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
(use your town pincode for cash on delivery)
Numerical Methods for Scientific &
Engineering computation
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