EN010501 b engineering Mathematics IV




НазваниеEN010501 b engineering Mathematics IV
Дата07.10.2012
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ТипДокументы
EN010501 B Engineering Mathematics IV


Teaching scheme Credits: 4

2 hours lecture and 2 hour tutorial per week
(CS, IT)



Objectives: To use basic numerical techniques for solving problems and to know the importance of learning theories in mathmatics and in queueing system.

MODULE 1 Finite differences (12 hours)

Finite difference operators   - interpolation using Newtons forward and backward formula –Newton’s divided difference formula - Numerical differentiation using Newtons forward and backward formula – Numerical integration – Trapezoidal rule – Simpsons 1/3rd and 3/8th rule

MODULE 2 Z transforms (12 hours)

Definition of Z transforms – transform of polynomial function and trignometric functions – shifting property , convolution property - inverse transformation – solution of 1st and 2nd order difference equations with constant coifficients using Z transforms.

MODULE 3 Discrete numeric functions (12 hours)

Discrete numeric functions – Manipulations of numeric functions- generating functions –Recurrence relations – Linear recurrence relations with constant coefficients – Homogeneous solutions – Particular solutions – Total solution – solution by the method of generating functions.

MODULE 4 Complex integration (12 hours)

Functions of complex variable – analytic function - Line integral – Cauchy’s integral theorem – Cauchy’s integral formula – Taylor’s series- Laurent’s series – Zeros and singularities – types of singularities – Residues – Residue theorem – evaluation of real integrals in unit circle – contour integral in semi circle when poles lie on imaginary axis.

MODULE 5 Queueing Theory (12 hours)

General concepts – Arrival pattern – service pattern – Queue disciplines – The Markovian model M/M/1/ , M/M/1/N – steady state solutions – Little’s formula.

References

  1. C.L.Liu and D.P. Mohapatra – Elements of Discrete Mathematics - Mc Graw Hill

  2. S.Lipschutz, M.L.Lipson – Discrete mathematics –Schaum’s outlines – Mc Graw Hill

  3. B.V. Ramana - Higher Engg. Mathematics – McGraw Hill

  4. Babu Ram – Engg. Mathematics -Pearson.

  5. K Venkataraman- Numerical methods in science and Engg -National publishing co

  6. V. Sundarapandian - probability ,Statistics and Queueing theory - PHI

  7. S.Bathul – text book of Engg.Mathematics – Special functions and complex variables –PHI

  8. H. Weif HSU – probability, random variables & Random processes – Schaum’s out lines - Mc Graw Hill

  9. T.Veerarajan - probability ,Statistics & Random processes - Mc Graw Hill

  10. H.C.Taneja – Advanced Engg. Mathematics Vol II – I.K.International

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