Numerical Analysis

Notes will be updated here periodically.

This page is last updated on 29 Oct 2026.

Pre-requisites: 

MA-I (MA001), MA-II (MA002), Numerical Linear Algebra (MA307), MATLAB.

Course Syllabus: 

[Unit-1] Mathematical Preliminaries: Rounding and chopping errors, condition and stability.  

[Unit-2] Roots of Non-Linear Equations: Bisection, fixed-point and secant method, Newton’s method for simple and multiple roots and applications, order of convergence.

[Unit-3] System of Linear Equations and Eigen Values: Gauss elimination method using pivoting strategies, LU decomposition, Matrix norm, Jacobi and Gauss-Seidel methods, power method, QR algorithm.

[Unit-4] Interpolations and Approximations: Lagrange and Newton’s divided difference interpolation, forward and backward differences, least squares approximation.

[Unit-5] Numerical Differentiation and Integration: Numerical differentiation, Newton-Cotes quadrature formulae (Trapezoidal and Simpson's rules) and their error analysis, Gauss-Legendre quadrature formulae.

[Unit-6] Numerical Methods to Solve Ordinary Differential Equation: Initial Value Problems Euler's, modified Euler’s, and Runge-Kutta methods, system of first order differential equations; Finite difference method for boundary value problems.   

Course Outcomes: 

The present course will provide a theoretical and computational perspective of the numerical analysis and its implementation. By attending the course, students will be able to understand 

1. Learn how to obtain numerical solution of nonlinear equations using bisection, secant, Newton, and fixed-point iteration methods. 

2. Solve system of linear equations numerically using direct and iterative methods.

3. Learn how to approximate the functions using interpolating polynomials.

4. Learn how to solve definite integrals and initial value problems numerically. 

Recommended Books:

Text Books:

1. Richard L. Burden, J. Douglas Faires and Annette Burden, Numerical Analysis, Cengage Learning, 10th edition, 2015.

2. Biswa Nath Dutta, Numerical Linear Algebra and Applications, SIAM, 2010.

3. E. Ward Cheney and David R. Kincaid, Numerical Mathematics and Computing, Cengage Learning, 7th edition, 2012.

4. K. Atkinson and W. Han, Elementary Numerical Analysis, 3rd edition, John Willey \& Sons, 2004.

Reference Books:

1. Steven C. Chapra and Raymond P. Canale, Numerical Methods for Engineers, McGraw-Hill Higher Education; 6th edition, 2010.

2. H A V. Sundarapandian, Numerical Linear Algebra, PHI, 2008.

3. Endre Suli and David F. Mayers, An Introduction to Numerical Analysis, Cambridge University Press, 2003.

4. Brian Bradie, A Friendly Introduction to Numerical Analysis, Pearson Prentice Hall, 2006.

Evaluation Scheme: 

Students will be evaluated on a scale of 160 = {MTE, ETE, component-1, component-2} where

MTE - Open Book Mid Term Exam - 30 Marks for 1.5 Hr duration

ETE - Open Book End Term Exam - 50 Marks for 2 Hr duration

There are 4 compnents. A student can choose any two (or best will be counted, in case more than 2 components opted). 

(Componet) Project - A two page report + 15 min presentation - 40 Marks 

(Component) Practical - MATLAB Coding of 40 Marks

(Component) Self-Learning - (a) Numerical Laplace Transform or (b) Numerical Methods to Solve PDE - two page creative writing - 40 Marks

(Component) Quiz - 40 Marks    

Note: A minimum of M = min{0.5*Class Average, 56} out of 160 marks is required to pass the course. The grading will be relative-scaled.

Exam/Test Schedule: 

1. Mid Term Exam will be held during Mid Term Exams (1-9 Oct 2026). 

2. Self-Learning written exam (open book, creative writing) will be held on 23 Oct 2026. 

3. Project presentations will be held in 10-20 Nov 2026. No further date extension request will be accepted. 

4. MATLAB Exam will be held on 13 Nov 2026. 

5. Quiz exam will be held on 26 Nov 2026. 

6. End Term Exam will be held during End Term Exams (9-18 Dec 2026).