Syllabus (MATHEMATICS)

Course Type: ME-8

Semester: 7

Course Code: BMTMMEB47T

Course Title: Numerical Methods & Basic Computer Programming in C

(L-P-Tu): 4-0-0

Credit: 4

Practical/Theory: Theory

Course Objective: To be done.

Learning Outcome: Course Outcomes (CO): The whole course will have the following outcomes: Upon completing this course, students will be able to: CO1: Understand the concepts of approximation and round-off errors, including the significance of decimal places and significan

Syllabus:

Unit-I: Numerical Methods [Credit: 2, 30 L]

Errors, Absolute & Relative Errors, Round off, Truncation.

Solution of Transcendental and Polynomial equations using Bisection method, Fixed Point Iteration, Newton-Raphson method, Geometrical interpretation, convergence conditions, Rate of convergence of these methods.

Solution of System of linear algebraic equations by Gaussian Elimination and Gauss Seidel method and their convergence.

Finite difference operators, Lagrange’s Interpolation Formula, Newton’s Forward and Backward Interpolation Formula.

Numerical Integration: Newton Cotes formula, Trapezoidal rule, Simpson’s 1/3rd rule, Composite Trapezoidal rule, Composite Simpson’s 1/3rd rule.

Unit-2: Basic Computer Programming in C [Credit: 2, 30 L]

Computer Languages: Machine language, Assembly language, computer-high level languages,

Introduction to C programming: Basic structures, Character set, Keywords, Identifiers, Constants, Variable-type declaration

Operators: Arithmetic, Relational, Logical, assignment, Increment, decrement, Conditional. Operator precedence and associativity, Arithmetic expression,

Statement: Input and Output, Define, Assignment, User define, Decision making (branching and looping) – Simple and nested IF, IF – ELSE, LADDER, SWITCH, GOTO, DO, WHILE – DO, FOR, BREAK AND CONTINUE Statements. Arrays- one and two dimensions, user defined functions.

Write simple problems in C programming language, like the following

1. Ascending, descending ordering of numbers.
2. Finite sum of a series.
3. Checking of prime numbers.
4. Factorial of a number.
5. Conversion of temperature from Fahrenheit to Centigrade and vice versa.
6. Area of a triangle.
7. To find simple and compound interest.
8. To find mean, standard deviation.

Reference Books

1. S.A. Mollah; Numerical Analysis and Computational Procedures; Books & Allied.
2. Yashavant Kanetkar; Let Us C; BPB Publications.
3. M.K. Jain, S.R.K. Iyengar and R.K. Jain, Numerical Methods for Scientific and Engineering Computation, 6th Ed., New age International Publisher, India, 2007.
4. Scarborough, James B., Numerical Mathematical Analysis, Oxford and IBH publishing co.
5. Xavier, C., C Language and Numerical Methods, (New Age Intl (P) Ltd. Pub.)
6. Balaguruswamy, E., Programming in ANSI C (TMH).
7. N. Datta, Computer Programming and Numerical Analysis-An Integrated Approach (Revised edition with C)-( Universities Press)
8. A.K. Jalan, U. Sarkar, Numerical Methods- A Programming-based Approach, Universities Press.