UNIVERSITY OF MADRAS
B.Sc. DEGREE PROGRAMME IN MATHEMATICS
SYLLABUS WITH EFFECT FROM 2023-2024
Title of the Course NUMERICAL METHODS WITH APPLICATIONS
Paper Number ELECTIVE COURSE - I
Category Elective Year I Credits 3 Course 134E1B
Semester I Code
Instructional Lecture Tutorial Lab Practice Total
Hours 4 1 -- 5
per week
Pre-requisite 12th Standard Mathematics
Objectives of the • To Solve Transcendental and Algebraic Equations
Course
• To understand the difference operators and their relations.
• To interpolate the given data using different methods.
• To use difference formula to compute derivatives and integrals.
`Course Outline UNIT-I: The Solutions of Numerical Algebraic and Transcendental
Equations: Introduction – Bisection method – Iteration method –
Regula Falsi method – Newton – Raphson method – Horner’s
Method Hours: 12
Chapter III: Sections – 1 to 5, 8
UNIT-II: Simultaneous Linear Algebraic equations: Introduction –
Gauss Elimination method – Computation of the inverse of a
matrix using Gauss Elimination method – Method of
Triangularisation – Iterative methods Hours: 12
Chapter IV: Sections – 1 to 4, 6
UNIT-III: Finite Differences: Backward differences – central
difference notations – Properties of the Operator △ - Difference of
polynomials – Factorial polynomials – The Operator E –
Relation between E and △ - Relation between D and △ –
Relation between the operators - Summation of Series Hours:12
Chapter V: Sections: 6, 8, 10 – 12, 14 – 16, 18, 19
UNIT-IV: Central Difference Interpolation Formulae: Gauss forward
and backward interpolation formula – Stirling’s formula – Bessel’s
formula
Chapter VII: Sections: 3 – 6 Hours: 12
UNIT-V: Interpolation with unequal intervals; Divided differences -
properties of divided differences – Newton’s interpolation formula for
unequal intervals - Lagrange’s formula for interpolation
Chapter 8: Sections: 1 – 4 Hours: 12
Total Hours:60
UNIVERSITY OF MADRAS
B.Sc. DEGREE PROGRAMME IN MATHEMATICS
SYLLABUS WITH EFFECT FROM 2023-2024
Extended
Professional
Questions related to the above topics, from various competitive
Component (is a
examinations UPSC / TNPSC / others to be solved
part of internal
component only, (To be discussed during the Tutorial hour)
Not to be included
in the External
Examination
question paper)
Skills acquired Knowledge, Problem Solving, Analytical ability, Professional
from this course Competency, Professional Communication and Transferrable Skill
Recommended Numerical Methods in Science and Engineering,Dr. M. K.
Text Venkatraman, The National Publishing Company, Madras – 600 001.
(Third Edition)
Reference Books 1. Numerical Method, P.Kandasamy, K.Thilagavathy,
K.Gunavathy, S.Chand and company Ltd., New Delhi
(Reprint 2002)
2. Numerical Methods for Scientific and Engineering
Computations, M.K.Jain, S.R.K.Iyankar, R.K.Jain, (Sixth
Edition), New Age International (P) Ltd. Publishers, New Delhi.
3. Numerical Methods, A.Singaravelu, Meenakshi Agencies,
Chennai – 601302.
Website and https://ocw.mit.edu/courses/mathematics/18-336-numerical-methods-
for-partial-differential-equations-spring-2009/
e-Learning Source
https://www.mathworks.com
Course Learning Outcome (for Mapping with POs and PSOs)
Students will able to
CLO 1: Solve algebraic and transcendental equations using bisection method, iteration
method, regula falsi method, and Newton Raphson method.
CLO 2: Solve simultaneous linear equations using Gauss elimination method, Gauss
Jordon method, and Gauss Seidel method.
CLO 3: Use finite differences to calculate differences of a polynomial, factorial
polynomials, differences of zero, and summation series.
CLO 4: Perform interpolation using central differences formulae, and Gauss forward
and backward formulae.
CLO 5: Perform Numerical differentiation and integeration.
POs PSOs
1 2 3 4 5 6 1 2 3
CLO 1 3 2 3 2 1 1 3 3 2
CLO 2 3 2 3 2 1 1 3 3 2
CLO 3 3 2 3 2 1 1 3 3 2
CLO 4 3 2 3 2 1 1 3 3 2
CLO 5 3 2 3 2 1 1 3 3 2
