MA3021 NUMERICAL METHODS SYLLABUS | ANNA UNIVERSITY BE MECHATRONICS ENGINEERING 4TH SEM SYLLABUS REGULATION 2008 2011 2012-2013 BELOW IS THE ANNA UNIVERSITY FOURTH SEMESTER B.E. MECHATRONICS 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
MA3021 NUMERICAL METHODS L T P C
3 1 0 4
UNIT I SOLUTION OF EQUATIONS AND EIGENVALUE PROBLEMS (10 +3)
Solution of algebraic and transcendental equations - Fixed point iteration method –Newton-
Raphson method- Solution of linear system of equations - Gauss Elimination method – Pivoting
- Gauss-Jordan methods – Iterative methods of Gauss-Jacobi and Gauss-Seidel - Matrix
Inversion by Gauss-Jordan method - Eigenvalues of a matrix by Power method and by Jacobi’s
method.
UNIT II INTERPOLATION AND APPROXIMATION (8 + 3)
Interpolation with unequal intervals - Lagrange interpolation – Newton’s divided difference
interpolation – Cubic Splines - Interpolation with equal intervals - Newton’s forward and
backward difference formulae.
UNIT III NUMERICAL DIFFERENTATION AND INTEGRATION (9 + 3)
Approximation of derivatives using interpolation polynomials - Numerical integration using
Trapezoidal, Simpson’s 1/3 and Simpson’s 3/8 rules – Romberg’s method – Two point and three
point Gaussian quadrature formulae – Evaluation of double integrals by Trapezoidal and
Simpson’s rules.
UNIT IV INITIAL VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL
EQUATIONS (9 + 3)
Single step-methods - Taylor’s series method - Euler’s method - Modified Euler’s method -
Fourth order Runge-Kutta method for solving first and second order equations –Multistep
methods - Milne’s and Adams-Bashforth predictor-corrector methods for solving first order
equations.
UNIT V BOUNDARY VALUE PROBLEMS IN ORDINARY AND PARTIAL
DIFFERENTIAL EQUATIONS (9 + 3)
Finite difference methods for solving two-point linear boundary value problems. Finite difference
techniques for the solution of two dimensional Laplace’s and Poisson’s equations on rectangular
domain – One dimensional heat-flow equation by explicit and implicit (Crank Nicholson)
methods - One dimensional wave equation by explicit method.
L: 45 T: 15 TOTAL : 60 PERIODS
31
TEXT BOOKS
1. Grewal, B.S. and Grewal,J.S., “ Numerical methods in Engineering and Science”, 6th Edition,
Khanna Publishers, New Delhi, 2004.
2. Sankara Rao, K. “Numerical methods for Scientists and Engineers’, 3rd Edition Prentice Hall
of India Private Ltd., New Delhi, 2007.
REFERENCES
1. Chapra, S. C and Canale, R. P. “Numerical Methods for Engineers”, 5th Edition, Tata
McGraw-Hill, New Delhi, 2007.
2. Gerald, C. F. and Wheatley, P. O., “Applied Numerical Analysis”, 6th Edition, Pearson
Education Asia, New Delhi, 2006.
3. Brian Bradie, “A friendly introduction to Numerical analysis”, Pearson Education Asia, New
Delhi, 2007.
MA3021 NUMERICAL METHODS L T P C
3 1 0 4
UNIT I SOLUTION OF EQUATIONS AND EIGENVALUE PROBLEMS (10 +3)
Solution of algebraic and transcendental equations - Fixed point iteration method –Newton-
Raphson method- Solution of linear system of equations - Gauss Elimination method – Pivoting
- Gauss-Jordan methods – Iterative methods of Gauss-Jacobi and Gauss-Seidel - Matrix
Inversion by Gauss-Jordan method - Eigenvalues of a matrix by Power method and by Jacobi’s
method.
UNIT II INTERPOLATION AND APPROXIMATION (8 + 3)
Interpolation with unequal intervals - Lagrange interpolation – Newton’s divided difference
interpolation – Cubic Splines - Interpolation with equal intervals - Newton’s forward and
backward difference formulae.
UNIT III NUMERICAL DIFFERENTATION AND INTEGRATION (9 + 3)
Approximation of derivatives using interpolation polynomials - Numerical integration using
Trapezoidal, Simpson’s 1/3 and Simpson’s 3/8 rules – Romberg’s method – Two point and three
point Gaussian quadrature formulae – Evaluation of double integrals by Trapezoidal and
Simpson’s rules.
UNIT IV INITIAL VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL
EQUATIONS (9 + 3)
Single step-methods - Taylor’s series method - Euler’s method - Modified Euler’s method -
Fourth order Runge-Kutta method for solving first and second order equations –Multistep
methods - Milne’s and Adams-Bashforth predictor-corrector methods for solving first order
equations.
UNIT V BOUNDARY VALUE PROBLEMS IN ORDINARY AND PARTIAL
DIFFERENTIAL EQUATIONS (9 + 3)
Finite difference methods for solving two-point linear boundary value problems. Finite difference
techniques for the solution of two dimensional Laplace’s and Poisson’s equations on rectangular
domain – One dimensional heat-flow equation by explicit and implicit (Crank Nicholson)
methods - One dimensional wave equation by explicit method.
L: 45 T: 15 TOTAL : 60 PERIODS
31
TEXT BOOKS
1. Grewal, B.S. and Grewal,J.S., “ Numerical methods in Engineering and Science”, 6th Edition,
Khanna Publishers, New Delhi, 2004.
2. Sankara Rao, K. “Numerical methods for Scientists and Engineers’, 3rd Edition Prentice Hall
of India Private Ltd., New Delhi, 2007.
REFERENCES
1. Chapra, S. C and Canale, R. P. “Numerical Methods for Engineers”, 5th Edition, Tata
McGraw-Hill, New Delhi, 2007.
2. Gerald, C. F. and Wheatley, P. O., “Applied Numerical Analysis”, 6th Edition, Pearson
Education Asia, New Delhi, 2006.
3. Brian Bradie, “A friendly introduction to Numerical analysis”, Pearson Education Asia, New
Delhi, 2007.
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