# Register now to access 7 million high quality study materials (What's Course Hero?) Course Hero is the premier provider of high quality online educational resources. With millions of study documents, online tutors, digital flashcards and free courseware, Course Hero is helping students learn more efficiently and effectively. Whether you're interested in exploring new subjects or mastering key topics for your next exam, Course Hero has the tools you need to achieve your goals.

7 Pages

### Chapter16

Course: EGM 3344, Spring 2012
School: University of Florida
Rating:

Word Count: 264

#### Document Preview

16.11 Problem Runge's function is written as f ( x) 1 1 25 x 2 Generate five equidistant points in the interval [1, 1] evaluate the function there and fit it using various options. First the data: &gt;&gt; x=linspace(1,1,5) x = 1.0000 0.5000 0 0.5000 1.0000 &gt;&gt; runge=@(x) 1./(1+25*x.^2) runge = @(x)1./(1+25*x.^2) &gt;&gt; y=runge(x) y =...

Register Now

#### Unformatted Document Excerpt

Coursehero >> Florida >> University of Florida >> EGM 3344

Course Hero has millions of student submitted documents similar to the one
below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.

Course Hero has millions of student submitted documents similar to the one below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.
16.11 Problem Runge's function is written as f ( x) 1 1 25 x 2 Generate five equidistant points in the interval [1, 1] evaluate the function there and fit it using various options. First the data: >> x=linspace(1,1,5) x = 1.0000 0.5000 0 0.5000 1.0000 >> runge=@(x) 1./(1+25*x.^2) runge = @(x)1./(1+25*x.^2) >> y=runge(x) y = 0.0385 0.1379 1.0000 0.1379 0.0385 Let us first use the crudest interpolation, which is to use the value of the nearest point >> xx=linspace(1,1); >> yy=runge(xx); >> yexact=runge(xx); >> yy=interp1(x,y,xx,'nearest'); >> plot(x,y,'o',xx,yy,xx,yexact,'') 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Next we will do linear interpolation, which is also linear spline, and the default method of interp1 >> ylin=interp1(x,y,xx); >> plot(x,y,'o',xx,ylin,xx,yexact,'') 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 we Next will fit it with a cubic spline. We can do that by choosing `spline' in the method in interp1, or with the spline function (which gives additional flexibility on end conditions) >> yspl=spline(x,y,xx); >> plot(x,y,'o',xx,yspl,xx,yexact,'') 1 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 We can reduce the oscillation by specifying zero slope end conditions >> yspl0=spline(x,[0 y 0],xx); >> plot(x,y,'o',xx,yspl0,xx,yexact,'') 1.2 1 0.8 0.6 0.4 0.2 0 -0.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Next we do Hermite (cubic interpolation) >> yher=interp1(x,y,xx,'cubic'); >> plot(x,y,'o',xx,yher,xx,yexact,'') 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Finally, we use polyfit to do a single quartic polynomial 1 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 yquart=polyval(p,xx); >> plot(x,y,'o',xx,yquart,xx,yexact,'')
Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more. Course Hero has millions of course specific materials providing students with the best way to expand their education.

Below is a small sample set of documents:

University of Florida - EGM - 3344
Part 4 Chapter 16Splines and Piecewise InterpolationPowerPoints organized by Dr. Michael R. Gustafson II, Duke UniversityAll images copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display.Chapter Objectives Understan
University of Florida - EGM - 3344
Problem 17.3. /2Given the integral (6 3cos x)dx (6 x 3sin x) |0 /20 3 3 12.4247 Evaluate it using 4 equally spaced points in the integration interval We first generate the data &gt; f=@(x) 6+3*cos(x) f = @(x)6+3*cos(x) &gt; x=linspace(0,pi/2,4) x = 0
University of Florida - EGM - 3344
Part 5 Chapter 17Numerical Integration FormulasPowerPoints organized by Dr. Michael R. Gustafson II, Duke UniversityAll images copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display.Chapter Objectives Recognizing th
University of Florida - EGM - 3344
GaussLegendre quadrature is used to calculate integrals 1 f ( x)dx c10f ( x0 ) c1 f ( x1 ) cn 1 f ( xn 1 ) The locations and weights for different values of n are given in Table 18.1 Integrals of the form f ( x)dx are transformed to the right l
University of Florida - EGM - 3344
Part 5 Chapter 18Numerical Integration of FunctionsPowerPoints organized by Dr. Michael R. Gustafson II, Duke UniversityAll images copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display.Chapter Objectives Understand
University of Florida - EGM - 3344
Problem 19.11 The following data was collected for the distance travelled versus time for a rocket: t, sec. y, km 0 0 25 32 50 58 75 78 100 92 125 100 Use numerical differentiation to calculate velocity and acceleration at each time. At time t=0, we can
University of Florida - EGM - 3344
Part 5 Chapter 19Numerical DifferentiationPowerPoints organized by Dr. Michael R. Gustafson II, Duke UniversityAll images copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display.Chapter Objectives Understanding the a
University of Florida - EGM - 3344
Consider the simple differential equation The solution is y e10ty ' 10 y y (0) 1 Consider now the solution of this equation with Euler's method. y (t t ) y(t ) y '(t )t y (t ) 10 y (t )t y (t )(1 10t ) If we take a large t the solution will be inac
University of Florida - EGM - 3344
Part 6 Chapter 20Initial-Value ProblemsPowerPoints organized by Dr. Michael R. Gustafson II, Duke UniversityAll images copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display.Chapter Objectives Understanding the mean
University of Florida - EGM - 3344
Part 6 Chapter 21Adaptive Methods and Stiff Systems S stemsPowerPoints organized by Dr. Michael R. Gustafson II, Duke UniversityAll images copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display.Chapter Objectives Un
University of Florida - EGM - 3344
To understand how the condition number of a matrix is related to inaccuracy consider the equations we had in Problem 9.3-1.1x1+10x2=120 -2x1+17.4x2=174For this right hand side the sensitivity of the solution to small changes in the right hand side was h
University of Florida - EAS - 4240c
AnalyticalExperimental y p Correlation for a Stiffened Composite Panel Loaded in Axial Compression Axial CompressionChristopher Thorn pIntroduction Panel Definition Linear Analysis NonLinear Analysis Results/ConclusionsPanel Definition Panel Definitio
University of Florida - EAS - 4240c
Basic concepts of genetic algorithmsKey elements Key elements Global optimization achieved by population of Global optimization achieved by population of designs that explore simultaneously different regions in design space. Discrete `genes' that allow
University of Florida - EAS - 4240c
Attracting Cracks for Arrestment in Bonelike CompositesJinhua Huang, Andrew J. Rapoff, Raphael T. HaftkaPresented By: Shahtaj Singh SandhuBackground : Imitation of nature to tackle failure due to cracks in composite. cracks in composite Crack causes fa
University of Florida - EAS - 4240c
Solving Integer Programming with Branch-and-Bound TechniqueThis is the divide and conquer method. We divide a large problem into a few smaller ones. (This is the &quot;branch&quot; part.) The conquering part is done by estimate how good a solution we can get for e
University of Florida - EAS - 4240c
Presentation by: Jason Cantrell EAS 6939 1/31/11RESIDUAL STRAIN MEASUREMENT IN COMPOSITES USING CURECURE REFERENCING METHODby: P.G Ifju, X. Niu, B.C Kilday, S.-C. Liu &amp; S.M. EttingerBackground gResidual stress results from thermal mismatch between fib
University of Florida - EAS - 4240c
Compressive strength of unidirectional composites: evaluation and comparison of prediction modelsN.K. Naik, Rajesh S. KumarEduardo Rondon EAS 6939Introduction Study of composites is a relatively new branch of Engineering Micromechanics dates back to t
University of Florida - EAS - 4240c
Topic of PaperEffect of Cryogenic Temperature on the Fracture Toughness of Graphite/Epoxy Composite (By B V Sankar and PG Ifju) B.V.Sankar P.G.Ifju) Presented by: Lokesh DahiyaKey Words in Paper Fracture Toughness Cryogenic Temperature DCB ( Double Can
University of Florida - EAS - 4240c
E1 E2 G12 nu12 t nu21 1.85E+07 1.89E+06 9.30E+05 3.00E01 5.00E03 0.030649 q11 q22 q12 q66 1.87E+07 1.91E+06 5.72E+05 9.30E+05 U1 U2 U3 U4 u5 5 8.33E+06 8.38E+06 1.96E+06 2.54E+06 2.89E+06 n0 12 n45 4 n90 1 nsym 21 h 0.21 Nx 10000 Nxy 3000V1* V3* 0.523809
University of Florida - EAS - 4240c
Microsoft Excel 12.0 Answer Report Worksheet: [ex4.2.5.xlsx]Sheet1 Report Created: 1/25/2011 4:54:02 PM Target Cell (Min) Cell Name \$E\$11 h Adjustable Cells Cell Name \$A\$11 n0 \$B\$11 n45_Original Value Final Value 0.03 0.2054383477Original Value Final Va
University of Florida - EAS - 4240c
Microsoft Excel 8.0 Answer Report Worksheet: [example7.2.1.xls]Sheet1 Report Created: 3/15/99 11:31:22 AM Target Cell (Min) Cell Name \$D\$5 t_tot Adjustable Cells Cell Name \$D\$1 n_0 \$D\$2 n_90 \$D\$3 n_45Original Value Final Value 80 44.96196627Original Val
University of Florida - EAS - 4240c
Flex Fatigue of Simple Composites Flex Fatigue of Simple CompositesDavid C. Timpe Jr. Arlon Sili l Silicone Technologies Division h l i i ii www.arlonstd.comPresented by: Thomas M. Reed Presented by: Thomas M. Reed March 14, 2011 EAS 6939ObjectiveMate
University of Florida - EAS - 4240c
Optimization Problem: Minimize f = x1+10x2 Such that, x1+2x27 2x1+x25 x1,x20 x1,x2 are integers The `ga' function in MATLAB is used to solve this optimization problem by creating an objective function as shown in the above optimization problem after using
University of Florida - EAS - 4240c
S.Nagendra, D.Jestin, Z.Gurdal, R.T.Haftka and L.T.WatsonComputers &amp; Structures, Vol. 58, No. 3, pp. 543-555, 1996.Presented by Vignesh Solai RameshbabuIntroductiongenetic algorithm. l h It consists of reproduction, crossover, mutation, permutation, p
University of Florida - EAS - 4240c
University of Florida - EAS - 4240c
Optimization with NonHomogeneous Failure C te a like o oge eous a u e Criteria e Tsai-Wu for Composite LaminatesPublished 2006 by Albert A. Groenwold and Raphael T. HaftkaKyle McDaniel y14 March 2011Optimization with Non-Homogeneous Failure Criteria (
University of Florida - EAS - 4240c
U1 7.64E+10 NxyU2 8.57E+10U3 1.97E+10U4U5 2.26E+10 2.69E+10h V1 V3 miki_in 3.00E+06 0.007907028 0.033036177 0.56118378 0.436633 a22s 6.81E+10 6.25E+10 nu1 5.00E+10 0.5 nu2 a12s 3.37E+10 a66s gamaxy 3.79E+10 0.01a11sE1t1 theta1 t2 theta2 0.5 0.5327
University of Florida - EAS - 4240c
Microsoft Excel 12.0 Answer Report Worksheet: [Book1]Sheet1 Report Created: 1/21/2011 5:43:43 PM Target Cell (Min) Cell Name \$B\$5 h Adjustable Cells Cell Name \$B\$5 h \$C\$5 V1_ \$D\$5 v3_ Constraints Cell Name \$E\$5 miki_in \$E\$8 gamaxy \$A\$11 E1 \$D\$5 v3_ \$C\$5 V
University of Florida - EAS - 4240c
J.Huang,R.T.HaftkaShreyas JoglekarAerospace Structural Compositesy p Symmetric composite p plate with central hole and loaded on opposite ends by uniformly distributed force p. Material:AS4/3501 EL= 138 GPa, ET= 8.96 Gpa GLT= 7.1 GPa, LT= 0.3 L=W=20 cm
University of Florida - EAS - 4240c
Comput. Methods Appl. Mech. Engrg. 186 (2000) 357372www.elsevier.com/locate/cmaPermutation genetic algorithm for stacking sequence design of composite laminatesBoyang Liu a, Raphael T. Haftka a,*, Mehmet A. Akgn a,1, Akira Todoroki b ua bDepartment o
University of Florida - EAS - 4240c
Microsoft Excel 12.0 Answer Report Worksheet: [ply-identity-vib.xlsx]Sheet1 Report Created: 4/8/2011 4:13:52 PM Target Cell (Max) Cell Name \$F\$16 alpha11 Adjustable Cells Cell Name \$A\$5 0 plies \$B\$5 90 plies \$C\$5 45 plies \$D\$5 m45 plies \$A\$6 0 plies \$B\$6
University of Florida - EAS - 4240c
Stiffness T il i for Improved C S iff Tailoring f I d Compressive i Strength of Composite Plates with HolesRaphael T. Haftka, James H. Starnes AIAA JournalAnirban ChaudhuriAerospace Structural CompositesPLATE WITH HOLESTwo ways to deal with minimizin
University of Florida - EAS - 4240c
PROJECT PHASE 1- Due 03/23 1HAVE TO SUBMIT A REPORT A cylindrical pressure vessel r = 2m, with p essu e a te pe atu e oa s pressure and temperature loads P = 1MPa T = -150 C Strains due to pressure x pr / 2t axial direction stress y pr / t hoop directio
University of Florida - EAS - 4240c
PROJECT PHASE 2- Due 04/18 2HAVE TO SUBMIT A REPORT Given A cylindrical pressure vessel, individual panel 30 x 20 cm simply supported cm, Radius 2m16 ply symmetric laminate (optional balanced) tply= 0.125 mm1Formulation of Step 1Maximize fundamental
University of Florida - EAS - 4240c
A Beam Theory for Laminated Composites and Application to Torsion ProblemsDr. Bhavani V. SankarPresented By:Sameer LuthraEAS 6939 Aerospace Structural Composites1Introduction Composite beams have become very common in applications p y pp like Auto
University of Florida - MAS - 4105
Answers for Practice Problem Set 2 1. (b) cfw_-1, X 2 + 2X (c) cfw_1 + X 2. (11, 2) 3. (b) rank(T )+nullity(T ) = n 4. (a) False: A = 1 0 0 -1(b) True (c) False, since (4, 2) = 2(2, 1) but (4, 3) = 2(1, 0) 1 0 2 5. (a) 0 0 0 0 1 -1 (b) cfw_1, X 2 (c) cf
University of Florida - MAS - 4105
Homework Set 6 for MAS 4105 Due Friday, February 24 1. Let T : V W be a linear transformation which is one-to-one, and let cfw_x1, . . . , xn be a linearly independent subset of V . Prove that cfw_T (x1), . . . , T (xn) is a linearly independent subset of
University of Florida - MAS - 4105
Homework Set 7 for MAS 4105 Due Wednesday, February 29 1. Let A and B be n n matrices such that AB is invertible. Prove that A and B are both invertible. 2. Give an example of matrices A and B such that AB is invertible but BA is not invertible. (Hint: Fi
University of Florida - MAS - 4105
Homework Set 8 for MAS 4105 Due Friday, March 16 1. Find the matrix which changes coordinates on V = P2 (R) from the basis B = cfw_2 + X, X + X 2 , 3 - X 2 to the basis B = cfw_2, -X 2, 3 + X. 2. Use elementary row operations to convert the matrix A = 0 2
University of Florida - MAS - 4105
Homework Set 9 for MAS 4105 Due Friday, March 23 1. Compute the inverse of A = 0 1 2 -1 3 2 0 1 1 M33(R).2. Let n &lt; m, let A Mmn(F ), and let B Mnm (F ). Prove that the m m matrix AB is not invertible. 3. Find a basis for the solution set of the fol
University of Florida - MAS - 4105
Homework Set 10 for MAS 4105 Due Friday, March 30 1. Let A be an n n matrix such that At = -A (we say that A is skew-symmetric). Prove that if n is odd then A is not invertible. ~ 2. Determine (with proof) a formula for det(A) in terms of det(An1), where
University of Florida - MAS - 4105
MAS 4105-Practice Problems for Exam #21. Define T : P2 (R) P2 (R) by T (f ) = (x + 1)f (x) - f (x). (a) Prove that T is a linear transformation. (b) Find a basis for R(T ). (c) Find a basis for N(T ). 2. (a) Let = cfw_1, x be a basis for P1 (R) and let =
University of Florida - STA - 3024
STA 3024Assignment 11. Suppose that, based on a random sample of 148 UF graduates with a certain major, a 95% confidence interval for the average starting salary (in thousands of dollars) for people with this major is (69.8, 74.8). True or false: We are
University of Florida - STA - 3024
STA 3024Assignment 2Suppose we want to investigate the gateway drug theory-the idea that marijuana use can lead to use of more serious drugs, such as cocaine and heroin. We distribute an anonymous questionnaire to a random sample of 188 high school stud
University of Florida - STA - 3024
STA 30241. Type or write neatly.Assignment Guidelines2. Brainstorm each question posed by the assignment, and do your exploratory work on scratch paper. Do not submit a rough draft of your solution. 3. Your final solutions should be presented in a sequ
University of Florida - STA - 3024
Useful FormulasExpected cell count = (Row total)(Column total) Total sample size (Observed count - Expected count)2 Expected countX2 = all cellsdf = (r - 1)(c - 1)Chi-Squared Tabledf 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 30 40 50 60 7
University of Florida - STA - 3024
STA 3024Exam 1 Sample Questions1. A researcher is conducting a chi-squared test with = 0.05 to see if happiness (not happy, pretty happy, or very happy) depends on level of income (low, medium, or high). She surveys a random sample of 2859 people, creat
University of Florida - STA - 3024
D B C B A A D B B E A B D A1 1. D&lt;br&gt; 2 2. B&lt;br&gt; 3 3. C&lt;br&gt; 4 4. B&lt;br&gt; 5 5. A&lt;br&gt; 6 6. A&lt;br&gt; 7 7. D&lt;br&gt; 8 8. B&lt;br&gt; 9 9. B&lt;br&gt; 10 10. E&lt;br&gt; 11 11. A&lt;br&gt; 12 12. B&lt;br&gt; 13 13. D&lt;br&gt; 14 14. A&lt;br&gt;
University of Florida - STA - 3024
Chapter 3 Contingency TablesMuch of what we'll do this semester can be condensed to a simple idea: examining whether a response variable depends on one or more explanatory variables, and if so, how. The procedures we'll use will depend on whether the var
University of Florida - STA - 3024
Chapter 4 Nonparametric MethodsFor the rest of the semester, we'll be discussing different ways to analyze data with a The methods you've seen before for dealing with a quantitative response variable have always assumed that the We'll make that same assu
University of Florida - STA - 3024
STA 3024 Section 7454Meeting Time and Location Course Website InstructorIntroduction to Statistics 2 Spring 2012MWF 3rd period (9:3510:25 a.m.) PUGH 170 http:/www.stat.ufl.edu/lmori80 Laura Mori Griffin-Floyd 116C lmori80@stat.ufl.edu Yeonhee Park Grif
University of Florida - MAC - 2312
MAC 2312 Homework 2 Selected Solutions4. Find a function f (x) satisfying f (x) = (1 + x)/(x - 1) for - &lt; x &lt; -1. Solution: In this problem, I wanted to be sure that in addition to knowing standard integration techniques, you were paying attention to eve
University of Florida - MAC - 2312
Name:Section:MAC 2312 Homework 3 Due March 13, 2012SHOW ALL OF YOUR WORK L18: The Integral Test for Series1. Use the integral test to determine whether the seriesne-nn=12converges. Be sure to verify all hypotheses of the integral test.12. Use th
University of Florida - MAC - 2312
Name:Section:MAC 2312 Homework 4 Due April 3, 2012SHOW ALL OF YOUR WORK L25-26: Representing Functions as Power Series1. Find a power series representation for the function f (x) = Include the interval of convergence. x . 4 + 9x212. Find a power ser
University of Florida - MAC - 2312
MAC 2312 Quiz 5 February 21, 2012SOLUTIONS1. Determine whether the sequence converges or diverges. If the sequence converges, compute its limit. n2 + 2n + 1 an = n = 1, 2, 3, 3n2 - 2 Solution: Use the related function f (x) = x2 + 2x + 1 . 3x2 - 2Notic
University of Florida - MAC - 2312
MAC 2312 Quiz 6 February 28, 2012SOLUTIONSx 1. Determine the nonzero values of x for which the series x2n -1 converges. n=1 Solution: First, observe that the numerator of the summand is independent of n, so n=15x5 1 = x5 . 2n - 1 2n - 1 x x n=1Theref
University of Florida - MAC - 2312
MAC 2312 Quiz 7 March 13, 2012SOLUTIONS1. Determine whether the series (-1)n (ln n)/n converges absolutely, converges n=1 conditionally or diverges. Solution: Set bn = (ln n)/n and an = (-1)n bn . Observe that bn 0 for all n = 1, 2, 3, . I claim that bn
University of Florida - AOE - 4643
AOM 4643 - INTRODUCTION Hydrologic science focuses on the global hydrologic cycle and the processes involved in the land phase of that cycle. It is the geoscience that describes and predicts: spatial and temporal distribution of water in the terrestrial,
University of Florida - AOE - 4643
AOM 4346 - BASIC HYDROLOGIC CONCEPTS As discussed last time - hydrologic cycle describes the continuous circulation of water from land and sea to the atmosphere and back again. The concept is based on mass balance and is simply that water changes state an
University of Florida - AOE - 4643
AOM 4932 - Earth's Energy Balance The hydrologic cycle is fueled by energy from the sun. Planetary geometry creates areas of energy surpluses and deficits which drive all active meteorological processes. These processes originate to redistribute energy th
University of Florida - AOE - 4643
qv90 N090 SRnlow 60 low N 0 90 moist. moist 30 60 90 S 30 high moist low intermed. temp. high temp temp high press anti cycloneAOM 4932 - Atmospheric Water and Precipitation Distribution of atmospheric moisture in space and time. In general: 1 - wat