Engineering Tutorials

ME – 311 E     APPLIED NUMERICAL TECHNIQUES AND COMPUTING

Sessional marks   :      50
Theory marks       :     100

UNIT – I    ERRORS IN NUMERICAL CALCULATIONS
Introduction, Numbers and their accuracy, Absolute, relative and percentage errors and their analysis, General error formula.

UNIT – II    INTERPOLATION AND CURVE FITTING
Taylor series and calculation of functions, Introduction to interpolation, Lagrange approximation, Newton Polynomials, Chebyshev Polynomials, Least squares line, curve fitting, Interpolation by spline functions.

UNIT – III    NUMERICAL DIFFERENTIATION AND INTEGRATION
Approximating the derivative, Numerical differentiation formulas, Introduction to Numerical quadrature, Newton-Cotes formula, Gaussion Quadrature.

UNIT – IV    SOLUTION OF NONLINEAR EQUATIONS
Bracketing  methods for locating a root, Initial approximations and convergence criteria, Newton- Raphson and Secant methods, Solution of problems through a structural programming language such as C or  Pascal.

UNIT – V    SOLUTION OF LINEAR SYSTEMS
Direct Methods, Gaussian elimination and pivoting, Matrix inversion, UV factorization, Iterative methods for linear systems, Solution of problems through a structured programming language such as C or  Pascal.

UNIT – VI    EIGEN VALUE PROBLEMS
Jacobi, Given’s and Householder’s methods for symmetric matrices, Rutishauser method for general matrices, Power and inverse power methods.

UNIT – VII    SOLUTION OF DIFFERENTIAL EQUATIONS
Introduction to differential equations, Initial value problems, Euler’s methods, Heun’s method, Runge-Kutta methods, Taylor series method, Predictor-Corrector methods, Systems of differential equations, Boundary valve problems, Finite-difference method, Solution of problems through a structured programming language such as C or  Pascal.

UNIT – VIII    PARTIAL DIFFERENTIAL EQUATIONS, EIGENVALUES AND EIGENVECTORS
Solution of hyperbolic, parabolic and elliptic equations, The eigenvalue problem, The power method and the Jacobi’s method for eigen value problems, Solution of problems through a structural programming language such as C or  Pascal.

Text Books:
Numerical Methods for Mathematics, Science and Engineering by John H.Mathews, PHI New Delhi.
Applied Numerical Methods – Carnahan, B.H., Luthar, H.A. and Wilkes, J.O., Pub.- J. Wiley, New York

Reference Books:
Numerical Solution of Differential Equations, by M.K. Jain, Published by Wiley Eastern, New York.
Introductory Methods of Numerical Analysis by S.D. Sastry, Published by Prentice Hall of India.
Numerical Methods – Hornbeck, R.W. , Pub.- Prentice Hall, Englewood Cliffs, N.J.

Note :      1.    Programming exercises may be done in MATLAB.
2.   The Instructor of the course may cover the use of software MATHEMATICA in the tutorial class.
3.  In the semester examination, the examiner will set eight questions, at least one question from each unit. The students will be required to attend only 5 questions.

Related posts:

1. ME- 319 E APPLIED NUMERICAL TECHNIQUES AND COMPUTING LAB.
2. PTU Syllabus | ME-309 Numerical Methods in Engineering
3. M-801-A-NUMERICAL ANALYSIS AND OPTIMIZATION
4. UPTU Syllabus | ECS-353 : Numerical Techniques Lab
5. MATH-204-E NUMERICAL METHODS LAB.