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# Syllabus | B.Tech-Computer Science & Engineering | Numerical Methods and Random process

 Numerical Methods and Random process Learning Schedule L T P C Pre-requisites: Maths 3 1 0 4

COURSE DESCRIPTION
This course is a study of mathematical techniques used to model engineering systems. It involves the development of mathematical models and the application of the computer to solve engineering problems using the various computational techniques: Taylor Series approximation, numerical differentiation, root-finding using bracketing and open methods, linear and polynomial curve fitting, solution methods for matrix equations, numerical integration etc.

COURSE OBJECTIVES:
To enhance problem solving skills of engineering students using a powerful problem solving tool namely numerical methods. The tool is capable of handling large systems of equations, nonlinearities and complicated geometries that are common in engineering practice but often impossible to solve analytically.

COURSE OUTCOMES :
On completion of this course, the students will be able to

• Apply various numerical methods and appreciate a trade off in using them.
• Understand the source of various types of errors and their effect in using these methods.
• To distinguish between Numerical and Analytical methods along with their Merits and demerits.
• Understand the use of digital computers in implementation of these methods.
• Develop a code in C/C++ for the solution of problems that may not be solved by analytical methods.

COURSE CONTENT:

Unit-I: Non- Linear Equations and system of Linear Equations
Introduction, error and error propagation, Bisection method, False position Method, Method of Iteration, Newton-Raphson Method, Secant Method, Gauss Elimination method Gauss – Jordan method, Gauss – Seidel method, convergence of iterative methods.

Unit-II: Interpolation:
Newton’s Forward and Backward Interpolation, Lagrange’s Interpolation, Newton’s Divided Difference Interpolation, Inverse Interpolation.

Unit-III : Numerical Differentiation and Integration
Derivations from difference tables, Higher order derivations. Newton – Cotes integra-tion formula, Trapezoidal rule, Simpson’s rule, Boole’s rule and Weddle’s rule, Romberg’s Integration .

Unit-IV:Numerical Solution of Ordinary
Taylor series method, Euler and modified Euler method, Runge Kutta methods, Milne’s method, Finite Difference method.

Unit-V: Partial Differential Equations
Finite difference approximations of partial derivatives, Solution of Laplace’s equation (Elliptic) by Liebmann’s iteration method, Solution of one dimensional heat equation (Parabolic) by Bender-Schmidt method and Crank – Nicolson method, Von-Neumann stability condition, Solution of one dimensional wave equation (Hyperbolic), CFL stability condition.

Text Books:

• Introductory Methods of Numerical Analysis: S.S. Sastry, PHI learning Pvt Ltd.

REFRENCE BOOKS:

• Numerical Methods for Scientific and Engineering computation: M.K Jain, S.R.K Iyengar and R.K Jain, New age Inter-national Publishers.

Numerical Method: E. Balagurusamy, Tata McGraw Hill Publication.