B.E. (Biomedical Engineering) Engineering Mathematics IV 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-IV
Module 1: Module: Complex Integration
- 1.1 Line Integral, Cauchy’s Integral theorem for simple connected and multiply connected regions (without proof), Cauchy’s Integral formula (without proof).
- 1.2 Taylor’s and Laurent’s series (without proof).
- 1.3 Definition of Singularity, Zeroes, poles of f(z), Residues, Cauchy’s Residue Theorem (without proof). Self-learning Topics: Application of Residue Theorem to evaluate real integrations ,Z- Transform.
Module 2: Module: Statistical Techniques
- 2.1 Karl Pearson’s Coefficient of correlation (r) .
- 2.2 Spearman’s Rank correlation coefficient (R) (repeated and non -repeated ranks)
- 2.3 Lines of regression.
- 2.4 Fitting of first and second degree curves. Self-learning Topics: Covariance, fitting of exponential curve.
Module 3: Module: Probability Distributions
- 2.1 Baye’s Theorem, Random variable: Probability distribution for discrete and continuous random variables, Density function and distribution function.
- 3.2 Expectation, mean and variance.
- 3.3 Probability distribution: Poisson & normal distribution. Self-learning Topics: Moments, Moment Generating Function, Applications of Probability Distributions in Engineering.
Module 4: Module: Linear Algebra: Vector Spaces:
- 4.1 Vectors in n-dimensional vector space, norm, dot product, The CauchySchwarz inequality (with proof), Unit vector.
- 4.2 Orthogonal projection, Orthonormal basis, Gram-Schmidt process for vectors.
- 4.3 Vector spaces over real field, subspaces. Self-Learning Topics:- Linear combinations, linear Dependence and Independence, QR decomposition.
Module 5: Module: Linear Algebra: Quadratic Forms
- 5.1 Quadratic forms over real field, Linear Transformation of Quadratic form, Reduction of Quadratic form to diagonal form using congruent transformation.
- 5.2 Rank, Index and Signature of quadratic form, Sylvester’s law of inertia, Value class of a quadratic form-Definite, Semidefinite and Indefinite.
- 5.3 Reduction of Quadratic form to a canonical form using congruent transformations.
- 5.4 Singular Value Decomposition. Self-learning Topics: Orthogonal Transformations, Applications of Quadratic forms and SVD in Engineering.
Module 6: Module: Calculus of Variations:
- 6.1 Euler- Lagrange equation (Without Proof), When F does not contain y, When F does not contain x, When F contains x, y, y’.
- 6.2 Isoperimetric problems- Lagrange Method.
- 6.3 Functions involving higher order derivatives: Rayleigh-Ritz Method. Self-Learning Topics:- Brachistochrone Problem, Variational Problem, Hamilton Principle, Principle of Least action , Several dependent variables.
References
- 1 Complex Variables and Applications, Brown and Churchill, McGraw-Hill education.
- 2 Probability, Statistics and Random Processes, T. Veerarajan, McGraw-Hill education.
- 3 Advanced engineering mathematics H.K. Das, S . Chand, Publications.
- 4 Higher Engineering Mathematics B. V. Ramana, Tata Mc-Graw Hill Publication
- 5 Advanced Engineering Mathematics, R. K. Jain and S. R. K. Iyengar, Narosa publication
- 6 Advanced Engineering Mathematics Wylie and Barret, Tata Mc-Graw Hill.
- 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 37
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
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