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2013/2014 ACADEMIC SESSION LECTURER-IN-CHARGE: PROF. B. A. OLUWADE CSC 403: NUMERICAL COMPUTATION II (with MATLAB) TUTORIAL QUESTIONS 1 (a) What do you understand by the Euler method ? (b) Let y/ = 3y + 1 y(0) = 2 be an initial value problem. Using Euler method‚ present an approximation of y(5) using a step size of 1. 2 (a) State Simpson’s rule. (b) Write MATLAB code for finding the numerical approximation of a definite integral using (a) above. 3 (a) Write the

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Numerical Methods Questions 1 f(x) = x3 – 2x – 5 a) Show that there is a root β of f(x) = 0 in the interval [2‚3]. The root β is to be estimated using the iterative formula ‚2 5 2 0 2 1 1 =         =++ x x x n n b) Calculate the values of x1‚ x2‚ x3‚ and x4‚ giving your answers to 4 sig fig. c) Prove that‚ to 5 significant figures‚ β is 2.0946 2 Use the iterative formula n n n cox x x − =+ 1 1 With x1 = 0.5 to find the limit of the sequence x1‚ x2‚ x3

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The Islamic University of Gaza Faculty of Engineering Civil Engineering Department Numerical Analysis ECIV 3306 Chapter 1 Mathematical Modeling 10:51:09 PM Part one : Approximation and Errors Specific Study Objectives • Recognize the difference between analytical and numerical solutions. • Recognize the distinction between truncation and round-off errors. • Understand the concepts of significant figures‚ accuracy‚ and precision. • Recognize the difference between true relative error

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CHENNAI INSTITUTE OF TECHNOLOGY Sarathy Nagar‚ Kundrathur‚ Pudupedu‚ Chennai– 600 069. Department of Mathematics Subject Name: Numerical Methods Subject Code: MA1251 Unit I 1) Write the Descartes rule of signs Sol: 1) An equation f ( x) = 0 cannot have more number of positive roots than there are changes of sign in the terms of the polynomial f ( x) . 2)An equation f ( x) = 0 cannot have more number of positive roots than there are changes of sign in the terms of the polynomial f

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Schrödinger’s equation by numerical integration Abstract The aim of this program is to solve Schrödinger’s equation via a numerical method and to compare our results with the analytical result. The harmonic oscillator potential was taken as the potential in the equation. This was used because the solutions to this one dimensional system are well known‚ and an analytic solution is relatively easy to program. The idea is that once we have verified that our numerical approach works for this

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TERM PAPER OF 5TH SEMESTER 2010 NUMERICAL ANALYSIS MTH204 TOPIC: Using trapezoidal rule and simpson’s rule‚ evaluate the integral [pic] DOA: DOS: 12th November‚ 2010 Submitted to:   Submitted by: Ms.Nitika Chugh                        Mr. William Anthony Deptt. Of Mathematics

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Problems on NUMBERS Q. 1 to Q. 10 Check the divisibility for the following numbers whether these are divisible by 2‚ 3‚ 4‚ 5‚ 6‚ 7‚ 8‚ 9‚ 11‚ and 12. Test for all Factors among the above mentioned numbers. 191 1221 11111 10101 512 3927 34632 4832718 583360 47900160 Q. 11. Simplify (46 + 18 * 6 + 4) / (12 * 12 + 8 *12) = ? Q. 12 On dividing a number by 999‚ the quotient is 366 and the remainder is 103. The number is Q. 13 Simplify (272 - 32)(124 + 176) / (17 * 15 - 15)

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Statistics Auburn University November 20‚ 2009 Yanzhao Cao Numerical SPDES November 20‚ 2009 1 / 35 Outline 1 Introduction Brownian sheet and elliptic SPDE Yanzhao Cao Numerical SPDES November 20‚ 2009 2 / 35 Outline 1 Introduction Brownian sheet and elliptic SPDE 2 SPDE with discretized white noise ˙ Discretization of white noise Wh Error estimate Yanzhao Cao Numerical SPDES November 20‚ 2009 2 / 35 Outline 1 Introduction

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NATIONAL UNIVERSITY OF SINGAPORE Department of Mathematics 2014/2015 MA2213 Numerical Analysis I Semester II Homework Assignment 2 Due: 3 March 2015‚ 5pm 1. Find an approximation to the root of f (x) = tan(x/4) − 1 in the interval [3.14‚ 3.15]‚ with the relative error |pn − p|/|p| accurate to within 10−4 using the Bisection method. Tabulate all your workings as in the answer to tutorial 2 question 2. Present all values of an ‚ bn and pn in full precision‚ and values of f (pn ) and the relative

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~~~~~~~~~~~~~~~~~~~~ www.MathWorks.ir ~~~~~~~~~~~~~~~~~~~~ An Introduction to Programming and Numerical Methods in MATLAB ~~~~~~~~~~~~~~~~~~~~ www.MathWorks.ir ~~~~~~~~~~~~~~~~~~~~ S.R. Otto and J.P. Denier An Introduction to Programming and Numerical Methods in MATLAB With 111 Figures ~~~~~~~~~~~~~~~~~~~~ www.MathWorks.ir ~~~~~~~~~~~~~~~~~~~~ S.R. Otto‚ BSc‚ PhD The R & A St Andrews Fife KY16 9JD Scotland J.P. Denier‚ BSc (Hons)‚ PhD School of Mathematical Sciences