COURSE INFORMATION

Course Code: M(CS)301/ M(CS)401

Course Name: Numerical Method

Contacts: 2L+1T

Credits: 3

COURSE OUTCOME

At the end of this course, the incumbent will be able to:

1. Remembering: Recalling the basic mathematical tools such as, derivative, real integration, solution of equations, existence of solution of system of linear equations and differential equation.
2. Understanding: Describe the concept of error, operators and interpolation. Numerical approach of solving missing term, finding of polynomials, integrated value, solution of algebraic equations, system of linear equations and differential equation.
3. Applying: Use interpolation, integration for data analysis and finding of volume of rough surface. Apply different numerical techniques to solve algebraic equations, system of linear equations in iterative way. Solve boundary value wave and heat equations using differential equations.
4. Analyzing: Analyze different real time problems and categorize them during the process of solving, by numerical technique mentioned.
5. Evaluating: Justify and make gradation of above mentioned numerical tools and determine the right approach to find the optimal solution for multidisciplinary engineering problems.
6. Creating: Design a working model and build a path by which a new approach can be generated to create a new problem appreciated by academics, research & emerging direction in industry.

PREREQUISITES

To understand this course, the incumbentmust have idea of:

·         Derivative of a function and fundamental theorems on calculus

·         Taylor series expansion of a single variable function

·         Rolle’s theorem and Intermediate Value theorem

SYLLABI

Approximation in numerical computation: Truncation and rounding errors, Fixed and floating-point arithmetic, Propagation of errors.(4L)

Interpolation: Newton forward/backward interpolation, Lagrange’s and Newton’s divided difference Interpolation.(5L)

Numerical integration: Trapezoidal rule, Simpson’s 1/3 rule, Expression for corresponding error terms. (3L)

Numerical solution of a system of linear equations:

Gauss elimination method, Matrix inversion, LU Factorization method, Gauss-Seidel iterative method.(6L)

Numerical solution of Algebraic equation:

Bisection method, Regula-Falsi method, Newton-Raphson method.(4L)

Numerical solution of ordinary differential equation: Euler’s method, Runge-Kutta methods, Predictor-Corrector methods and FiniteDifference method.

(6L)

BEYOND SYLLABI COVERAGE

Gauss Jordan method.

Gauss Jacobi iterative method.

LECTURE PLAN

M(CS)301 &M(CS)401

LECTURE  NOTE

LECTURE  NOTE  BEYOND SYLLABUS

HOMEWORK/ASSIGNMENT

TEXT

1.      Dutta& Jana: Introductory Numerical Analysis.

2.      Numerical Analysis,  S.N. Mollah

REFERENCE

1.      Balagurusamy:      Numerical  Methods, Scitech.