UNIVERSITY OF CALICUT
MATHEMATICS FOR INSTRUMENTATION AND CONTROL ENGINEERING
Module I (13 Hours) Linear Algebra:Vector spaces, subspaces, Linear dependence, Basis and Dimension, Inner product spaces, Gram-Schmidt Orthogonalization, Linear transformations, Kernels and Images , Matrix representation of linear transformation, Change of basis, Eigenvalues and Eigen vectors of linear operator, Quadratic form. Module II (14 Hours) Operations on Random Variables: Random Variables, Distributions and Density functions, Moments and Moment generating function, Multivariate distributions, Independent Random Variables, Marginal and Conditional distributions , Conditional Expectation, Transformation of Random Variables , Elements of stochastic processes, Classification of general stochastic processes. Module III (14 Hours) Random Processes: Markov Chains: Definition, Examples, Classification of states , Limiting distribution of Markov chains, Poisson processes, Birth and death processes, Second Order Stochastic Processes, Stationary processes, Wide sense Stationary processes, Spectral density function. Module IV (13 Hours) Introduction to Mathematical Programming: Linear Programming Problems, Simplex Method, Non Linear Programming Problems, Unconstrained optimization, Search Methods, Constrained optimization. Text Books: Module I: K.B.Datta, Matrix and Linear Algebra,PHI,2006 Sections: 5.1 to 5.5, 6.1 to 6.4, 7.1 to 7.1.1, 8.2, 8.3. Module II: Irwin Miller and Marylees Miller, John E. Freund’s Mathematical Statistics, 6th Edition, PHI, 2002. Module III: T.Veerarajan, Probability Statistics and Random Processes, Tata McGraw-Hill, 2nd Edition. Chapters: 7 and 8.Module IV: Hillier F S and Liebermann G J, Introduction to Operations Research, 7th Edition, McGraw Hill. Sections: 3.1 to 3.4, 4.1 to 4.7, 6.1 to 6.3, 7.1, 13.1 to 13.6. References: 1. Kenneth Hoffman and Ray Kunze, Linear Algebra,2nd Edition, PHI, 1992. 2. Erwin Kreyszig, Introductory Functional Analysis with Applications, John Wiley & Sons, 2004. 3. Irwin Miller and Marylees Miller, John E. Freund’s Mathematical Statistics, 6th Edition, , PHI, 2002. 4. J. Medhi, Stochastic Processes, New Age International, New Delhi. 5. A Papoulis, Probability, Random Variables and Stochastic Processes, 3rd Edition, McGraw Hill. 6. John B Thomas, An Introduction to Applied Probability and Random Processes, John Wiley & Sons. 7. Hillier F S and Liebermann G J, Introduction to Operations Research, 7th Edition, McGraw Hill. 8. Simmons D M, Non Linear Programming for Operations Research, PHI. 9. T.Veerarajan, Probability Statistics and Random Processes, Tata McGraw-Hill, 2nd Edition. Internal continuous assessment: 100 marks Internal continuous assessment is in the form of periodical tests, assignments, seminars or a combination of these. There will be a minimum of two tests in each subject. End semester Examination: 100 marks Question pattern: Answer any 5 questions by choosing at least one question from each module.
Click here to whole syllabus
Fore more details click here or visit http://www.universityofcalicut.info
MATHEMATICS FOR INSTRUMENTATION AND CONTROL ENGINEERING
Module I (13 Hours) Linear Algebra:Vector spaces, subspaces, Linear dependence, Basis and Dimension, Inner product spaces, Gram-Schmidt Orthogonalization, Linear transformations, Kernels and Images , Matrix representation of linear transformation, Change of basis, Eigenvalues and Eigen vectors of linear operator, Quadratic form. Module II (14 Hours) Operations on Random Variables: Random Variables, Distributions and Density functions, Moments and Moment generating function, Multivariate distributions, Independent Random Variables, Marginal and Conditional distributions , Conditional Expectation, Transformation of Random Variables , Elements of stochastic processes, Classification of general stochastic processes. Module III (14 Hours) Random Processes: Markov Chains: Definition, Examples, Classification of states , Limiting distribution of Markov chains, Poisson processes, Birth and death processes, Second Order Stochastic Processes, Stationary processes, Wide sense Stationary processes, Spectral density function. Module IV (13 Hours) Introduction to Mathematical Programming: Linear Programming Problems, Simplex Method, Non Linear Programming Problems, Unconstrained optimization, Search Methods, Constrained optimization. Text Books: Module I: K.B.Datta, Matrix and Linear Algebra,PHI,2006 Sections: 5.1 to 5.5, 6.1 to 6.4, 7.1 to 7.1.1, 8.2, 8.3. Module II: Irwin Miller and Marylees Miller, John E. Freund’s Mathematical Statistics, 6th Edition, PHI, 2002. Module III: T.Veerarajan, Probability Statistics and Random Processes, Tata McGraw-Hill, 2nd Edition. Chapters: 7 and 8.Module IV: Hillier F S and Liebermann G J, Introduction to Operations Research, 7th Edition, McGraw Hill. Sections: 3.1 to 3.4, 4.1 to 4.7, 6.1 to 6.3, 7.1, 13.1 to 13.6. References: 1. Kenneth Hoffman and Ray Kunze, Linear Algebra,2nd Edition, PHI, 1992. 2. Erwin Kreyszig, Introductory Functional Analysis with Applications, John Wiley & Sons, 2004. 3. Irwin Miller and Marylees Miller, John E. Freund’s Mathematical Statistics, 6th Edition, , PHI, 2002. 4. J. Medhi, Stochastic Processes, New Age International, New Delhi. 5. A Papoulis, Probability, Random Variables and Stochastic Processes, 3rd Edition, McGraw Hill. 6. John B Thomas, An Introduction to Applied Probability and Random Processes, John Wiley & Sons. 7. Hillier F S and Liebermann G J, Introduction to Operations Research, 7th Edition, McGraw Hill. 8. Simmons D M, Non Linear Programming for Operations Research, PHI. 9. T.Veerarajan, Probability Statistics and Random Processes, Tata McGraw-Hill, 2nd Edition. Internal continuous assessment: 100 marks Internal continuous assessment is in the form of periodical tests, assignments, seminars or a combination of these. There will be a minimum of two tests in each subject. End semester Examination: 100 marks Question pattern: Answer any 5 questions by choosing at least one question from each module.
Click here to whole syllabus
Fore more details click here or visit http://www.universityofcalicut.info