Indicative contents

The typical proportion of class content time is shown in brackets

• Introduction to Linear algebra (30%)
  Fundamental Algebraic Concepts; Sets, functions, relations, operations; Algebraic Structures; group, rings, fields, homomorphism, polynomials; Vector Spaces and Linear Operators; representations, matrices and linear algebraic equations, orthogonality, equivalence and similarity transformations, optimisation in Vector space.
  Eigen values and eigenvectors, canonical forms, functions of a square matrix, quadratic forms and congruence transformations, orthogonal transformations; Introduction to Polynomial Matrices; Applications to Communications and Control Theory.
• Probability (20%)
  Introductory probability, sample space and random variables, examples of discrete and continuous probability distribution functions, averages, moments and characteristic function, multivariate distributions, change of variables and functions of variables, central limit theorem
•  Stochastic Processes (20%)
  Description of stochastic vectors. General concepts of stochastic processes, stationary and ergodicity, stochastic continuity and differentiation, the Gaussian process, linear systems with stochastic inputs, correlation functions and power spectra, matched filtering, stochastic orthogonality and linear mean-square estimation filtering and prediction.
• Partial Difference equations (30%)
  Difference equations, relaxed & non-relaxed initial conditions, constant co-efficient difference equations, natural response, forced response, solutions for linear constant co-efficient difference equations, homogeneous solution of a difference equation, the particular solution of a difference equation, the total solution of a difference equation.

Recommended reading

• Books
  1. Michel K ochi, Applied Probability and stochastic processes in engineering and physical Sciences (wiley series in probability and mathematical statistics. Applied Probability), Wiley-Interscience, 1990.
  2. George E. P. Box, George C. Tiao, Bayesian Inference in Statistical Analysis (Wiley Classics Library), Wiley, 1992
  3. R. A. Horn and C. R. Johnson, Topics in Matrix Analysis, Cambridge University Press, London, 1991.
  4. Katta G. Murty, Computational and Algorithmic linear Algebra and n-Dimensional Geometry, Internet Edition
  5. Abdul J Jerri, Linear difference equations with transforms method, Kluwer Academic Publishers, London, 1996
     
      

• Journals

  1. ACM Transactions on Modeling and Computer Simulation
  2. Journal of Computational and Applied Mathematics
  3. SIAM journal on mathematical analysis
  4. Journal of differential equations
  5. Journal of engineering mathematics.
   

• Magazines
  1. Advances in Applied Mathematics
• Internet Sites

• Laboratory
  Hardware Required: PCs
  Software Required:MATLAB
  Software Manuals: MATLAB User Manuals