Thursday, November 22, 2012

MA9222 NUMERICAL METHODS AND GRAPH THEORY - ME(Manufacturing Engineering) I Semester


MA9222    NUMERICAL METHODS AND GRAPH THEORY        

UNIT   I SYSTEMS OF EQUATIONS                  12        
Simultaneous linear equations – Direct method – LU decomposition methods - Gauss
elimination, Gauss Jordan methods  – Iterative methods  – Jacobi and Gauss-Seidel
methods.

UNIT  II INTERPOLATION AND INTEGRATION                                           12        
Hermite’s interpolation – Cubic Spline Interpolation – Gaussian – Numerical Integration –
Trapezoidal and Simpson rules  – Newton-Cotes formula  – Gaussian quadrature  –
cubature.

UNIT III NUMERICAL METHODS FOR ODE                                           12
       
Single step methods – multi step methods – Taylor series and Euler methods – Runge
Kutta method of fourth order – Multi step methods – Adams-Bashforth, Milnes PredictorCorrector methods – Boundary value problems by Finite difference method.

UNIT  IV FUNDAMENTALS OF GRAPHS                                           12
       
Graphs – sub graphs - Complements – Graph isomorphism – vertex degree: Eulerian
graphs – Planar graphs – Hamiltonian paths, tree and Cut-sets.
UNIT  V TREES AND ALGORITHMS                               12      
Kruskal’s algorithm  – Dijkstra’s shortest path algorithm, Prim’s algorithm  – Transport
Networks.



TEXT BOOKS:
1. Jain, M.K., Iyengar, S.R.K., and Jain, R.K., Numerical Methods for Scientific &
Engineering computation, Wiley Eastern Ltd., 1987.
2. Froberg, C.E. Numerical Mathematics, the Benjamin/Cummings Publishing Co., Inc.,
1985.
3. Grimaldi R.P., Discrete and Combinatorial Mathematics, Pearson Education Inc.,
1999.

REFERENCES:
1. Froberg, C.E. Numerical Mathematics, The  Benjamin/Cummings Publishing Co.,
Inc., 1985.
2. Jain, M.K., Iyengar, S.R.K., and Jain, R.K., Numerical Methods for Scientific &
Engineering computation, Wiley Eastern Ltd., 1987.
3. Bondy, J.A. and Murthy, U.S.R., Graph Theory with Applications, Macmillan


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Numerical Methods for Scientific &
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