YMA005 NUMERICAL METHODS SYLLABUS | ANNA UNIVERSITY BCA 4TH SEMESTER SYLLABUS REGULATION 2010 2011 2012-2013 BELOW IS THE ANNA UNIVERSITY 4TH SEMESTER BCA BACHELOR OF COMPUTER APPLICATIONS) 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) 2010 REGULATION OF ANNA UNIVERSITY CHENNAI AND STUDENTS ADMITTED IN ANNA UNIVERSITY CHENNAI DURING 2010
YMA005 NUMERICAL METHODS L T P C
3 1 0 4
UNIT SOLUTION OF EQUATIONS AND EIGENVALUE PROBLEMS 9+3
Linear interpolation methods (method of false position) – Newton’s method – Statement of Fixed
Point Theorem – Fixed point iteration: x=g(x) method – Solution of linear system by Gaussian
elimination and Gauss-Jordon methods- Iterative methods: Gauss Jacobi and Gauss-Seidel
methods- Inverse of a matrix by Gauss Jordon method – Eigenvalue of a matrix by power
method.
UNIT II INTERPOLATION AND APPROXIMATION 9+ 3
Lagrangian Polynomials – Divided differences – Interpolating with a cubic spline – Newton’s
forward and backward difference formulas.
UNIT III NUMERICAL DIFFERENTIATION AND INTEGRATION 9+ 3
Derivatives from difference tables – Divided differences and finite differences –Numerical
integration by trapezoidal and Simpson’s 1/3 and 3/8 rules – Romberg’s method – Two and
Three point Gaussian quadrature formulas – Double integrals using trapezoidal and Simpson’s
rules.
UNIT IV INITIAL VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL
EQUATIONS 9+ 3
Single step methods: Taylor series method – Euler and modified Euler methods – Fourth order
Runge – Kutta method for solving first and second order equations – Multistep methods: Milne’s
and Adam’s predictor and corrector methods.
UNIT V BOUNDARY VALUE PROBLEMS IN ORDINARY AND PARTIAL
DIFFERENTIAL EQUATIONS 9+ 3
Finite difference solution of second order ordinary differential equation – Finite difference solution
of one dimensional heat equation by explicit and implicit methods – One dimensional wave
equation and two dimensional Laplace and Poisson equations.
TUTORIAL 15 TOTAL : 60 PERIODS
REFERENCES :
1. Gerald, C.F, and Wheatley, P.O, “Applied Numerical Analysis”, Sixth Edition, Pearson
Education Asia, New Delhi, 2002.
2. Kandasamy, P., Thilagavathy, K. and Gunavathy, K., “Numerical Methods”, S.Chand Co.
Ltd., New Delhi, 2003
3. Balagurusamy, E., “Numerical Methods”, Tata McGraw-Hill Pub.Co.Ltd, New Delhi, 1999.
4. Burden, R.L and Faires, T.D., “Numerical Analysis”, Seventh Edition, Thomson Asia Pvt.
Ltd., Singapore, 2002
YMA005 NUMERICAL METHODS L T P C
3 1 0 4
UNIT SOLUTION OF EQUATIONS AND EIGENVALUE PROBLEMS 9+3
Linear interpolation methods (method of false position) – Newton’s method – Statement of Fixed
Point Theorem – Fixed point iteration: x=g(x) method – Solution of linear system by Gaussian
elimination and Gauss-Jordon methods- Iterative methods: Gauss Jacobi and Gauss-Seidel
methods- Inverse of a matrix by Gauss Jordon method – Eigenvalue of a matrix by power
method.
UNIT II INTERPOLATION AND APPROXIMATION 9+ 3
Lagrangian Polynomials – Divided differences – Interpolating with a cubic spline – Newton’s
forward and backward difference formulas.
UNIT III NUMERICAL DIFFERENTIATION AND INTEGRATION 9+ 3
Derivatives from difference tables – Divided differences and finite differences –Numerical
integration by trapezoidal and Simpson’s 1/3 and 3/8 rules – Romberg’s method – Two and
Three point Gaussian quadrature formulas – Double integrals using trapezoidal and Simpson’s
rules.
UNIT IV INITIAL VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL
EQUATIONS 9+ 3
Single step methods: Taylor series method – Euler and modified Euler methods – Fourth order
Runge – Kutta method for solving first and second order equations – Multistep methods: Milne’s
and Adam’s predictor and corrector methods.
UNIT V BOUNDARY VALUE PROBLEMS IN ORDINARY AND PARTIAL
DIFFERENTIAL EQUATIONS 9+ 3
Finite difference solution of second order ordinary differential equation – Finite difference solution
of one dimensional heat equation by explicit and implicit methods – One dimensional wave
equation and two dimensional Laplace and Poisson equations.
TUTORIAL 15 TOTAL : 60 PERIODS
REFERENCES :
1. Gerald, C.F, and Wheatley, P.O, “Applied Numerical Analysis”, Sixth Edition, Pearson
Education Asia, New Delhi, 2002.
2. Kandasamy, P., Thilagavathy, K. and Gunavathy, K., “Numerical Methods”, S.Chand Co.
Ltd., New Delhi, 2003
3. Balagurusamy, E., “Numerical Methods”, Tata McGraw-Hill Pub.Co.Ltd, New Delhi, 1999.
4. Burden, R.L and Faires, T.D., “Numerical Analysis”, Seventh Edition, Thomson Asia Pvt.
Ltd., Singapore, 2002
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