Applied Mathematics – IV detailed syllabus scheme for Instrumentation Engineering (IS), 2017 regulation has been taken from the University of Mumbai official website and presented for the Bachelor of Engineering students. For Course Code, Course Title, Test 1, Test 2, Avg, End Sem Exam, Team Work, Practical, Oral, Total, and other information, do visit full semester subjects post given below.
For all other Mumbai University Instrumentation Engineering 4th Sem Syllabus 2017 Pattern, do visit IS 4th Sem 2017 Pattern Scheme. The detailed syllabus scheme for applied mathematics – iv is as follows.
Applied Mathematics – IV Syllabus for Instrumentation Engineering SE 4th Sem 2017 Pattern Mumbai University
Course Objectives:
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Course Outcomes:
The students will be able to:
- Check the given set of vectors is the vector space.
- Find eigenvalues and eigenvectors of matrix and can diagonalize the matrix.
- Find the probability distribution, expectation, variance and moments for the given data.
- Use binomial distribution and Poisson distribution and normal distribution for the data for required probability.
- Apply Cauchys integral formula and theorem and residue theorem to solve the integral problem.
- Find the correlation coefficients and rank correlation coefficients and lines regression between the two data.
Prerequisites:
Basics of Complex numbers, Analytic Function, Matrices, Symmetric, Orthogonal and Unitary matrices, Rank, Normal form, Solution of system of linear equations, L. I. & L. D. vectors, Basics of Probability.
Module 1
Linear Algebra: Vector Spaces Vectors in n-dimensional vector space: properties, dot product, cross product, norm and distance properties in n-dimensional vector space. Vector spaces over real field, properties of vector spaces over real field, subspaces. The Cauchy-Schwarz inequality, Orthogonal Subspaces, Gram-Schmidt process. 06 CO1
Module 2
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Module 3
Random Variables Discrete & continuous random variables, expectation, Variance, Probability mass function and Density Function, Probability distribution for random variables Moments, Moment Generating Function. Functions of one random variable and their distribution and density functions 10 CO3
Module 4
Probability distribution Probability distribution: Binomial distribution, Poisson & normal distribution (For detailed study. 6 CO4
Module 5
Complex integration Complex Integration: Line Integral, Cauchys Integral theorem for simply connected regions, Cauchys Integral formula. Taylors and Laurents Series Zeros, singularities, poles of f(z), residues, Cauchys Residue theorem. Applications of Residue theorem to evaluate real Integrals of different types. 12 CO5
Module 6
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Text Books:
- Higher Engineering Mathematics by Dr. B. S. Grewal 42th edition, Khanna Publication.
- Advanced Engineering Mathematics by Kreyszig E. 9th edition, John Wiley.
Reference Books:
- A Text Book of Applied Mathematics Vol. II by P. N. Wartilar & J. N. Wartikar, Pune, Vidyarthi Griha Prakashan., Pune.
- Advanced Engineering Mathematics by C. Ray Wylie & Louis Barrett. TMH International Edition.
- Mathematical Methods of Science and Engineering by Kanti B. Datta, Cengage Learning.
- Theory and Problems of Statistics by Murry R. Spieget, Schaums outline series-McGraw Hill Publication.
For detail syllabus of all other subjects of Instrumentation Engineering (IS) 4th Sem 2017 regulation, visit IS 4th Sem Subjects syllabus for 2017 regulation.