MA9222 NUMERICAL METHODS AND GRAPH THEORY SYLLABUS | ANNA UNIVERSITY ME MANUFACTURING ENGINEERING 1ST SEM SYLLABUS REGULATION 2009 2011 2012-2013 BELOW IS THE ANNA UNIVERSITY FIRST SEMESTER ME MANUFACTURING ENGINEERING DEPARTMENT SYLLABUS, TEXTBOOKS, REFERENCE BOOKS,EXAM PORTIONS,QUESTION BANK,PREVIOUS YEAR QUESTION PAPERS,MODEL QUESTION PAPERS, CLASS NOTES, IMPORTANT 2 MARKS, 8 MARKS, 16 MARKS TOPICS. IT IS APPLICABLE FOR ALL STUDENTS ADMITTED IN THE YEAR 2011 2012-2013 (ANNA UNIVERSITY CHENNAI,TRICHY,MADURAI,TIRUNELVELI,COIMBATORE), 2009 REGULATION OF ANNA UNIVERSITY CHENNAI AND STUDENTS ADMITTED IN ANNA UNIVERSITY CHENNAI DURING 2009
MA9222 NUMERICAL METHODS AND GRAPH THEORY L T P C
3 1 0 4
AIM:
To solve some engineering models and problems by using Numerical Analysis and Graph Theoretical concepts.
OBJECTIVES:
The engineers will have an exposure on various topics such as Systems of Equation, Interpolation and Numerical Integration, Initial and Boundary Value Problems, Fundamentals of Graphs, Graphs Algorithms to understand their applications in engineering problems.
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 Predictor-
Corrector 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.
TOTAL : 60 PERIODS
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,
MA9222 NUMERICAL METHODS AND GRAPH THEORY L T P C
3 1 0 4
AIM:
To solve some engineering models and problems by using Numerical Analysis and Graph Theoretical concepts.
OBJECTIVES:
The engineers will have an exposure on various topics such as Systems of Equation, Interpolation and Numerical Integration, Initial and Boundary Value Problems, Fundamentals of Graphs, Graphs Algorithms to understand their applications in engineering problems.
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 Predictor-
Corrector 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.
TOTAL : 60 PERIODS
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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