Syllabus (MATHEMATICS)

Course Type: MAJ-10

Semester: 6

Course Code: BMTMMAJ10T

Course Title: Numerical Methods & Computer Programming in C

(L-P-Tu): 5-0-1

Credit: 6

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 -1: Numerical Methods [Credit: 3, 45L]

• Approximation of numbers, decimal places, significant figures, Round off Errors: Relative, Absolute and Percentage. Truncation, Inherrent.
• Solution of Transcendental and Polynomial equations using Bisection method, Regula-falsi method, fixed point iteration, Newton-Raphson method. Geometrical interpretation, convergency conditions, Rate of convergence of these methods.
• System of linear algebraic equations: Gaussian Elimination, Gauss Seidel method and their convergence analysis.
• Interpolation: Finite difference operators, Lagrange’s interpolation formula, Newton’s forward and backward interpolation formula, divided difference, Newton’s general interpolation formula, Interpolating Errors.
• Numerical Integration: Newton-Cotes’ formula, Trapezoidal rule, Simpson’s 1/3rd rule, Composite Trapezoidal rule, Composite Simpson’s 1/3rd rule, Inherent errors, degree of precision.
• Ordinary Differential Equations: The method of successive approximations, Euler’s method, the modified Euler method, Runge-Kutta methods of orders two and four (Proof of order four is not required).

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

• Computer Languages: Machine language, Assembly language, computer-high level languages, Compiler, Interpreter, Operating system, Source programs and objects programs.
• Binary number system, Conversions and arithmetic operation, Representation for Integers and Real numbers, Fixed and floating point.
• 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.

• Statistical and other simple programming:

(a) To find mean, median, mode, standard deviation

(b) Ascending, descending ordering of numbers

(c) Finite sum of a series

(d) Fibonacci numbers

(e) Checking of prime numbers

(f) Factorial of a number

(g) Solution of a quadratic equation

(h) L.C.M. & G.C.D. of two positive integers.

(i) Conversion of temperature from Fahrenheit to Centigrade and vice versa

(j) Area of a triangle

(k) To find simple and compound interest

Reading References:

1. S.A. Mollah; Numerical Analysis and Computational Procedures.
2. Yashavant Kanetkar; Let Us C; BPB Publications.
3. K.E. Atkinson; An Introduction to Numerical Analysis; John Wiley and Sons; 1978.
4. C. Xavier; C Language and Numerical Methods; New Age Intl (P) Ltd. Pub.
5. B.S. Gottfried; Programming with C; TMH.
6. E. Balaguruswamy; Programming in ANSI C; TMH.
7. N. Datta; Computer Programming and Numerical Analysis-An Integrated Approach (Revised edition with C); Universities Press.