University : Anna University of Technology Coimbatore
Discipline : Computer Science and Engineering
Degree : Master of Engineering (M.E)
Regular : Part time
Subject Title: APPLIED MATHEMATICS
UNIT – I ADVANCED MATRIX THEORY
Matrix norms – Jordan canonical form – Generalized eigenvectors – Singular value decomposition – Pseudo inverse – Least square approximations – QR algorithm.
UNIT – II CALCULUS OF VARIATIONS
Variation and its properties – Euler's equation – Functionals dependent on first and higher order derivatives – Functionals dependent on functions of several independent variables – Some applications – Direct methods: Ritz and Kantorovich methods.
UNIT III LINEAR PROGRAMMING
Basic concepts – Graphical and Simplex methods –Transportation problem – Assignment problem.
UNIT – IV Z – TRANSFORMS
Transform of standard functions – Convolution – Initial and Final value problems – Shifting Theorem – Inverse transform (Using Partial Fraction – Residues) – Solution of difference Equations using Z – Transform.
UNIT – V RANDOM PROCESSES
Classification – Stationary random processes – Auto Correlation – Cross Correlations – Power spectral density – Linear system with random input – Gaussian Process.
•M.K.Venkataraman, "Higher Mathematics for Engineering & Science", National Publishing Company, 2000.
•Bronson, R, "Matrix Operations ", Schaums outline Series, McGraw Hill, New York.1989.
•Elsgoltis, "Differential Equations and Calculus of Variations ", MIR Publishers, Moscow (1970)
•Gupta.A.S., "Calculus of Variations with Applications ", Prentice Hall of India, NewDelhi, 1999.
•T.Veerarajan, "Probability, Statistics & Random Processes", Tata McGraw Hill., 2000.
• Gupta, P.K.and Hira, D.S., "Operations Research ", S.Chand & Co., New Delhi, 1999.
•T.Veerarajan, "Mathematics – III", Tata McGraw Hill., 2000.
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