Institute of Engineering & Management

Course: M(CS) 401 Numerical Methods PROGRAMME:

COMPUTER SCIENCE & ENGINEERING

COURSE: NUMERICAL METHODS COURSE CODE: REGULATION:

M ( CS ) 401

DEGREE: BTECH SEMESTER: IV

CREDITS: 2

COURSE TYPE: THEORY

2015

COURSE AREA/DOMAIN: DESIGNING OF COMPUTERS

CONTACT HOURS: 2L/WEEK + 1T/WEEK

CORRESPONDING LAB COURSE CODE (IF ANY): M(CS)491

LAB COURSE NAME: NUMERICAL

LAB

METHODS

Course pre-requisites CODE

COURSE NAME

DESCRIPTION

SEM

Course Objectives The primary goal is to provide engineering majors with a basic knowledge of numerical methods including: root-finding, elementary numerical linear algebra, integration, interpolation, solving systems of linear equations, curve fitting, and numerical solution to ordinary differential equations. ‘C’ language and SCILAB is the software environment used for implementation and application of these numerical methods. The numerical techniques learned in this course enable students to work with mathematical models of technology and systems.

Course Outcomes 1. 2. 3. 4.

Students would be able to assess the approximation techniques to formulate and apply appropriate strategy to solve real world problems. Be aware of the use of numerical methods in modern scientific computing. Be familiar with finite precision computation. Be familiar with numerical solution of integration, linear equations, ordinary differential equations, interpolations.

Programme Outcomes addressed in this course (a) An ability to apply knowledge of mathematics, science, and engineering. (b) An ability to design and conduct experiments, as well as to analyze and interpret data. (c) An ability to design a system, component, or process to meet desired needs within realistic constraints such as economic, environmental, social, political, ethical, health and safety, manufacturability, and sustainability (d) An ability to function on multidisciplinary teams

Department of CSE

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Institute of Engineering & Management Syllabus MODULE

I

DETAILS

LECTURE

Approximation in numerical computation: Truncation and rounding errors, Fixed and floating-point arithmetic, Propagation of errors. 4

II

Interpolation: Newton forward/backward interpolation, Lagrange’s and Newton’s divided difference Interpolation.

5

III

Numerical integration: Trapezoidal rule, Simpson’s 1/3 rule, Expression for corresponding error terms. 3

IV

V

VI

Numerical solution of a system of linear equations: Gauss elimination method, Matrix inversion, LU Factorization method, Gauss-Seidel iterative method.

6

Numerical solution of Algebraic equation: Bisection method, Regula-Falsi method, Newton-Raphson method.

4

Numerical solution of ordinary differential equation: Euler’s method, Runge-Kutta methods, Predictor-Corrector methods and Finite Difference method.

6

TOTAL HOURS

28

Gaps in the syllabus - to meet industry/profession requirements S.NO.

1.

DESCRIPTION

Weddle’s rule and Simpson’s 3/8 rule

PROPOSED ACTIONS

Extra classes

PO MAPPING a

Topics beyond syllabus/advanced topics S.NO.

Department of CSE

DESCRIPTION

HOURS

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Institute of Engineering & Management

1

Numerical integration – Weddle’s rule, Simpson’s 3/8 rule

3

Delivery/Instructional Methodologies S.NO.

DESCRIPTION

1

Chalk and Talk

2

Study Material

Assessment Methodologies S.NO.

DESCRIPTION

TYPE

2

Student Assignment . Tests

3

University Examination

Direct

4

Student Feedback

Indirect

1

Direct Direct

Course Plan S. NO. 1 2 3 4 5 6 7 8 9

Day Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7 Day 8 Day 9

Module I I I I II II II II II

10

Day 10

III

11 12

Day 11 Day 12

III III

Department of CSE

Topic Introduction Different types of Errors; Different types of Errors; Different types of Errors; Interpolation technique – Equal and unequal intervals Newton’s forward interpolation; Newton’s Backward interpolation; Unequal interpolation - Newton’s divided difference; Lagrange’s Interpolation; Numerical integration – Newton cotes quadrature formula; Trapezoidal rule; Trapezoidal rule; Simpson’s 1/3 rule; Weddle rule; Simpson’s 3/8 rule; Page 3

Institute of Engineering & Management

13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

Day 13 Day 14 Day 15 Day 16 Day 17 Day 18 Day 19 Day 20 Day 21 Day 22 Day 23 Day 24 Day 25 Day 26 Day 27 Day 28

III V V V IV IV IV IV VI VI VI VI VI VI VI VI

Error terms of Trapezoidal rule and Simpson’s 1/3 rule; Error terms of Trapezoidal rule and Simpson’s 1/3 rule; Bisection method; Rgula falsi method; Newton Raphson Method; System of linear equations: Matrix inversion; Gauss elimination method; LU factorization; Gauss-seidal method. ODE: Euler’s method Modified Euler’s method Runge-kutta order 2 Runge-kutta order 4 Predictor Corrector method Predictor Corrector method Finite difference method Finite difference method

Assignment Set I S. NO.

Question

1

State sufficient condition for convergence of Gauss-Seidel method.

2

Assesses CO

Find the solutions of the following system of equations by L-U factorization

CO.1 CO.1

method 2x-3y+10z=3 -x+4y+2z=20 5x+2y+z=-12

3

Solve the following system of equations by Matrix inversion method. 3x+y+2z = 3

CO.1

2x-3y-z = -3 x+2y+z = 4

4

Find the smallest positive root of the equation f(x) = x3-3x-5=0 for five iterations.

Department of CSE

CO.1

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Institute of Engineering & Management

Department of CSE

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