JNTU 2007-2008 1ST YEAR B.Tech -NUMERICAL METHODS

Posted Date: 09 Dec 2007 Resource Type: Articles/Knowledge Sharing Category: Syllabus

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JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY
HYDERABAD
I Year B. Tech. AE T P C
3+1* 0 6
NUMERICAL METHODS
UNIT-I
Solutions of Algebraic and Transcendental Equations: Introduction-The Bisection Method-The method of False Position- The Iteration Method- Newton-Raphson Method.

UNIT-II
Interpolation: Introduction –Errors in polynomial Interpolation- Finite differences – Forward Differences- Backward differences –Symbolic relations and separation of symbols- Differences of a polynomial –Newton’s formulae for Interpolation- central difference Interpolation formulae-Gauss central Difference Formulae- Interpolation with unevenly spaced points- Lagrange’s Interpolation formula.

UNIT-III
Fitting a straight line – Nonlinear curve fitting- curve fitting by a sum of Exponentials- Weighted least squares approximation –Linear weighted least squares approximation- Nonlinear weighted least square.

UNIT-IV
Orthogonal polynomials-Grams Schmidt orthogonalization process- Least-square solution- Representation of B-splines- Computation of B-splines- The Fourier Transform-The Fast Fourier transform.

UNIT-V
Numerical Differentiation and Integration: The cubic Spline method- Trapezoidal rule – Simpson’s one-third rule- Simpson’s 3/8 rule – Boole’s and Weddle’s Rules.

UNIT-VI
Matrices and linear systems of Equations: Solution of Linear Systems- Direct Methods –LU Decomposition- LU Decomposition from Gauss Elimination – Solution of Tridiagonal Systems – Solution of Linear Systems.

UNIT-VII
Numerical Solutions of ordinary Differential Equations: Solutions by Taylor’s Series –Picard’s Method of successive Approximations – Euler’s method- Runge-Kutta Methods- Predictor – Corrector Methods – Adams Moulton Method – Milne’s Method.

UNIT-VIII
Numerical Solutions of Partial Differential Equations: Introduction- Finite Difference Approximations to Derivatives –Laplace’s Equation –Jacobi’s Method – Gauss-Seidel Method.

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