Numerical Analysis -II:

Numerical analysis is one of the important branch of mathematics. It helps us to solve the different numerical problems with different techniques. It also helps to construct the algorithm on computer to solve the numericals of large data. 

Prerequisite :Numerical analysis -I. 

Learning out comes:

After completion of this course,  students will  be able to

(i)  Construct farward, backward, shift, central, average and differential operator. 

(ii)  To find the interpolation of polynomial by different methods. 

(iii) To evaluate nuemriacl differentiation and integration by different methods. 

(iv)  To form difference equations  and  to solve different types of difference equations. 

(v)  To find  the value of functions at particular value whose differential equatios with initial conditions are given. 

Course contents :

Forward, backward and central difference formula. Lagrange interpolation, Newton divided difference formula. Interpolation with cubic spline, Hermit interpolation Least square approximation. Rechardson's extrapolation, Newton cotes formulae, Numerical integration:

Rectangular rule, Trapezoidal rule, Simpson's 1/3 and 3/8 rules,Bool's and Weddle's rule, Gaussian quadrature. 

Difference and differential equations, Formulation of difference equations. Solutions of linear homogeneous and inhomogeneous difference equations with constant coefficients. 

The Euler and Modified Euler method. Rang-Kutta method and predictor -corrector type methods for solving initial value problems along with convergence and instability criteria. Finite difference, collocation and variational method for boundary value problems. 

Recmended Books:

1-Gerald. C. F.  and Wheatley P. O., Applied Numerical analysis, Pearson Education Singapore 2005.

2-Burdon R. L and Faires J. D.,  Numerical analysis, latest edition PWS pub. Co.

3-Mathews J. H., Numerical methods for mathematics. Latest Edition, Prentice Hall international. 

4-Chapra S. C. and canal R. P Numerical methods for engineering, 6th edition McGraw Hill. 

5-Sankara K., Numerical methods for scientist and engineering 2nd edition. New Delhi Prentice Hall 2005.

Research project/Practicals/Labs/Assignments:

(i)  Relations between different operators of Numerical analysis. 

(ii)  Find the Area  under the cuve by  different methods. 

(iii) Applications  of Numerical integration. 

Assessment criteria :

Sessional :20 (Assignment 10, Attandance 05, Quiz 05).

Mid-Term Exam :30

Final -Term Exam:  50

Key Dates and Time of class meeting:

Tuesday : 2:00 pm -3:30 pm. 

Thursday: 3:30pm-5:00pm.

Commencement of classes :Jan, 13,2020.

Mid-Term Exam: March 09-13,2020.

Final Examination :May, 04-08,2020.

Declaration of Result :May 19,2020.