobian’s of two and three independent variables (simple problems) Lagrange’s Multiplier method.

Module 05: Matrices 3 2 hours

  • Pre-requisite: Inverse of a matrix, addition, multiplication , and transpose of a matrix, symmetric, skew-symmetric Matrix (Only Definition).
  • 5.1 Types of Matrices (Hermitian, Skew Hermitian, Unitary, Orthogonal Matrices and properties of Matrices (without proof)). The rank of a Matrix using Echelon form, reduction to normal form, and PAQ form (Only 3X3 Matrix)
  • 5.2 System of homogeneous and non –non-homogeneous equations, their consistency, and solutions. # Self-learning topics: Application of inverse of a matrix to coding theory. Reduction to normal form and PAQ form.( m x n Matrix)

Module 06: Numerical Solutions of Transcendental Equations and System of Linear Equations and Expansion of Function. 2 2 hours

  • 6.1 Solution of Transcendental Equations: Solution by Newton Raphson method and Regula –Falsi method.
  • 6.2 Solution of a system of linear algebraic equations, by (1) Gauss Jacobi Iteration Method, (2) Gauss Seidel Iteration Method. # Self-learning topics: Indeterminate forms, L‐ Hospital Rule, Gauss Elimination Method, Gauss Jordan Method.

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 Subodh, C.Bhunia, Oxford University Press
  • 4 Matrices, Shanti Narayan , S. Chand publication.
  • 5 Applied Numerical Methods with Matlab for Engineers and Scientists by Steven Chapra, McGraw Hill
  • 6 Elementary Linear Algebra with Application by Howard Anton and Christ Rorres. 6th edition. John Wiley & Sons, INC.
  • 7 A textbook of Engineering Mathematics by N.P. Bali & Manish Goyal. Laxmi Publication.
  • 8 A textbook of Applied Mathematics Vol-I & Vol-II by P. N. Wartikar & J.N. Wartikar.

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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