MA2264 NUMERICAL METHODS SYLLABUS | ANNA UNIVERSITY B.TECH. CHEMICAL ENGINEERING 5TH SEMESTER SYLLABUS REGULATION 2008 2011 2012-2013 BELOW IS THE ANNA UNIVERSITY FIFTH SEMESTER B.TECH. CHEMICAL ENGINEERING DEPARTMENT SYLLABUS, TEXTBOOKS, REFERENCE BOOKS, 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
MA2264 NUMERICAL METHODS L T P C
3 1 0 4
AIM
With the present development of the computer technology, it is necessary to develop
efficient algorithms for solving problems in science and engineering. This course gives a
complete procedure for solving different kinds of problems occur in Engineering
numerically.
OBJECTIVES
At the end of the course, the students would be acquainted with the basic concepts in
numerical methods. The uses of numerical methods are summarized as follows:
The roots of nonlinear (algebraic or transcendental) equations which arise in
engineering applications can be obtained numerically where analytical methods
fail to give solution. Solutions of large system of linear equations are also
obtainable using the different numerical techniques discussed. The Eigen value
problem is one of the important concepts in dynamic study of structures.
When huge amounts of experimental data are involved in some engineering
application, the methods discussed on interpolation will be useful in constructing
approximate polynomial to represent the data and to find the intermediate values.
The numerical differentiation and integration find application when the function in
the analytical form is too complicated or the huge amounts of data are given such
as series of measurements, observations or some other empirical information.
Many physical laws are couched in terms of rate of change of quantity. Therefore
most of the engineering problems are characterized in the form of nonlinear
ordinary differential equations. The methods introduced in the solution of ordinary
differential equations will be useful in attempting any engineering problem.
When the behavior of a physical quantity is expressed in terms of rate of change
with respect to two or more independent variables, the problem is characterized
as a partial differential equation. The knowledge gained may be used in solving
any problem that has been modeled in the form of partial differential equation.
UNIT I SOLUTION OF EQUATIONS AND EIGENVALUE PROBLEMS 9+3
Linear interpolation methods (method of false position) – Newton’s method - 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.
40
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.
L : 45 T :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., Thilagavathy, K. and Gunavathy, K., “Numerical Methods”, S.Chand
Co. Ltd., New Delhi, 2003.
2. Burden, R.L and Faires, T.D., “Numerical Analysis”, Seventh Edition, Thomson Asia
Pvt. Ltd., Singapore, 2002.
MA2264 NUMERICAL METHODS L T P C
3 1 0 4
AIM
With the present development of the computer technology, it is necessary to develop
efficient algorithms for solving problems in science and engineering. This course gives a
complete procedure for solving different kinds of problems occur in Engineering
numerically.
OBJECTIVES
At the end of the course, the students would be acquainted with the basic concepts in
numerical methods. The uses of numerical methods are summarized as follows:
The roots of nonlinear (algebraic or transcendental) equations which arise in
engineering applications can be obtained numerically where analytical methods
fail to give solution. Solutions of large system of linear equations are also
obtainable using the different numerical techniques discussed. The Eigen value
problem is one of the important concepts in dynamic study of structures.
When huge amounts of experimental data are involved in some engineering
application, the methods discussed on interpolation will be useful in constructing
approximate polynomial to represent the data and to find the intermediate values.
The numerical differentiation and integration find application when the function in
the analytical form is too complicated or the huge amounts of data are given such
as series of measurements, observations or some other empirical information.
Many physical laws are couched in terms of rate of change of quantity. Therefore
most of the engineering problems are characterized in the form of nonlinear
ordinary differential equations. The methods introduced in the solution of ordinary
differential equations will be useful in attempting any engineering problem.
When the behavior of a physical quantity is expressed in terms of rate of change
with respect to two or more independent variables, the problem is characterized
as a partial differential equation. The knowledge gained may be used in solving
any problem that has been modeled in the form of partial differential equation.
UNIT I SOLUTION OF EQUATIONS AND EIGENVALUE PROBLEMS 9+3
Linear interpolation methods (method of false position) – Newton’s method - 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.
40
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.
L : 45 T :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., Thilagavathy, K. and Gunavathy, K., “Numerical Methods”, S.Chand
Co. Ltd., New Delhi, 2003.
2. Burden, R.L and Faires, T.D., “Numerical Analysis”, Seventh Edition, Thomson Asia
Pvt. Ltd., Singapore, 2002.
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