School of Sciences Indira Gandhi National Open University Maidan Garhi, New Delhi (For January 2012 cycle)

Size: px
Start display at page:

Download "School of Sciences Indira Gandhi National Open University Maidan Garhi, New Delhi (For January 2012 cycle)"

Transcription

1 MTE-0 ASSIGNMENT BOOKLET Bachelor's Degree Programme Numerical Analysis (MTE-0) (Valid from st January, 0 to st December, 0) School of Sciences Indira Gandhi National Open University Maidan Garhi, New Delhi-0068 (For January 0 cycle)

2 Dear Student, Please read the section on assignments in the Programme Guide for Elective courses that we sent you after your enrolment. A weightage of 0 per cent, as you are aware, has been earmarked for continuous evaluation, which would consist of one tutor-marked assignment for this course. The assignment is in this booklet. Instructions for Formating Your Assignments Before attempting the assignment please read the following instructions carefully. ) On top of the first page of your answer sheet, please write the details exactly in the following format: ROLL NO : NAME : ADDRESS : COURSE CODE:. COURSE TITLE :. ASSIGNMENT NO.. STUDY CENTRE:.... DATE:.... PLEASE FOLLOW THE ABOVE FORMAT STRICTLY TO FACILITATE EVALUATION AND TO AVOID DELAY. ) Use only foolscap size writing paper (but not of very thin variety) for writing your answers. ) Leave 4 cm margin on the left, top and bottom of your answer sheet. 4) Your answers should be precise. ) While solving problems, clearly indicate which part of which question is being solved. 6) This assignment is to be submitted to the Study Centre as per the schedule made by the study centre. Answer sheets received after the due date shall not be accepted. We strongly suggest that you retain a copy of your answer sheets. 7) This assignment is valid only upto December, 0. If you have failed in this assignment or fail to submit it by December, 0, then you need to get the assignment for the year 0 and submit it as per the instructions given in the programme guide. 8) You cannot fill the exam form for this course till you have submitted this assignment. So solve it and submit it to your study centre at the earliest. We wish you good luck.

3 Assignment (MTE 0) (January 0 December 0) Course Code: MTE-0 Assignment Code: MTE-0/0 Maximum Marks: 00. a) A negative root of smallest magnitude of the equation x + x + 0 = 0 is to be determined i) Find an interval of unit length which contains this root ii) iii) Perform two iterations of the bisection method Taking the end points of the last interval as initial approximations perform one iteration of the secant method. () b) Find a root of the equation x + 0x + 0x + 7 = 0 which is close to. 0 using the Birge-Vieta method. Perform two iterations of the method. () c) Obtain the cube root of using Newton-Raphson formula. (). a) Derive a suitable iteration function φ (x), such that the sequence of iterates obtained from the formula x k = φ(x k ), k = + 0,,, converge to the root of f (x) = 0 for f (x) = x log0 x 7 = 0. Using this formula and initial approximation x 0 =. 8, find the root correct to four decimal places. (4) b) Set up the Gaussi-Jacobi iteration scheme in matrix form for the linear system of equations x + 4x x 4x x x + 4x = = = Show that the iteration scheme is convergent. Hence find the rate of convergence of this method. (6). a) Find all the roots of the polynomial x 6x + x 6 = 0 by the Graeffe s root squaring method using three squarings. (7) b) How many maximum positive and negative roots does the equation 8x 4 + x 0x + 7x 8x + = 0 has? () 4. a) The Gauss elimination method is used to solve the system of equations x + 4x + αx = x x + αx = α x + x + x = 6 Find the value of α for which the system has (i) a unique solution (ii) no solution (iii) infinitely many solutions. (4) b) Find the eigenvalue of the matrix A, nearest to and also the corresponding eigenvector using four iterations of the inverse power method where

4 4 0 A = 4 (6) 0 4. a) i) Set up the Gauss-Seidel iteration scheme in matrix form for solving the system of equations x x 7 ii) iii) = x + x x = x x = Show that this iteration scheme converges and find the rate of convergence. Perform two iterations of this method taking the zero vector as the initial approximation. (6) b) Find the inverse of the matrix A = 4 using LU decomposition method. (4) 6. a) Find the interpolating polynomial that fits the following data: x f(x) () b) Using the Lagrange s form of an interpolating polynomial find the value of x when y = from the following table of values: x y 4 () c) Using Lagrange s interpolation formula, prove that y = y 0.(y y ) + 0.(y y ) approximately. (4) 7. a) Given log0 64 =.86, log0 68 =.88, log0 69 =.889, log0 66 =. 80, find log () b) Prove that the third divided differences with arguments a, b, c, d of the function is equal x to. () abcd c) Determine the spacing h in a table of equally spaced values of the function f (x) = x between 0 and, so that quadratic interpolation in this table yields accuracy of 0. (4) 8. a) Find the value of f () from the following table 6 the constants x f(x) a, b, c in the numerical differentiation formula () b) Find the value of 4

5 y (x i ) = ay(x i h) + by(x i ) + cy(x i + h) such that the method is of highest possible order. Derive the corresponding Richardson extrapolation scheme. () c) Using Stirling s formula find the number of persons at age years, given where, y =, y 0 = 49, y 40 = 46, y 0 0 = 4 y x represents the number of persons at age x years in a life table. (4) 9. a) The following table of values of f (x) is given Find f (0.) using an 0(h ) method (using all the three values.) () b) Evaluate by Simpson s one-third rule an approximate value of sin x + cos x dx using 7 ordinates. (4) c) Determine the value of the integral I x f(x) = x( + 0 x / ) dx by composite trapezoidal rule with and ordinates. Improve the result by using extrapolation technique. (4) 0. a) Find the solution of the difference equation y k + 4y k+ + 4y k = 0; k = 0,,. Also find the particular solution when y 0 = and y = 6. () b) Solve the IVP, y = ; y(4) = 4 using Euler s method. Find y (4.) with h = 0. x 4y and 0. and extrapolate the value y (4.). () c) Solve the IVP y = + y, y(0) = 0 using classical R-K method of 0(h 4 ). Find y (0.4) taking h = 0.. Compare the solution obtained with the exact solution and find the error. (6) 0

ASSIGNMENT BOOKLET. Numerical Analysis (MTE-10) (Valid from 1 st July, 2011 to 31 st March, 2012)

ASSIGNMENT BOOKLET. Numerical Analysis (MTE-10) (Valid from 1 st July, 2011 to 31 st March, 2012) ASSIGNMENT BOOKLET MTE-0 Numerical Analysis (MTE-0) (Valid from st July, 0 to st March, 0) It is compulsory to submit the assignment before filling in the exam form. School of Sciences Indira Gandhi National

More information

ASSIGNMENT BOOKLET. Bachelor's Degree Programme LINEAR ALGEBRA. It is compulsory to submit the assignment before filling in the exam form.

ASSIGNMENT BOOKLET. Bachelor's Degree Programme LINEAR ALGEBRA. It is compulsory to submit the assignment before filling in the exam form. ASSIGNMENT BOOKLET MTE- Bachelor's Degree Programme LINEAR ALGEBRA (Valid from st January, to st December, ) It is compulsory to submit the assignment before filling in the exam form. School of Sciences

More information

ASSIGNMENT BOOKLET. M.Sc. (Mathematics with Applications in Computer Science) Differential Equations and Numerical Solutions (MMT-007)

ASSIGNMENT BOOKLET. M.Sc. (Mathematics with Applications in Computer Science) Differential Equations and Numerical Solutions (MMT-007) ASSIGNMENT BOOKLET MMT-007 M.Sc. (Mathematics with Applications in Computer Science) Differential Equations and Numerical Solutions (MMT-007) School of Sciences Indira Gandhi National Open University Maidan

More information

ASSIGNMENT BOOKLET. Mathematical Methods (MTE-03) (Valid from 1 st July, 2011 to 31 st March, 2012)

ASSIGNMENT BOOKLET. Mathematical Methods (MTE-03) (Valid from 1 st July, 2011 to 31 st March, 2012) ASSIGNMENT BOOKLET MTE-03 Mathematical Methods (MTE-03) (Valid from 1 st July, 011 to 31 st March, 01) It is compulsory to submit the assignment before filling in the exam form. School of Sciences Indira

More information

M.Sc.(Mathematics with Applications in Computer Science) Probability and Statistics

M.Sc.(Mathematics with Applications in Computer Science) Probability and Statistics MMT-008 Assignment Booklet M.Sc.(Mathematics with Applications in Computer Science) Probability and Statistics (Valid from 1 st July, 013 to 31 st May, 014) It is compulsory to submit the assignment before

More information

Bachelor s Degree Programme Discrete Mathematics (Valid from 1st January, 2013 to 31st December, 2013.)

Bachelor s Degree Programme Discrete Mathematics (Valid from 1st January, 2013 to 31st December, 2013.) MTE-13 ASSIGNMENT BOOKLET Bachelor s Degree Programme Discrete Mathematics (Valid from 1st January, 2013 to 31st December, 2013.) It is compulsory to submit the assignment before filling in the exam form.

More information

Bachelor s Degree Programme Operations Research (Valid from 1st January, 2012 to 30th November, 2012.)

Bachelor s Degree Programme Operations Research (Valid from 1st January, 2012 to 30th November, 2012.) AOR-01 ASSIGNMENT BOOKLET Bachelor s Degree Programme Operations Research (Valid from 1st January, 2012 to 30th November, 2012.) It is compulsory to submit the assignment before filling in the exam form.

More information

BACHELOR OF COMPUTER APPLICATIONS (BCA) (Revised) Term-End Examination December, 2015 BCS-054 : COMPUTER ORIENTED NUMERICAL TECHNIQUES

BACHELOR OF COMPUTER APPLICATIONS (BCA) (Revised) Term-End Examination December, 2015 BCS-054 : COMPUTER ORIENTED NUMERICAL TECHNIQUES No. of Printed Pages : 5 BCS-054 BACHELOR OF COMPUTER APPLICATIONS (BCA) (Revised) Term-End Examination December, 2015 058b9 BCS-054 : COMPUTER ORIENTED NUMERICAL TECHNIQUES Time : 3 hours Maximum Marks

More information

ASSIGNMENT BOOKLET Bachelor s Degree Programme (B.Sc.) ORGANIC REACTION MECHANISM. Please Note

ASSIGNMENT BOOKLET Bachelor s Degree Programme (B.Sc.) ORGANIC REACTION MECHANISM. Please Note ASSIGNMENT BOOKLET Bachelor s Degree Programme (B.Sc.) ORGANIC REACTION MECHANISM CHE-06 Valid from 1 st January to 31 st December 2014 It is compulsory to submit the Assignment before filling in the Term-End

More information

ASSIGNMENT BOOKLET. Organic Chemistry. Bachelor s Degree Programme (B.Sc.) Please Note

ASSIGNMENT BOOKLET. Organic Chemistry. Bachelor s Degree Programme (B.Sc.) Please Note CE-05 ASSIGNMENT BOOKLET Organic Chemistry Bachelor s Degree Programme (B.Sc.) (Valid from st July, 03 to 3 st March, 04) Please Note You can take electives (56 to 64 credits) from a minimum of TWO and

More information

ASSIGNMENT BOOKLET. Organic Chemistry. Bachelor s Degree Programme (B.Sc.) (Valid from July 1, 2011 to March 31, 2012) Please Note

ASSIGNMENT BOOKLET. Organic Chemistry. Bachelor s Degree Programme (B.Sc.) (Valid from July 1, 2011 to March 31, 2012) Please Note ASSIGNMENT BKLET HE-05 rganic hemistry Bachelor s Degree Programme (B.Sc.) (Valid from July 1, 2011 to March 31, 2012) It is compulsory to submit the assignment before filling in the exam form Please Note

More information

ASSIGNMENT BOOKLET Bachelor s Degree Programme (B.Sc./B.A./B.Com.) MATHEMATICAL MODELLING

ASSIGNMENT BOOKLET Bachelor s Degree Programme (B.Sc./B.A./B.Com.) MATHEMATICAL MODELLING ASSIGNMENT BOOKLET Bachelor s Degree Prograe (B.Sc./B.A./B.Co.) MTE-14 MATHEMATICAL MODELLING Valid fro 1 st January, 18 to 1 st Deceber, 18 It is copulsory to subit the Assignent before filling in the

More information

Review. Numerical Methods Lecture 22. Prof. Jinbo Bi CSE, UConn

Review. Numerical Methods Lecture 22. Prof. Jinbo Bi CSE, UConn Review Taylor Series and Error Analysis Roots of Equations Linear Algebraic Equations Optimization Numerical Differentiation and Integration Ordinary Differential Equations Partial Differential Equations

More information

ASSIGNMENT BOOKLET Bachelor's Degree Programme (B.Sc.) ELEMENTARY MECHANICS. Please Note

ASSIGNMENT BOOKLET Bachelor's Degree Programme (B.Sc.) ELEMENTARY MECHANICS. Please Note ASSIGNMENT BOOKLET Bachelor's Degree Programme (B.Sc.) BPHE-101/PHE-01 PHE-01 ELEMENTARY MECHANICS Valid from January 1, 2013 to December 31, 2013 It is compulsory to submit the Assignment before filling

More information

Jim Lambers MAT 460/560 Fall Semester Practice Final Exam

Jim Lambers MAT 460/560 Fall Semester Practice Final Exam Jim Lambers MAT 460/560 Fall Semester 2009-10 Practice Final Exam 1. Let f(x) = sin 2x + cos 2x. (a) Write down the 2nd Taylor polynomial P 2 (x) of f(x) centered around x 0 = 0. (b) Write down the corresponding

More information

Numerical Analysis Solution of Algebraic Equation (non-linear equation) 1- Trial and Error. 2- Fixed point

Numerical Analysis Solution of Algebraic Equation (non-linear equation) 1- Trial and Error. 2- Fixed point Numerical Analysis Solution of Algebraic Equation (non-linear equation) 1- Trial and Error In this method we assume initial value of x, and substitute in the equation. Then modify x and continue till we

More information

Hence a root lies between 1 and 2. Since f a is negative and f(x 0 ) is positive The root lies between a and x 0 i.e. 1 and 1.

Hence a root lies between 1 and 2. Since f a is negative and f(x 0 ) is positive The root lies between a and x 0 i.e. 1 and 1. The Bisection method or BOLZANO s method or Interval halving method: Find the positive root of x 3 x = 1 correct to four decimal places by bisection method Let f x = x 3 x 1 Here f 0 = 1 = ve, f 1 = ve,

More information

5. Hand in the entire exam booklet and your computer score sheet.

5. Hand in the entire exam booklet and your computer score sheet. WINTER 2016 MATH*2130 Final Exam Last name: (PRINT) First name: Student #: Instructor: M. R. Garvie 19 April, 2016 INSTRUCTIONS: 1. This is a closed book examination, but a calculator is allowed. The test

More information

ASSIGNMENT BOOKLET Bachelor's Degree Programme ASTRONOMY AND ASTROPHYSICS. Please Note

ASSIGNMENT BOOKLET Bachelor's Degree Programme ASTRONOMY AND ASTROPHYSICS. Please Note ASSIGNMENT BOOKLET Bachelor's Degree Programme PHE-15 ASTRONOMY AND ASTROPHYSICS Valid from July 1, 2011 to March 31, 2012 It is compulsory to submit the Assignment before filling in the Term-End Examination

More information

NUMERICAL METHODS. x n+1 = 2x n x 2 n. In particular: which of them gives faster convergence, and why? [Work to four decimal places.

NUMERICAL METHODS. x n+1 = 2x n x 2 n. In particular: which of them gives faster convergence, and why? [Work to four decimal places. NUMERICAL METHODS 1. Rearranging the equation x 3 =.5 gives the iterative formula x n+1 = g(x n ), where g(x) = (2x 2 ) 1. (a) Starting with x = 1, compute the x n up to n = 6, and describe what is happening.

More information

M.SC. PHYSICS - II YEAR

M.SC. PHYSICS - II YEAR MANONMANIAM SUNDARANAR UNIVERSITY DIRECTORATE OF DISTANCE & CONTINUING EDUCATION TIRUNELVELI 627012, TAMIL NADU M.SC. PHYSICS - II YEAR DKP26 - NUMERICAL METHODS (From the academic year 2016-17) Most Student

More information

Subbalakshmi Lakshmipathy College of Science. Department of Mathematics

Subbalakshmi Lakshmipathy College of Science. Department of Mathematics ॐ Subbalakshmi Lakshmipathy College of Science Department of Mathematics As are the crests on the hoods of peacocks, As are the gems on the heads of cobras, So is Mathematics, at the top of all Sciences.

More information

Virtual University of Pakistan

Virtual University of Pakistan Virtual University of Pakistan File Version v.0.0 Prepared For: Final Term Note: Use Table Of Content to view the Topics, In PDF(Portable Document Format) format, you can check Bookmarks menu Disclaimer:

More information

TABLE OF CONTENTS INTRODUCTION, APPROXIMATION & ERRORS 1. Chapter Introduction to numerical methods 1 Multiple-choice test 7 Problem set 9

TABLE OF CONTENTS INTRODUCTION, APPROXIMATION & ERRORS 1. Chapter Introduction to numerical methods 1 Multiple-choice test 7 Problem set 9 TABLE OF CONTENTS INTRODUCTION, APPROXIMATION & ERRORS 1 Chapter 01.01 Introduction to numerical methods 1 Multiple-choice test 7 Problem set 9 Chapter 01.02 Measuring errors 11 True error 11 Relative

More information

NUMERICAL ANALYSIS SYLLABUS MATHEMATICS PAPER IV (A)

NUMERICAL ANALYSIS SYLLABUS MATHEMATICS PAPER IV (A) NUMERICAL ANALYSIS SYLLABUS MATHEMATICS PAPER IV (A) Unit - 1 Errors & Their Accuracy Solutions of Algebraic and Transcendental Equations Bisection Method The method of false position The iteration method

More information

SOLUTION OF EQUATION AND EIGENVALUE PROBLEMS PART A( 2 MARKS)

SOLUTION OF EQUATION AND EIGENVALUE PROBLEMS PART A( 2 MARKS) CHENDU COLLEGE OF ENGINEERING AND TECHNOLOGY (Approved by AICTE New Delhi, Affiliated to Anna University Chennai. Zamin Endathur Village, Madurntakam Taluk, Kancheepuram Dist.-603311.) MA6459 - NUMERICAL

More information

Unit I (Testing of Hypothesis)

Unit I (Testing of Hypothesis) SUBJECT NAME : Statistics and Numerical Methods SUBJECT CODE : MA645 MATERIAL NAME : Part A questions REGULATION : R03 UPDATED ON : November 07 (Upto N/D 07 Q.P) Unit I (Testing of Hypothesis). State level

More information

INTRODUCTION, FOUNDATIONS

INTRODUCTION, FOUNDATIONS 1 INTRODUCTION, FOUNDATIONS ELM1222 Numerical Analysis Some of the contents are adopted from Laurene V. Fausett, Applied Numerical Analysis using MATLAB. Prentice Hall Inc., 1999 2 Today s lecture Information

More information

The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 72.

The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 72. ADVANCED SUBSIDIARY GCE UNIT 4776/01 MATHEMATICS (MEI) Numerical Methods WEDNESDAY 20 JUNE 2007 Additional materials: Answer booklet (8 pages) Graph paper MEI Examination Formulae and Tables (MF2) Afternoon

More information

Computational Methods

Computational Methods Numerical Computational Methods Revised Edition P. B. Patil U. P. Verma Alpha Science International Ltd. Oxford, U.K. CONTENTS Preface List ofprograms v vii 1. NUMER1CAL METHOD, ERROR AND ALGORITHM 1 1.1

More information

x x2 2 + x3 3 x4 3. Use the divided-difference method to find a polynomial of least degree that fits the values shown: (b)

x x2 2 + x3 3 x4 3. Use the divided-difference method to find a polynomial of least degree that fits the values shown: (b) Numerical Methods - PROBLEMS. The Taylor series, about the origin, for log( + x) is x x2 2 + x3 3 x4 4 + Find an upper bound on the magnitude of the truncation error on the interval x.5 when log( + x)

More information

Regent College Maths Department. Further Pure 1 Numerical Solutions of Equations

Regent College Maths Department. Further Pure 1 Numerical Solutions of Equations Regent College Maths Department Further Pure 1 Numerical Solutions of Equations Further Pure 1 Numerical Solutions of Equations You should: Be able use interval bisection, linear interpolation and the

More information

Numerical Methods. Scientists. Engineers

Numerical Methods. Scientists. Engineers Third Edition Numerical Methods for Scientists and Engineers K. Sankara Rao Numerical Methods for Scientists and Engineers Numerical Methods for Scientists and Engineers Third Edition K. SANKARA RAO Formerly,

More information

MA1023-Methods of Mathematics-15S2 Tutorial 1

MA1023-Methods of Mathematics-15S2 Tutorial 1 Tutorial 1 the week starting from 19/09/2016. Q1. Consider the function = 1. Write down the nth degree Taylor Polynomial near > 0. 2. Show that the remainder satisfies, < if > > 0 if > > 0 3. Show that

More information

Do not turn over until you are told to do so by the Invigilator.

Do not turn over until you are told to do so by the Invigilator. UNIVERSITY OF EAST ANGLIA School of Mathematics Main Series UG Examination 216 17 INTRODUCTION TO NUMERICAL ANALYSIS MTHE612B Time allowed: 3 Hours Attempt QUESTIONS 1 and 2, and THREE other questions.

More information

Preface. 2 Linear Equations and Eigenvalue Problem 22

Preface. 2 Linear Equations and Eigenvalue Problem 22 Contents Preface xv 1 Errors in Computation 1 1.1 Introduction 1 1.2 Floating Point Representation of Number 1 1.3 Binary Numbers 2 1.3.1 Binary number representation in computer 3 1.4 Significant Digits

More information

Name of the Student: Unit I (Solution of Equations and Eigenvalue Problems)

Name of the Student: Unit I (Solution of Equations and Eigenvalue Problems) Engineering Mathematics 8 SUBJECT NAME : Numerical Methods SUBJECT CODE : MA6459 MATERIAL NAME : University Questions REGULATION : R3 UPDATED ON : November 7 (Upto N/D 7 Q.P) (Scan the above Q.R code for

More information

MEI STRUCTURED MATHEMATICS 4777

MEI STRUCTURED MATHEMATICS 4777 OXFORD CAMBRIDGE AND RSA EXAMINATIONS Advanced Subsidiary General Certificate of Education Advanced General Certificate of Education MEI STRUCTURED MATHEMATICS Numerical Computation Wednesday 21 JUNE 2006

More information

KINGS COLLEGE OF ENGINEERING DEPARTMENT OF MATHEMATICS ACADEMIC YEAR / EVEN SEMESTER QUESTION BANK

KINGS COLLEGE OF ENGINEERING DEPARTMENT OF MATHEMATICS ACADEMIC YEAR / EVEN SEMESTER QUESTION BANK KINGS COLLEGE OF ENGINEERING MA5-NUMERICAL METHODS DEPARTMENT OF MATHEMATICS ACADEMIC YEAR 00-0 / EVEN SEMESTER QUESTION BANK SUBJECT NAME: NUMERICAL METHODS YEAR/SEM: II / IV UNIT - I SOLUTION OF EQUATIONS

More information

(f(x) P 3 (x)) dx. (a) The Lagrange formula for the error is given by

(f(x) P 3 (x)) dx. (a) The Lagrange formula for the error is given by 1. QUESTION (a) Given a nth degree Taylor polynomial P n (x) of a function f(x), expanded about x = x 0, write down the Lagrange formula for the truncation error, carefully defining all its elements. How

More information

Page No.1. MTH603-Numerical Analysis_ Muhammad Ishfaq

Page No.1. MTH603-Numerical Analysis_ Muhammad Ishfaq Page No.1 File Version v1.5.3 Update: (Dated: 3-May-011) This version of file contains: Content of the Course (Done) FAQ updated version.(these must be read once because some very basic definition and

More information

BACHELOR'S DEGREE PROGRAMME (BDP) Term-End Examination June, 2017

BACHELOR'S DEGREE PROGRAMME (BDP) Term-End Examination June, 2017 No. of Printed Pages : 8 MTE-10 BACHELOR'S DEGREE PROGRAMME (BDP) Term-End Examination June, 2017 1 E- 27D ELECTIVE COURSE : MATHEMATICS MTE-10 : NUMERICAL ANALYSIS Time : 2 hours Maximum Marks : 50 (Weightage

More information

Applied Numerical Analysis

Applied Numerical Analysis Applied Numerical Analysis Using MATLAB Second Edition Laurene V. Fausett Texas A&M University-Commerce PEARSON Prentice Hall Upper Saddle River, NJ 07458 Contents Preface xi 1 Foundations 1 1.1 Introductory

More information

USHA RAMA COLLEGE OF ENGINEERING & TECHNOLOGY

USHA RAMA COLLEGE OF ENGINEERING & TECHNOLOGY Code No: R007/R0 Set No. I B.Tech I Semester Supplementary Examinations, Feb/Mar 04 MATHEMATICAL METHODS ( Common to Civil Engineering, Electrical & Electronics Engineering, Computer Science & Engineering,

More information

Numerical Methods for Engineers. and Scientists. Applications using MATLAB. An Introduction with. Vish- Subramaniam. Third Edition. Amos Gilat.

Numerical Methods for Engineers. and Scientists. Applications using MATLAB. An Introduction with. Vish- Subramaniam. Third Edition. Amos Gilat. Numerical Methods for Engineers An Introduction with and Scientists Applications using MATLAB Third Edition Amos Gilat Vish- Subramaniam Department of Mechanical Engineering The Ohio State University Wiley

More information

Numerical and Statistical Methods

Numerical and Statistical Methods F.Y. B.Sc.(IT) : Sem. II Numerical and Statistical Methods Time : ½ Hrs.] Prelim Question Paper Solution [Marks : 75 Q. Attempt any THREE of the following : [5] Q.(a) What is a mathematical model? With

More information

Assignment for M.Sc. (Maths) Part I (Sem. - II) Distance Mode.

Assignment for M.Sc. (Maths) Part I (Sem. - II) Distance Mode. Assignment for M.Sc. (Maths) Part I (Sem. - II) Distance Mode. Last Date for Assignment Submission: - 10 th October, 2016 16 th Mar. 2016 These assignments are to be submitted only by those students who

More information

SBAME CALCULUS OF FINITE DIFFERENCES AND NUMERICAL ANLAYSIS-I Units : I-V

SBAME CALCULUS OF FINITE DIFFERENCES AND NUMERICAL ANLAYSIS-I Units : I-V SBAME CALCULUS OF FINITE DIFFERENCES AND NUMERICAL ANLAYSIS-I Units : I-V Unit I-Syllabus Solutions of Algebraic and Transcendental equations, Bisection method, Iteration Method, Regula Falsi method, Newton

More information

MATHEMATICAL METHODS INTERPOLATION

MATHEMATICAL METHODS INTERPOLATION MATHEMATICAL METHODS INTERPOLATION I YEAR BTech By Mr Y Prabhaker Reddy Asst Professor of Mathematics Guru Nanak Engineering College Ibrahimpatnam, Hyderabad SYLLABUS OF MATHEMATICAL METHODS (as per JNTU

More information

Numerical and Statistical Methods

Numerical and Statistical Methods F.Y. B.Sc.(IT) : Sem. II Numerical and Statistical Methods Time : ½ Hrs.] Prelim Question Paper Solution [Marks : 75 Q. Attempt any THREE of the following : [5] Q.(a) What is a mathematical model? With

More information

Exact and Approximate Numbers:

Exact and Approximate Numbers: Eact and Approimate Numbers: The numbers that arise in technical applications are better described as eact numbers because there is not the sort of uncertainty in their values that was described above.

More information

Numerical Analysis. Introduction to. Rostam K. Saeed Karwan H.F. Jwamer Faraidun K. Hamasalh

Numerical Analysis. Introduction to. Rostam K. Saeed Karwan H.F. Jwamer Faraidun K. Hamasalh Iraq Kurdistan Region Ministry of Higher Education and Scientific Research University of Sulaimani Faculty of Science and Science Education School of Science Education-Mathematics Department Introduction

More information

INSTITUTE OF AERONAUTICAL ENGINEERING Dundigal, Hyderabad MECHANICAL ENGINEERING TUTORIAL QUESTION BANK

INSTITUTE OF AERONAUTICAL ENGINEERING Dundigal, Hyderabad MECHANICAL ENGINEERING TUTORIAL QUESTION BANK Course Name Course Code Class Branch INSTITUTE OF AERONAUTICAL ENGINEERING Dundigal, Hyderabad - 500 043 Mathematics-II A30006 II-I B. Tech Freshman Engineering Year 016 017 Course Faculty MECHANICAL ENGINEERING

More information

Mathematical Methods for Numerical Analysis and Optimization

Mathematical Methods for Numerical Analysis and Optimization Biyani's Think Tank Concept based notes Mathematical Methods for Numerical Analysis and Optimization (MCA) Varsha Gupta Poonam Fatehpuria M.Sc. (Maths) Lecturer Deptt. of Information Technology Biyani

More information

MTE-10 BACHELOR'S DEGREE PROGRAMME (BDP)

MTE-10 BACHELOR'S DEGREE PROGRAMME (BDP) CO No. of Printed Pages : 8 MTE-0 BACHELOR'S DEGREE PROGRAMME (BDP) CO Term-End Examination CV CD December, 0 ELECTIVE COURSE : MATHEMATICS MTE-0 : NUMERICAL ANALYSIS Time : hours Maximum Marks : 50 (Weightage

More information

CS 323: Numerical Analysis and Computing

CS 323: Numerical Analysis and Computing CS 323: Numerical Analysis and Computing MIDTERM #2 Instructions: This is an open notes exam, i.e., you are allowed to consult any textbook, your class notes, homeworks, or any of the handouts from us.

More information

The iteration formula for to find the root of the equation

The iteration formula for to find the root of the equation SRI RAMAKRISHNA INSTITUTE OF TECHNOLOGY, COIMBATORE- 10 DEPARTMENT OF SCIENCE AND HUMANITIES SUBJECT: NUMERICAL METHODS & LINEAR PROGRAMMING UNIT II SOLUTIONS OF EQUATION 1. If is continuous in then under

More information

Numerical Analysis & Computer Programming

Numerical Analysis & Computer Programming ++++++++++ Numerical Analysis & Computer Programming Previous year Questions from 07 to 99 Ramanasri Institute W E B S I T E : M A T H E M A T I C S O P T I O N A L. C O M C O N T A C T : 8 7 5 0 7 0 6

More information

Numerical Methods. King Saud University

Numerical Methods. King Saud University Numerical Methods King Saud University Aims In this lecture, we will... find the approximate solutions of derivative (first- and second-order) and antiderivative (definite integral only). Numerical Differentiation

More information

BACHELOR'S DEGREE PROGRAMME (BDP) Term-End Examination December, Time : 2 hours Maximum Marks : 50 (Weightage : 70%)

BACHELOR'S DEGREE PROGRAMME (BDP) Term-End Examination December, Time : 2 hours Maximum Marks : 50 (Weightage : 70%) 01287 No. of Printed Pages : 12 MTE-10 BACHELOR'S DEGREE PROGRAMME (BDP) Term-End Examination December, 2014 ELECTIVE COURSE : MATHEMATICS MTE-10 : NUMERICAL ANALYSIS Time : 2 hours Maximum Marks : 50

More information

Introduction to Numerical Analysis

Introduction to Numerical Analysis Introduction to Numerical Analysis S. Baskar and S. Sivaji Ganesh Department of Mathematics Indian Institute of Technology Bombay Powai, Mumbai 400 076. Introduction to Numerical Analysis Lecture Notes

More information

MATHEMATICS. Course Syllabus. Section A: Linear Algebra. Subject Code: MA. Course Structure. Ordinary Differential Equations

MATHEMATICS. Course Syllabus. Section A: Linear Algebra. Subject Code: MA. Course Structure. Ordinary Differential Equations MATHEMATICS Subject Code: MA Course Structure Sections/Units Section A Section B Section C Linear Algebra Complex Analysis Real Analysis Topics Section D Section E Section F Section G Section H Section

More information

INSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous) Dundigal, Hyderabad

INSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous) Dundigal, Hyderabad 1 P a g e INSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous) Dundigal, Hyderabad - 500 04 Name : Mathematics-II Code : A0006 Class : II B. Tech I Semester Branch : CIVIL Year : 016 017 FRESHMAN ENGINEERING

More information

you expect to encounter difficulties when trying to solve A x = b? 4. A composite quadrature rule has error associated with it in the following form

you expect to encounter difficulties when trying to solve A x = b? 4. A composite quadrature rule has error associated with it in the following form Qualifying exam for numerical analysis (Spring 2017) Show your work for full credit. If you are unable to solve some part, attempt the subsequent parts. 1. Consider the following finite difference: f (0)

More information

UNIT - 2 Unit-02/Lecture-01

UNIT - 2 Unit-02/Lecture-01 UNIT - 2 Unit-02/Lecture-01 Solution of algebraic & transcendental equations by regula falsi method Unit-02/Lecture-01 [RGPV DEC(2013)] [7] Unit-02/Lecture-01 [RGPV JUNE(2014)] [7] Unit-02/Lecture-01 S.NO

More information

INSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous) Dundigal, Hyderabad

INSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous) Dundigal, Hyderabad Course Title Course Code INSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous) Dundigal, Hyderabad - 500 043 CIVIL ENGINEERING COURSE DESCRIPTION MATHEMATICS-II A30006 Course Structure Lectures Tutorials

More information

Question Bank (I scheme )

Question Bank (I scheme ) Question Bank (I scheme ) Name of subject: Applied Mathematics Subject code: 22206/22224/22210/22201 Course : CH/CM/CE/EJ/IF/EE/ME Semester: II UNIT-3 (CO3) Unit Test : II (APPLICATION OF INTEGRATION)

More information

NUMERICAL METHODS FOR ENGINEERING APPLICATION

NUMERICAL METHODS FOR ENGINEERING APPLICATION NUMERICAL METHODS FOR ENGINEERING APPLICATION Second Edition JOEL H. FERZIGER A Wiley-Interscience Publication JOHN WILEY & SONS, INC. New York / Chichester / Weinheim / Brisbane / Singapore / Toronto

More information

1. to apply Simpson s 1/3 rule, the number of intervals in the following must be Answer: (select your correct answer)

1. to apply Simpson s 1/3 rule, the number of intervals in the following must be Answer: (select your correct answer) 1. to apply Simpson s 1/3 rule, the number of intervals in the following must be Answer: (select your correct answer) 6 7 9 11 2. In integrating by dividing the interval into eight equal parts, width of

More information

F I F T H E D I T I O N. Introductory Methods of Numerical Analysis. S.S. Sastry

F I F T H E D I T I O N. Introductory Methods of Numerical Analysis. S.S. Sastry F I F T H E D I T I O N Introductory Methods of Numerical Analysis S.S. Sastry Introductory Methods of Numerical Analysis Introductory Methods of Numerical Analysis Fifth Edition S.S. SASTRY Formerly,

More information

AIMS Exercise Set # 1

AIMS Exercise Set # 1 AIMS Exercise Set #. Determine the form of the single precision floating point arithmetic used in the computers at AIMS. What is the largest number that can be accurately represented? What is the smallest

More information

MATHEMATICS (MEI) 4776 Numerical Methods

MATHEMATICS (MEI) 4776 Numerical Methods ADVANCED SUBSIDIARY GCE MATHEMATICS (MEI) 4776 Numerical Methods * OCE / V 0 221 5 * Candidates answer on the Answer Booklet OCR Supplied Materials: 8 page Answer Booklet Graph paper MEI Examination Formulae

More information

STATISTICS AND NUMERICAL METHODS

STATISTICS AND NUMERICAL METHODS STATISTICS AND NUMERICAL METHODS Question IV November / December 2011 Part-A 1. The heights of college students in Chennai are normally distributed with standard deviation 6 cm and sample of 100 students

More information

Numerical Analysis Preliminary Exam 10 am to 1 pm, August 20, 2018

Numerical Analysis Preliminary Exam 10 am to 1 pm, August 20, 2018 Numerical Analysis Preliminary Exam 1 am to 1 pm, August 2, 218 Instructions. You have three hours to complete this exam. Submit solutions to four (and no more) of the following six problems. Please start

More information

COURSE CONTRACT Course Name

COURSE CONTRACT Course Name COURSE CONTRACT Course Name Numerical Methods Course Code KPL Semester Odd /4 Days/ hours Tuesday/ 7.-. Place F8 Course Status compulsory Course Prerequisites. Calculus I. Calculus II. Linear Algebra 4.

More information

Lecture 44. Better and successive approximations x2, x3,, xn to the root are obtained from

Lecture 44. Better and successive approximations x2, x3,, xn to the root are obtained from Lecture 44 Solution of Non-Linear Equations Regula-Falsi Method Method of iteration Newton - Raphson Method Muller s Method Graeffe s Root Squaring Method Newton -Raphson Method An approximation to the

More information

MTH603 FAQ + Short Questions Answers.

MTH603 FAQ + Short Questions Answers. Absolute Error : Accuracy : The absolute error is used to denote the actual value of a quantity less it s rounded value if x and x* are respectively the rounded and actual values of a quantity, then absolute

More information

BACHELOR'S DEGREE PROGRAMME (BDP) Term-End Examination December, 2012 ELECTIVE COURSE : MATHEMATICS MTE-10 : NUMERICAL ANALYSIS

BACHELOR'S DEGREE PROGRAMME (BDP) Term-End Examination December, 2012 ELECTIVE COURSE : MATHEMATICS MTE-10 : NUMERICAL ANALYSIS No. of Printed Pages : 11 MTE-10 L. BACHELOR'S DEGREE PROGRAMME (BDP) Term-End Examination December, 2012 ELECTIVE COURSE : MATHEMATICS MTE-10 : NUMERICAL ANALYSIS Time : 2 hours Maximum Marks : 50 (Weightage

More information

Engineering. Mathematics. GATE 2019 and ESE 2019 Prelims. For. Comprehensive Theory with Solved Examples

Engineering. Mathematics. GATE 2019 and ESE 2019 Prelims. For. Comprehensive Theory with Solved Examples Thoroughly Revised and Updated Engineering Mathematics For GATE 2019 and ESE 2019 Prelims Comprehensive Theory with Solved Examples Including Previous Solved Questions of GATE (2003-2018) and ESE-Prelims

More information

Midterm for Introduction to Numerical Analysis I, AMSC/CMSC 466, on 10/29/2015

Midterm for Introduction to Numerical Analysis I, AMSC/CMSC 466, on 10/29/2015 Midterm for Introduction to Numerical Analysis I, AMSC/CMSC 466, on 10/29/2015 The test lasts 1 hour and 15 minutes. No documents are allowed. The use of a calculator, cell phone or other equivalent electronic

More information

Numerical Analysis Comprehensive Exam Questions

Numerical Analysis Comprehensive Exam Questions Numerical Analysis Comprehensive Exam Questions 1. Let f(x) = (x α) m g(x) where m is an integer and g(x) C (R), g(α). Write down the Newton s method for finding the root α of f(x), and study the order

More information

Elementary Numerical Mathematics

Elementary Numerical Mathematics Lecture on Elementary Numerical Mathematics Winter Term 2017/18 Prof. Dr. Gerhard Wellein Department for Computer Science HPC Services, Regionales Rechenzentrum Erlangen (RRZE) Organization Lecture (4

More information

NUMERICAL ANALYSIS WEEKLY OVERVIEW

NUMERICAL ANALYSIS WEEKLY OVERVIEW NUMERICAL ANALYSIS WEEKLY OVERVIEW M. AUTH 1. Monday 28 August Students are encouraged to download Anaconda Python. Anaconda is a version of Python that comes with some numerical packages (numpy and matplotlib)

More information

Fundamental Numerical Methods for Electrical Engineering

Fundamental Numerical Methods for Electrical Engineering Stanislaw Rosloniec Fundamental Numerical Methods for Electrical Engineering 4y Springei Contents Introduction xi 1 Methods for Numerical Solution of Linear Equations 1 1.1 Direct Methods 5 1.1.1 The Gauss

More information

Department of Mathematics California State University, Los Angeles Master s Degree Comprehensive Examination in. NUMERICAL ANALYSIS Spring 2015

Department of Mathematics California State University, Los Angeles Master s Degree Comprehensive Examination in. NUMERICAL ANALYSIS Spring 2015 Department of Mathematics California State University, Los Angeles Master s Degree Comprehensive Examination in NUMERICAL ANALYSIS Spring 2015 Instructions: Do exactly two problems from Part A AND two

More information

Numerical methods. Examples with solution

Numerical methods. Examples with solution Numerical methods Examples with solution CONTENTS Contents. Nonlinear Equations 3 The bisection method............................ 4 Newton s method.............................. 8. Linear Systems LU-factorization..............................

More information

6.3 METHODS FOR ADVANCED MATHEMATICS, C3 (4753) A2

6.3 METHODS FOR ADVANCED MATHEMATICS, C3 (4753) A2 6.3 METHODS FOR ADVANCED MATHEMATICS, C3 (4753) A2 Objectives To build on and develop the techniques students have learnt at AS Level, with particular emphasis on the calculus. Assessment Examination (72

More information

CS 323: Numerical Analysis and Computing

CS 323: Numerical Analysis and Computing CS 323: Numerical Analysis and Computing MIDTERM #2 Instructions: This is an open notes exam, i.e., you are allowed to consult any textbook, your class notes, homeworks, or any of the handouts from us.

More information

NUMERICAL METHODS USING MATLAB

NUMERICAL METHODS USING MATLAB NUMERICAL METHODS USING MATLAB Dr John Penny George Lindfield Department of Mechanical Engineering, Aston University ELLIS HORWOOD NEW YORK LONDON TORONTO SYDNEY TOKYO SINGAPORE Preface 1 An introduction

More information

DEPARTMENT OF MANAGEMENT AND ECONOMICS Royal Military College of Canada. ECE Modelling in Economics Instructor: Lenin Arango-Castillo

DEPARTMENT OF MANAGEMENT AND ECONOMICS Royal Military College of Canada. ECE Modelling in Economics Instructor: Lenin Arango-Castillo Page 1 of 5 DEPARTMENT OF MANAGEMENT AND ECONOMICS Royal Military College of Canada ECE 256 - Modelling in Economics Instructor: Lenin Arango-Castillo Final Examination 13:00-16:00, December 11, 2017 INSTRUCTIONS

More information

Two hours. To be provided by Examinations Office: Mathematical Formula Tables. THE UNIVERSITY OF MANCHESTER. 29 May :45 11:45

Two hours. To be provided by Examinations Office: Mathematical Formula Tables. THE UNIVERSITY OF MANCHESTER. 29 May :45 11:45 Two hours MATH20602 To be provided by Examinations Office: Mathematical Formula Tables. THE UNIVERSITY OF MANCHESTER NUMERICAL ANALYSIS 1 29 May 2015 9:45 11:45 Answer THREE of the FOUR questions. If more

More information

Lösning: Tenta Numerical Analysis för D, L. FMN011,

Lösning: Tenta Numerical Analysis för D, L. FMN011, Lösning: Tenta Numerical Analysis för D, L. FMN011, 090527 This exam starts at 8:00 and ends at 12:00. To get a passing grade for the course you need 35 points in this exam and an accumulated total (this

More information

Page 1 / 5 =. %. Material 2 %

Page 1 / 5 =. %. Material 2 % Page 1 / 5 FACULTY OF ENGINEERING/EUROPEAN UNIVERSITY OF LEFKE MATH 224 (MATH 208/302/305) ENGINEERING MATHEMATICS (NUMERICAL METHODS) SPRING 14-15 GRADUATION MAKEUP EXAM Date/Time/Place: 24. 06. 2015/09:00-11:00/AS2XX

More information

BASIC EXAM ADVANCED CALCULUS/LINEAR ALGEBRA

BASIC EXAM ADVANCED CALCULUS/LINEAR ALGEBRA 1 BASIC EXAM ADVANCED CALCULUS/LINEAR ALGEBRA This part of the Basic Exam covers topics at the undergraduate level, most of which might be encountered in courses here such as Math 233, 235, 425, 523, 545.

More information

Exam 2. Average: 85.6 Median: 87.0 Maximum: Minimum: 55.0 Standard Deviation: Numerical Methods Fall 2011 Lecture 20

Exam 2. Average: 85.6 Median: 87.0 Maximum: Minimum: 55.0 Standard Deviation: Numerical Methods Fall 2011 Lecture 20 Exam 2 Average: 85.6 Median: 87.0 Maximum: 100.0 Minimum: 55.0 Standard Deviation: 10.42 Fall 2011 1 Today s class Multiple Variable Linear Regression Polynomial Interpolation Lagrange Interpolation Newton

More information

Numerical Methods for Engineers

Numerical Methods for Engineers Numerical Methods for Engineers SEVENTH EDITION Steven C Chopra Berger Chair in Computing and Engineering Tufts University Raymond P. Canal Professor Emeritus of Civil Engineering of Michiaan University

More information

NAME: MA Sample Final Exam. Record all your answers on the answer sheet provided. The answer sheet is the only thing that will be graded.

NAME: MA Sample Final Exam. Record all your answers on the answer sheet provided. The answer sheet is the only thing that will be graded. NAME: MA 300 Sample Final Exam PUID: INSTRUCTIONS There are 5 problems on 4 pages. Record all your answers on the answer sheet provided. The answer sheet is the only thing that will be graded. No books

More information

Reduction to the associated homogeneous system via a particular solution

Reduction to the associated homogeneous system via a particular solution June PURDUE UNIVERSITY Study Guide for the Credit Exam in (MA 5) Linear Algebra This study guide describes briefly the course materials to be covered in MA 5. In order to be qualified for the credit, one

More information

BHARATHIAR UNIVERSITY, COIMBATORE. B.Sc. Mathematics CA (Revised papers with effect from onwards)

BHARATHIAR UNIVERSITY, COIMBATORE. B.Sc. Mathematics CA (Revised papers with effect from onwards) Page 1 of 7 SCAA Dt. 06-02-2014 BHARATHIAR UNIVERSITY, COIMBATORE. B.Sc. Mathematics CA (Revised papers with effect from 2014-15 onwards) Note : The revised syllabi for the following papers furnished below

More information

MecE 390 Final examination, Winter 2014

MecE 390 Final examination, Winter 2014 MecE 390 Final examination, Winter 2014 Directions: (i) a double-sided 8.5 11 formula sheet is permitted, (ii) no calculators are permitted, (iii) the exam is 80 minutes in duration; please turn your paper

More information