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Home / Syllabus / B.E. (Biomedical Engineering) / First Year Biomedical NEP 2020 / Semester 1 / Applied Mathematics I

B.E. (Biomedical Engineering) Applied Mathematics I 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.

Applied-Mathematics-I.pdf
Semester 1 · First Year Biomedical NEP 2020 · 2 credits · 100 marks

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Syllabus for Applied Mathematics-I

Semester 1 · First Year Biomedical NEP 2020 · 2 credits · 100 marks

Module 1: 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, cos nθ 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 2: 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 3: 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 4: 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 5: 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 6: 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. (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.

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