Class:S.E-Branch:-Instrumentation-Semester:-IV- Engineering Mathematics-IV -University of Mumbai |MU|
University of Mumbai
|Class: S.E.||Branch:Instrumentation||Semester: IV|
|Subject: Engineering Mathematics-IV (Abbreviated as EM-IV)|
|Periods per Week(60 min. each)||
|Practical and Oral||—||—|
|1||Vector Analysis:Scalar and Vector point functions, Curl, gradient and
Divergence, Conservative, Irrotational and Solenoidal fields. Line Integral, Greens Theorem for plane regions and properties of line integral, Stoke’s theorem, Gauss’s Divergence theorem (without proof) related identities and deductions.
|2||Matrices :Types of matrices, adjoint of a matrix inverse of a matrix,
rank of a matrix, linear dependence and independence of rows and columns of a matrix over a real field, reduction to normal form and partitioning of a matrix.
Systems of homogeneous and non-homogeneous equations, their consistency and solutions.
Brief revision of vectors over real fields, inner product, norm, linear independence and orthogonality of vectors.
Characteristic Polynomial, characteristic equation, characteristic roots, and characteristic vectors of square matrix, properties of characteristic roots and vectors of different types of matrices such as orthogonal matrix, Hermitian matrix, Skew-Hermitian matrix, Diagonal matrix, Cayley-Hamilton theorem (without proof), functions of square matrix , minimal polynomial and derogatory matrix.
Quadratic forms, Congruent and orthogonal reduction of quadratic form, rank, index, signature and class value of quadratic form.
3. Probability and Statistics : 23
Concept of probability, conditional probability. Baye’s
theorem (without proof).
Probability distribution for discrete and continuous random
variables. Density function and distribution function. Expected value, variance, moments, moment generating function, binomial, Poission, normal distributions for detailed study with proof,
Correlation, Karl Pearson coefficient & Spearman’s rank
correlation coefficient (without proof), regression, lines of regression.
1. Question paper will consist of total 7 questions, of 20 marks each.
2. Only 5 questions need to be attempted.
3. Q.1 will be compulsory covering entire syllabus.
4. Remaining questions will be of mixed nature.
5. In question paper weightage of each module will be proportional to the number of respective lecture hours as mentioned in the syllabus.
1. Wartikar P.N. / Wartikar J. N., Textbook of Applied Mathematics, Pune Vidyarthi
Griha Prakashan, 1981.
2. Shastri S.S., Engineering Mathematics, Prentice Hall.
3. Shantinarayan, Matrices, S. Chand & co.
4. Gupta Kapoor, Mathematical Statistics.
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