MA3201 NUMERICAL METHODS SYLLABUS | ANNA UNIVERSITY BE MECHANICAL AND AUTOMATION ENGINEERING 6TH SEMESTER SYLLABUS REGULATION 2008 2011 2012-2013 BELOW IS THE ANNA UNIVERSITY SIXTH SEMESTER B.E MECHANICAL AND AUTOMATION 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), 2008 REGULATION OF ANNA UNIVERSITY CHENNAI AND STUDENTS ADMITTED IN ANNA UNIVERSITY CHENNAI DURING 2009
MA3201 NUMERICAL METHODS L T P C
3 0 0 3
(Common to Mechanical, Production, Automobile and IV Semester core for Metallurgy,
Mechatronics and Aeronautical)
OBJECTIVES
With the present development of the computer technology, it is necessary to develop efficient
algorithms for solving problems in science, engineering and technology. This course gives a
complete procedure for solving different kinds of problems occur in engineering numerically. At the
end of the course, the students would be acquainted with the basic concepts in numerical methods
and their uses.
UNIT I SOLUTION OF EQUATIONS AND EIGEN VALUE PROBLEMS 9
Linear interpolation methods (method of false position) - Newton’s method - Statement of Fixed
Point Theorem - Fixed pointer iteration x=g(x) method - Solution of linear system of Gaussian
elimination and Gauss-Jordan methods - Iterative methods: Gauss Jacobi and Gauss – Seidel
methods- Inverse of a matrix by Gauss-Jordan method. Eigen value of a matrix by power methods.
UNIT II INTERPOLATION AND APPROXIMATION 9
Lagrangian Polynomials - Divided difference - Interpolation with a cubic spline - Newton forward and
backward difference formulae.
UNIT III NUMERICAL DIFFERENTIATION AND INTEGRATION 9
Derivatives from difference table - Divided difference and finite difference - 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
Single step Methods : Taylor Series and methods - 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.
67
UNIT V BOUNDARY VALUE PROBLEMS 9
Finite difference solution for the second order ordinary differential equations. Finite difference
solution for one dimensional heat equation by implict and explict methods - one dimensional wave
equation and two dimensional Laplace and Poisson equations.
TUTORIAL 15 TOTAL : 60 PERIODS
TEXT BOOKS:
1. Gerald, C.F, and Wheatley, P.O, “Applied Numerical Analysis”, Sixth Edition, Pearson Education
Asia, New Delhi.2002.
2. Balagurusamy, E., “Numerical Methods”, Tata McGraw-Hill Pub. Co. Ltd., New Delhi, 1999.
REFERENCES:
1. Kandasamy, P.Thilakavthy, K and Gunavathy, K. “Numerical Methods”, S.Chand and Co. New
Delhi.1999
2. Burden, R.L and Faries, T.D., “Numerical Analysis”, Seventh Edition, Thomson Asia Pvt. Ltd.,
Singapore, 2002.
3. Venkatraman M.K, “Numerical Methods” National Pub. Company, Chennai, 1991
4. Sankara Rao K., “Numerical Methods for Scientists and Engineers”, 2nd Ed. Prentice Hall India.
2004
MA3201 NUMERICAL METHODS L T P C
3 0 0 3
(Common to Mechanical, Production, Automobile and IV Semester core for Metallurgy,
Mechatronics and Aeronautical)
OBJECTIVES
With the present development of the computer technology, it is necessary to develop efficient
algorithms for solving problems in science, engineering and technology. This course gives a
complete procedure for solving different kinds of problems occur in engineering numerically. At the
end of the course, the students would be acquainted with the basic concepts in numerical methods
and their uses.
UNIT I SOLUTION OF EQUATIONS AND EIGEN VALUE PROBLEMS 9
Linear interpolation methods (method of false position) - Newton’s method - Statement of Fixed
Point Theorem - Fixed pointer iteration x=g(x) method - Solution of linear system of Gaussian
elimination and Gauss-Jordan methods - Iterative methods: Gauss Jacobi and Gauss – Seidel
methods- Inverse of a matrix by Gauss-Jordan method. Eigen value of a matrix by power methods.
UNIT II INTERPOLATION AND APPROXIMATION 9
Lagrangian Polynomials - Divided difference - Interpolation with a cubic spline - Newton forward and
backward difference formulae.
UNIT III NUMERICAL DIFFERENTIATION AND INTEGRATION 9
Derivatives from difference table - Divided difference and finite difference - 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
Single step Methods : Taylor Series and methods - 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.
67
UNIT V BOUNDARY VALUE PROBLEMS 9
Finite difference solution for the second order ordinary differential equations. Finite difference
solution for one dimensional heat equation by implict and explict methods - one dimensional wave
equation and two dimensional Laplace and Poisson equations.
TUTORIAL 15 TOTAL : 60 PERIODS
TEXT BOOKS:
1. Gerald, C.F, and Wheatley, P.O, “Applied Numerical Analysis”, Sixth Edition, Pearson Education
Asia, New Delhi.2002.
2. Balagurusamy, E., “Numerical Methods”, Tata McGraw-Hill Pub. Co. Ltd., New Delhi, 1999.
REFERENCES:
1. Kandasamy, P.Thilakavthy, K and Gunavathy, K. “Numerical Methods”, S.Chand and Co. New
Delhi.1999
2. Burden, R.L and Faries, T.D., “Numerical Analysis”, Seventh Edition, Thomson Asia Pvt. Ltd.,
Singapore, 2002.
3. Venkatraman M.K, “Numerical Methods” National Pub. Company, Chennai, 1991
4. Sankara Rao K., “Numerical Methods for Scientists and Engineers”, 2nd Ed. Prentice Hall India.
2004
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