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B.E. (Artificial Intelligence and Data Science) Applied Mathematics I 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-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 2 2 hours

  • Complex Numbers 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 3 1 hours

  • Hyperbolic Functions & Logarithms of Complex Numbers 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 3 2 hours

  • Partial Differentiation 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 1 3 hours

  • Applications of Partial Differentiation and Successive Differentiation. 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 3 2 hours

  • Matrices 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 2 2 hours

  • Numerical Solutions of Transcendental Equations and System of Linear Equations and Expansion of Function. 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, 9thEd.
  • 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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