Numerical Methods for Engineers, Second edition: Chapter 1 Errata

Similar documents
Corrections and Minor Revisions of Mathematical Methods in the Physical Sciences, third edition, by Mary L. Boas (deceased)

6x 2 8x + 5 ) = 12x 8

Georgia Tech PHYS 6124 Mathematical Methods of Physics I

Solutionbank Edexcel AS and A Level Modular Mathematics

ERRATA MATHEMATICS FOR THE INTERNATIONAL STUDENT MATHEMATICS HL (CORE) (2nd edition)

CSL361 Problem set 4: Basic linear algebra

AIMS Exercise Set # 1


i x i y i

ENGINEERING MATH 1 Fall 2009 VECTOR SPACES

6x 2 8x + 5 ) = 12x 8. f (x) ) = d (12x 8) = 12

HOMEWORK PROBLEMS FROM STRANG S LINEAR ALGEBRA AND ITS APPLICATIONS (4TH EDITION)

Some Notes on Linear Algebra

Errata for Instructor s Solutions Manual for Gravity, An Introduction to Einstein s General Relativity 1st printing

Chapter 4. Higher-Order Differential Equations

Problem Max. Possible Points Total

OR MSc Maths Revision Course

Errata Instructor s Solutions Manual Introduction to Electrodynamics, 3rd ed Author: David Griffiths Date: September 1, 2004

Math 322. Spring 2015 Review Problems for Midterm 2

WRT in 2D: Poisson Example

Fall 2013 Hour Exam 2 11/08/13 Time Limit: 50 Minutes

Mathematics 1 Lecture Notes Chapter 1 Algebra Review

Linear Algebra I Lecture 8

Math 1060 Linear Algebra Homework Exercises 1 1. Find the complete solutions (if any!) to each of the following systems of simultaneous equations:

Matrix Arithmetic. a 11 a. A + B = + a m1 a mn. + b. a 11 + b 11 a 1n + b 1n = a m1. b m1 b mn. and scalar multiplication for matrices via.

Integration of Rational Functions by Partial Fractions

Electromagnetism HW 1 math review

Math Exam III - Spring

Iterative Methods for Ax=b

Chapter 1: Systems of Linear Equations and Matrices

Solutionbank Edexcel AS and A Level Modular Mathematics

Machine Learning Linear Models

Errata List Numerical Mathematics and Computing, 7th Edition Ward Cheney & David Kincaid Cengage Learning (c) March 2013

6.4 Krylov Subspaces and Conjugate Gradients

Deterministic Operations Research Errata. Updated: October 17, 2013

Integration of Rational Functions by Partial Fractions

CHAPTER 8: Matrices and Determinants

AP Calculus (BC) Chapter 9 Test No Calculator Section Name: Date: Period:

2011 Form B Solution. Jim Rahn

Tangent Planes, Linear Approximations and Differentiability

PHYS XXXX-L. Title (of Lab) Name (your name) Date of the lab (date performed) Dr. Thomas Eaves

Errata for SOLIDIFICATION (First Edition, 2009)

Quantum Mechanics: A Paradigms Approach David H. McIntyre. 27 July Corrections to the 1 st printing

Elementary Statistics for Geographers, 3 rd Edition

Applied Linear Algebra

3 a = 3 b c 2 = a 2 + b 2 = 2 2 = 4 c 2 = 3b 2 + b 2 = 4b 2 = 4 b 2 = 1 b = 1 a = 3b = 3. x 2 3 y2 1 = 1.

Singular Value Decompsition

Introduction Linear system Nonlinear equation Interpolation

Chapter 13: General Solutions to Homogeneous Linear Differential Equations

Exponential Family and Maximum Likelihood, Gaussian Mixture Models and the EM Algorithm. by Korbinian Schwinger

integration integration

Numerical Analysis Comprehensive Exam Questions

Errata and suggested changes for Understanding Advanced Statistical Methods, by Westfall and Henning

Mathematics 136 Calculus 2 Everything You Need Or Want To Know About Partial Fractions (and maybe more!) October 19 and 21, 2016

June 2011 PURDUE UNIVERSITY Study Guide for the Credit Exam in (MA 262) Linear Algebra and Differential Equations

Errata for Robot Vision

Jim Lambers MAT 419/519 Summer Session Lecture 13 Notes

Vector Calculus, Linear Algebra and Differential Forms: A Unified Approach 5th Edition

Math 308 Week 8 Solutions

Errata for the book A First Course in Numerical Methods, by Uri Ascher and Chen Greif

1.1 SOLUTIONS. Replace R2 by R2 + (2)R1 and obtain: 2. Scale R2 by 1/3: Replace R1 by R1 + ( 5)R2:

Coupled differential equations

ERRATA FOR. A First Course in Geometric Topology and Differential Geometry Ethan D. Bloch Birkhäuser, Last Updated August 20, 2005

M GENERAL MATHEMATICS -2- Dr. Tariq A. AlFadhel 1 Solution of the First Mid-Term Exam First semester H

Linear Algebra, 4th day, Thursday 7/1/04 REU Info:

Errata and Updates for ASM Exam MAS-I (First Edition) Sorted by Date

Errata and Updates for ASM Exam MAS-I (First Edition) Sorted by Page

Errata to Introduction to Lie Algebras

Math 1314 Week #14 Notes

Lecture 9 Approximations of Laplace s Equation, Finite Element Method. Mathématiques appliquées (MATH0504-1) B. Dewals, C.

M.SC. PHYSICS - II YEAR

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)

min 4x 1 5x 2 + 3x 3 s.t. x 1 + 2x 2 + x 3 = 10 x 1 x 2 6 x 1 + 3x 2 + x 3 14

Legendre s Equation. PHYS Southern Illinois University. October 13, 2016

Errata for Stochastic Calculus for Finance II Continuous-Time Models September 2006

Errata Dynamic General Equilibrium Modelling, Springer: Berlin August 2015

Lecture 10: Finite Differences for ODEs & Nonlinear Equations

LECTURE NOTES ELEMENTARY NUMERICAL METHODS. Eusebius Doedel

We could express the left side as a sum of vectors and obtain the Vector Form of a Linear System: a 12 a x n. a m2

Department of Applied Mathematics and Theoretical Physics. AMA 204 Numerical analysis. Exam Winter 2004

Systems of Linear ODEs

y = x 3 and y = 2x 2 x. 2x 2 x = x 3 x 3 2x 2 + x = 0 x(x 2 2x + 1) = 0 x(x 1) 2 = 0 x = 0 and x = (x 3 (2x 2 x)) dx

Linear Algebra Primer

Higher-order ordinary differential equations

Instructions: No books. No notes. Non-graphing calculators only. You are encouraged, although not required, to show your work.

1 Matrices and matrix algebra

CPE 310: Numerical Analysis for Engineers

Math 315: Linear Algebra Solutions to Assignment 7

CS100: DISCRETE STRUCTURES. Lecture 3 Matrices Ch 3 Pages:

1.8. Integration using Tables and CAS

1MA6 Partial Differentiation and Multiple Integrals: I

Here is an example of a block diagonal matrix with Jordan Blocks on the diagonal: J

18.02 Multivariable Calculus Fall 2007

12.0 Properties of orthogonal polynomials

Intersection of Ellipsoids

Engg. Math. II (Unit-IV) Numerical Analysis

MAC 2311 Calculus I Spring 2004

Fourth Order RK-Method

FP3 mark schemes from old P4, P5, P6 and FP1, FP2, FP3 papers (back to June 2002)

Problem 1 (Equations with the dependent variable missing) By means of the substitutions. v = dy dt, dv

Transcription:

Numerical Methods for Engineers, Second edition: Chapter 1 Errata 1. p.2 first line, remove the Free Software Foundation at 2. p.2 sixth line of the first proper paragraph, fe95.res should be replaced by nm95.res 3. p.10 third line should be multiplication

Numerical Methods for Engineers, Second edition: Chapter 2 Errata 1. p.26, the superscript in equation (2.22) should not be bold and should be as follows [U] = [D][U 1 ] 2. p.32, The matrix expression in Solution 2.5 has a u 22 and u 33 which should be l 22 and l 33 as follows 16 4 8 4 5 4 8 4 22 = l 11 0 0 l 21 l 22 0 l 31 l 32 l 33 l 11 l 21 l 31 0 l 22 l 32 0 0 l 33 3. On p.49 in the Jacobi iteration Solution 2.6, it should state x 1 x 2 x 3 2 = 0.1273 0.8364 0.4818 0.25 1.0 0.5 4. p.52, just below Table 2.3, remove a repeated than. (after many iterations) 5. p.54, The matrices on p.54 in Solution 2.7 should read 0.3636 in the (3,1) position and not 0.2626. 6. p.65, equation (2.65)(d) should read {r} k+1 = {r} k α k {u} k 7. p.81, Remove, between Kelley and 1995. 8. p.83 the vector of unknowns is missing from question 7. 9. p.83 the vector of unknowns is missing from question 8. 10. p.87, question 25, spelling of Exercises.

Numerical Methods for Engineers, Second edition: Chapter 3 Errata 1. p.96, Table near bottom of page. Entry 13.35 should be 13.28 and entry 8.41 should be 8.29. 2. pp.122-123, In two places it should be { f1 f 2 } = { e x 1 x 2 x 1 cosh x 2 + 3.5 } 3. p.123, Just above the start of Program 3.8 the Updated values should be x 1 = 2.4968 + 0.0002 = 2.4966 x 2 = 0.0819 0.0004 = 0.0823 etc. 4. p.130, top line, r = 10 (instead of r = 100)

Numerical Methods for Engineers, Second Edition: Chapter 4 Errata 1. p.144. The first equation in Solution 4.2 is missing a closing parenthesis after the matrix A. It should be [B] = [[A] p [I]] 1 2. p.145, just before Program 4.3 should state, and after many iterations {x} = { 1.0 1.0 } λ = 1.0000 The eigenvalue of [A] closest to 2 is then retrieved as 1 1 + 2 = 1 3. Strange line break at the top line of p.151. stiffness matrix should all be on second line. 4. Strange line break in the title of Section 4.4.1 on p.154. standard form should all be on second line of the title. 5. p.159, eq. (4.65), should be [P] instead of [P] T 6. p.160, third paragraph, comma should be at the end of the line (not the beginning) 7. p.188 For consistency with the text, question 6 should be:...can be reduced to the standard symmetrical form [ 0.4 0.2 0.2 2.6 ] { z1 z 2 } = λ { } z1 z 2

Numerical Methods for Engineers, Second edition: Chapter 5 Errata 1. On p. 219, last line of Section 5.4.2 should state Tables 5.2, 5.3 and 5.4 respectively. 2. p.230, Table 5.5, the penultimate row, third column should have X = x Y = ln y x 3. On p.239, question 7 the solutions should be, Answer: First order 0.4803, second order 0.4710, third order 0.4695, fourth order 0.4695. 4. On p.239, question 12 should say Rework Exercise 7... 5. On p.240, question 17, first Answer should be -0.971 6. On p.240, question 20, Answer should be f(x) = 15.35x 1.23 7. On p.241, question 21, should say...equation of the form y = ae bx to the data

Numerical Methods for Engineers, Second edition: Chapter 6 Errata 1. p.246, near the bottom of the page there is an unnecessary line break. It should read ; however rules will also be described... 2. p.252, Both of equations (6.15) and (6.16) are missing h from the weighting terms. They should be h F (x) dx 1 3 h F ( h) + 4 3 h F (0) + 1 h F (h) (6.15) 3 h x3 x 1 f(x) dx 1 3 h f(x 1) + 4 3 h f(x 2) + 1 3 h f(x 3) (6.16) 3. p.253, In equation (6.18), the closing parenthesis is missing on the xf(x 1 ) term on the right hand side. 4. p.272, The third line should be continuous with the second line and equation (6.53) should be b 1 f(x) dx g(ξ) dξ a 5. p.277, The term being integrated in equation (6.57) should be x 4 rather than x 2. 6. p.293, Just below section 6.6.1.1 there is an unnecessary line break. It should read...over the rectangular region... 7. p.294, Three lines from the bottom should state...in both (6.78) and (6.79) come from... 8. p.295, Solution 6.12 should be I 1 hk [f(1, 1) + f(2, 1) + f(1, 3) + f(2, 3)] 4 = 16.0000 (cf. exact solution 15.3333) 9. p.295, Solution 6.13 should state...so from equation (6.79) 10. p.297, Several problems with Solution 6.14. (i) it should state...so from equations (6.80) and (6.81). (ii) one of the sampling points should be y 2 = 0.2113, (iii) it should state Hence from equation (6.82), (iv) Working to 4 DP, solution should be 0.7779 rather than 0.7778 1

11. p.299, Solution 6.15 should state...so from equations (6.83) and (6.84) 12. p.300 One line below equation (6.89) should be This is analogous to equation (6.53)... 13. On p.308, question 3, the answer should be (e) 1.5454b 2 14. On p.308, question 6, the answer should be 10 repetitions 15. p.310, The second integral in question 18 should be labeled (b) 16. p.310, q12 has many errors. It should be as follows: 12. Use Polynomial Substitution to find the weighting coefficients w 1, w 2 and w 3, and the sampling points x 1, x 2, and x 3 in the Gauss- Legendre formula 1 1 f(x) dx = w 1 f(x 1 ) + w 2 f(x 2 ) + w 3 f(x 3 ) You may assume symmetry of weights and sampling points about the middle of the range. Answer: w 1 = w 3 = 5/9, w 2 = 8/9, x 1 = x 3 = 3/5, x 2 = 0 17. On p.310, question 13, the answer should be Answer: 19.1067 (Exact: 18.8496) 18. On p.311, question 24 should be, 0 1 2 0 e x sin y dx dy

Numerical Methods for Engineers, Second edition: Chapter 7 Errata 1. p.331, eq. (7.44) initial values of x should be included in all the terms, thus y(x 0 ) = A 1, dy dx (x 0) = A 2, d 2 y dx 2 (x 0) = A 3,, dn 1 y dx n 1 (x 0) = A n 2. On p.386, question 6 should state with θ = 0.5 3. On p.387, question 12 should state g = 9.81 m/s 2 4. On p.387, question 16 should state Answer: 0.9152 (Exact: 0.9152) 5. On p.388, question 18, first line of table should be 0.0 0.1000 6. On p.388, question 22, solution should be (b) 0.335 7. On p.389, question 27, solution should be (b) 0.0496 8. On p.391, question 35, should state (Exact: 4.8245)

Numerical Methods for Engineers, Second edition: Chapter 8 Errata 1. On p.407, Figure 8.6, the label in the middle of the figure should be h i,j (not u i,j ). 2. On p.435, question 3, should state Answer: T 3 = 85.71, T 2 = T 6 = 71.43, T 1 = T 5 = T 9 = 50, T 4 = T 8 = 28.57, T 7 = 14.29 3. On p.435, question 4, should state Answer: T 1 = 40.18, T 2 = 65.22, T 3 = 83.73, T 4 = 25.81, T 5 = 50.00, T 6 = 74.19, T 7 = 16.27, T 8 = 34.78, T 9 = 59.82 4. On p.436, question 5, solutions should be negative and state Answer: φ 1 = φ 3 = φ 7 = φ 9 = 5.5, φ 2 = φ 4 = φ 6 = φ 8 = 7, φ 5 = 9 5. On p.437, Figure 8.21, the dependent variable should be labelled as T (not φ) and the bottom right grid point should be labelled T = 10 o 6. On p.437, question 7, should state Answer: T 1 = T 3 = 76.12, T 2 = T 4 = 26.71, Q = 1.45 GJ 7. On p.438/489, question 9, solutions should be Answer: T = 60. Change in bc leads to a 2-d analysis where T = 63.33 8. On p.439, question 10, should state Answer: 49% 9. On p.440, question 13, the answers should be in upper case for consistency with Figure 8.24, hence Answer: Case 1: 3H i,j 2H i,j+1 H i+1,j = 0, Case 2: 5H i,j 2H i,j+1 2H i+1,j H i,j 1 = 0 10. On p.443, question 22, the first solution should be Answer: u(2, 20) = 38