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# Syllabus of University of Pune M.E (Instrumentation & Control)Semester I-Mathematical Methods

 Posted Date: 13-Sep-2008 Category: Syllabus Author: S.Yamininagarajan Member Level: Gold Points: 2

(5061102) Mathematical Methods in Instrumentation
Teaching scheme: 3 lectures/week Credits: 3
Exam scheme: Paper- 100 marks

1. Vector Spaces and Transformation: Vector spaces, subspace and linear dependence, concept of basis,
representation, norms of vectors and orthonormalization, Linear transformations, concept of symmetry,
inner products, singular value decomposition.
2. Orthogonal and Unitary Transformation: Orthogonal projections, products of projections, orthogonal
direct sums, Unitary and orthogonal transformations, closed subspaces and the projection theorem for
Hilbert spaces.
3. Numerical method for algebraic and differential equations: Least square method, Gauss-Jordon method,
Gauss-Seidal method, Gauss elimination method, Newton-Raphson method, Euler’s method, modified
Euler’s method, Runge-Kutta methods, Adam-Bashforth method.
4. Basic concept of Probability: Random experiments, sample spaces, axioms of probability, conditional
probability, Bayes theorem.
5. Probability distributions: Probability distribution function, probability density function, Binomial,
Normal, Poisson and uniform distribution
6. Mathematical expectations: Mean variance, standard deviation, moments, covariance and correlation.

Reference Books:
1. Chen C. T., ‘Linear Systems: Theory & Design’, (Oxford University Press New York), (1999).
2. Charles W. Curtis, ‘Linear Algebra: An Introductory Approach’, (Springer (India) Pvt. Ltd.), (2004).
3. Strang G., ‘Linear Algebra And Its Applications’. (Thomson Brooks, Australia), (1998).
4. Lay D. C., ‘Linear Algebra and Applications’, (Addison Wesley, Massachusetts), (1996).
5. Gilbert Jimmie and Gilbert Linda, ‘Linear Algebra and Matrix Theory’, (Elsevier India Publishing Co.,
New Delhi), (2005).
6. Grewal B. S., ‘Higher Engineering Mathematics’, (Khanna Publishers, New Delhi), (2004).
7. Rajaraman V., ‘Computer Oriented Numerical Methods’. (Prentice Hall of India New Delhi), (1990).
8. Murray Spiegel, John Schiller and R. Alu Srinivasan, ‘Probability and Statistics’, (Tata McGraw- Hill
edition, New Delhi), (2004).
8. Miller I & Freund J., ‘Probability & Statistics For Engineering’. (Prentice Hall Of India New Delhi),
(1987).
9. Walpole R. E., Myers R. H. & Myers S. L., ‘Probability & Statistics For Engineers & Scientist’.
(Prentice Hall Inc. New Jercy), (1998).

Reference http://www.unipune.ernet.in/stud_info/Syllabi/Syllabus_2008.html

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