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Teaching scheme Credits: 4
2 hours lecture and 2 hour tutorial per week
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.
|Engineering mathematics – III||Applied Engineering Mathematics|
|Applied Engineering Mathematics||Me 501 Advanced Engineering Mathematics (4 0 0 8)|
|Advanced Engineering Mathematics, 2nd edition||09EA01 / 09EE01 applied mathematics for systems engineering|
|Doctor of Philosophy, Aerospace Engineering, Minor in Mathematics||Strategic Review of Faculty of Engineering, Computing and Mathematics|
|2 gce ‘A’ Level Passes in Mathematics and one of the following subjects: Physics, Physical Science, Engineering Science, Physics with Chemistry. (I) Minimum Requirements for Degree Award||Students will demonstrate competence in; Engineering Curriculum; basic concepts such as significant digits, length, and mass; Engineering Drawing; the use of the computer as an engineering tool; designing a project|