B.E. (Biomedical Engineering) Engineering Mathematics III Syllabus - Mumbai University

This is the Second Year Biomedical Rev 2019 C Scheme syllabus under REV-2019 'C' Scheme, in force from the academic year 2020-21. The University also publishes a NEP 2020 syllabus for Semesters III and IV, which is what the current second year is taught; this scheme is what ATKT candidates of the earlier batches still sit. Check which scheme your examination form names before you revise.

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Syllabus for Engineering Mathematics-III

Semester 3 · Second Year Biomedical Rev 2019 C Scheme · 4 credits · 125 marks

Module 1: Module: Laplace Transform

1.1 Definition of Laplace transform, Condition of Existence of Laplace Transform.
1.2 Laplace Transform (L) of standard functions like 𝑒 𝑎𝑡 , 𝑠𝑖𝑛(𝑎𝑡), 𝑐𝑜𝑠(𝑎𝑡), 𝑠𝑖𝑛ℎ(𝑎𝑡), 𝑐𝑜𝑠ℎ(𝑎𝑡) and 𝑡𝑛 , 𝑛 ≥ 0.
1.3 Properties of Laplace Transform: Linearity, First Shifting Theorem, Second Shifting Theorem, Change of Scale Property, Multiplication by t, Division by t, Laplace Transform of derivatives and integrals (Properties without proof).
1.4 Evaluation of integrals by using Laplace Transformation. Self-learning Topics: Heaviside’s Unit Step function, Laplace Transform of Periodic functions, Dirac Delta Function.

Module 2: Module: Inverse Laplace Transform

2.1 Inverse Laplace Transform, Linearity property, use of standard formulae to find inverse Laplace Transform, finding Inverse Laplace Transform using derivatives.
2.2 Partial fractions method to find inverse Laplace Transform.
2.3 Inverse Laplace Transform using Convolution theorem (without proof). Self-learning Topics: Applications to solve initial and boundary value problems involving ordinary differential equations.

Module 3: Module: Fourier Series:

3.1 Dirichlet’s conditions, Definition of Fourier series and Parseval’s Identity (without proof).
3.2 Fourier series of periodic function with period 2𝜋 and 2 l.
3.3 Fourier series of even and odd functions.
3.4 Half range Sine and Cosine Series. Self-learning Topics: Complex form of Fourier Series, Orthogonal and orthonormal set of functions. Fourier Transform.

Module 4: Module: Complex Variables:

4.1 Function f(z) of complex variable, limit, continuity and differentiability of f(z)Analytic function, necessary and sufficient conditions for f(z) to be analytic (without proof).
4.2 Cauchy-Riemann equations in cartesian coordinates (without proof).
4.3 Milne-Thomson method to determine analytic function f(z)when real part (u) or Imaginary part (v) or its combination (u+v or u-v) is given.
4.4 Harmonic function, Harmonic conjugate and orthogonal trajectories. Self-learning Topics: Conformal mapping, linear, bilinear mapping, cross ratio, fixed points and standard transformations.

Module 5: Module: Linear Algebra: Matrix Theory

5.1 Characteristic equation, Eigen values and Eigen vectors, Example based on properties of Eigen values and Eigen vectors.(Without Proof).
5.2 Cayley-Hamilton theorem (Without proof), Examples based on verification of Cayley- Hamilton theorem and compute inverse of Matrix.
5.3 Similarity of matrices, Diagonalization of matrices, Functions of square matrix. Self-learning Topics: Application of Matrix Theory in machine learning and google page rank algorithms, derogatory and non-derogatory matrices.

Module 6: Module: Vector Differentiation and Integral

6.1 Vector differentiation : Basics of Gradient, Divergence and Curl (Without Proof).
6.2 Properties of vector field: Solenoidal and Irrotational (conservative) vector fields.
6.3 Vector integral: Line Integral, Green’s theorem in a plane (Without Proof), Stokes’ theorem (Without Proof) only evaluation. Self-learning Topics: Gauss’ divergence Theorem and applications of Vector calculus.

References

1 Advanced engineering mathematics, H.K. Das, S.Chand, Publications
2 Higher Engineering Mathematics, B. V. Ramana, Tata Mc-Graw Hill Publication
3 Advanced Engineering Mathematics, R. K. Jain and S. R. K. Iyengar, Narosa publication
4 Advanced Engineering Mathematics, Wylie and Barret, Tata Mc-Graw Hill.
5 Theory and Problems of Fourier Analysis with applications to BVP, Murray Spiegel, Schaum’s Outline Series
6 Vector Analysis Murry R. Spiegel, Schaum’s outline series, Mc-Graw Hill Publication
7 Beginning Linear Algebra, Seymour Lipschutz, Schaum’s outline series, Mc-Graw Hill Publication
8 Higher Engineering Mathematics, Dr. B. S. Grewal, Khanna Publication University of Mumbai, Biomedical Engineering, Rev 2020-21 11

Reproduced from the University of Mumbai syllabus for B.E. (Biomedical Engineering) under REV-2019 'C' Scheme, in force from the academic year 2020-21. 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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