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 Understand the concepts of finite differences, derive the interpolation formulae, and
understand its applications.

THEORY (45 Hours)

UNIT I (12 Hours)
Errors: Relative Error, Absolute Error, Round off Error, Truncation Error. Transcendental and
Polynomial equations: Bisection method, Newton-Raphson method, Secant method. Method of
False Position, Fixed point iterative method, Order, and rate of convergence of these methods.
UNIT II (9 Hours)
System of linear equations: Gauss Elimination and Gauss Jordan methods. Gauss Jacobi
method, Gauss Seidel method and their convergence analysis.

UNIT III (9Hours)

Interpolation: Lagrange Interpolating Polynomial, Newton‘s Gregory forward and backward
difference interpolating polynomial, Newton‘s Divided Difference Interpolating Polynomial,
Error analysis in each method.

UNIT IV (15 Hours)
Numerical Integration: Trapezoidal rule, Simpson‘s rule, Simpson‘s 1/3rule, Simpsons 3/8th rule.
Ordinary Differential Equations: Euler‘s method, Modified Euler‘s method, Runge-Kutta method.

*TUTORIAL (15 Hours (1 Hour per week))

SUGGUESTED READINGS:

1. Sastry, S. S. (2012). Introductory methods of numerical analysis. PHI Learning Pvt. Ltd..
2. Gerald, C. F., & Wheatley, P. O. (2008). Applied Numerical Analysis (7th ed.). Pearson
Education. India.
3. Bradie, Brian. (2006). A Friendly Introduction to Numerical Analysis. Pearson
17. Education, India. Dorling Kindersley (India) Pvt. Ltd. Third impression 2011.
4. Mudge, M. R. (2003). An introduction to numerical methods and analysis,(Wiley).
5. Jain, M. K., Iyengar, S. R. K., & Jain, R. K. (2012). Numerical Methods for Scientific
18. and Engineering Computation. (6th ed.). New Age International Publisher, India, 2016.
6. Spectrum- Numerical Methods, Sharma Publications, Jalandhar

DISCIPLINE ELECTIVE COURSES:

Math.212 Elements of Number Theory 3+1*

LEARNING OBJECTIVES:

The primary objective of this course is to introduce:
 The Euclidean algorithm and linear Diophantine equations, the Fundamental theorem of
19. arithmetic and some of the open problems of number theory viz. the Goldbach conjecture.
 The modular arithmetic, linear congruence equations, system of linear congruence
20. equations, arithmetic functions, and multiplicative functions, e.g., Euler‘s Phi-function.
 Introduction of the simple encryption and decryption techniques, and the numbers of
21. specific forms viz. Mersenne numbers, Fermat numbers etc.

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