Numerieke integratie Numerieke methoden voor het oplossen van integralen SADBT Stuivenberg Koninklijk Instituut voor de Marine 30-11-2008 Samenvatting Een integraal is behalve exact ook numeriek op te lossen. Daarvoor bestaan een aantal methoden zoals de Trapeziumregel en de Simpsonregel‚ die elk weer varianten kennen‚ de Matlab commando’s QUAD en QUADL en daarnaast kunnen ook eigen integratieregels ontworpen worden. De keuze voor een methode hangt af van de gewenste nauwkeurigheid van de
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000009|=0.000003 and the relative error is Error Analysis 1 REz z* z z 0.000003 0.000012 4 0.25 In the practice of numerical analysis it is important to be aware that computed solutions are not exact mathematical solutions. The precision of a numerical solution can be diminished in several subtle ways. Understanding these difficulties can often guide the practitioner in the proper implementation and/or development of numerical algorithms. Definition 1.1 Suppose x is an approximation
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Equations Reducible to Quadratic Equations Exercise 4.2 Solve the following equations: 1. x 4 − 6 x 2 + 8 = 0 Solution: x4 − 6 x2 + 8 = 0 Let y = x 2 and y 2 = x 4 The above equation becomes: y 2 − 6 y + 8 = 0 y2 − 6 y + 8 = 0 y2 − 4 y − 2 y + 8 = 0 y ( y − 4) − 2( y − 4) = 0 ( y − 2)( y − 4) = 0 y − 2 = 0 and y − 4 = 0 y=2 y=4 2 As‚ y = x x2 = 2 x2 = 4 x = ±2 x=± 2 solution set = { 2‚ − 2‚ 2‚ −2} 2. x −2 − 10 = 3 x−1 Solution: x −2 − 10 = 3 x −1 x −2 − 3 x −1 − 10 = 0 Let
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their rates of return on equity. Which of these two firms has the greater dividend yield? Explain. Use no numerical examples in your answer. 2. (10 marks) A public firm is considering a general cash offer of new common shares. Describe and explain how this firm’s “primary market” share price and its “secondary market” share price are related to one another. Explain. Use no numerical examples in your answer. 3. (10 marks) What are the primary factors that influence a firm’s rate of return
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Method Analysis Paper Option 6 The first five student learning outcomes listed on the syllabus focus on evaluating‚ understanding‚ and analyzing components of research‚ ranging from research ethics to research measurement. The methods analysis papers each serve to assist students in these five learning objectives. There are six method analysis papers in this class. You are only required to complete three of the method analysis papers. Should you choose to complete more than three of the six
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MATLAB Programs 1. Chapter No. Two Program 2.1 MATLAB m-file for the Bisection Method function sol=bisect(fn‚a‚b‚tol) f a = f eval(f n‚ a); f b = f eval(f n‚ b); if f a∗f b > 0; fprintf(’Endpoints have same sign’) return end while abs (b − a) > tol c = (a + b)/2; f c = f eval(f n‚ c); if f a ∗ f c < 0; b = c; else a = c; end end; sol=(a + b)/2; Program 2.2 MATLAB m-file for the Fixed-Point Method function sol=fixpt(fn‚x0‚tol) old= x0+1; while abs(x0-old) > tol; old=x0; x0 = f eval(f n‚ old);
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use systems analysis and design methodologies when building a system? Why not just build the system in whatever way seems to be “quick and easy?” What value is provided by using an “engineering” approach? Ans: While analyzing and designing a system‚ we take into consideration the flexibility‚ scalability‚ performance‚ maintainability and testability. When these capabilities are not taken into consideration‚ we see a high probability for system failure. Conversely‚ if too much of analysis and design
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PEST Analysis We are going to produce a PEST analysis to find out what external influences may be affecting the product (Milo) and to what extent to which customers decide to buy them. The purpose of the PEST analysis is to analyse the organization (Nestle Milo) operates and to identify how it may influence marketing decisions. A PEST analysis analyses the external environment in which an organization operates and identifies how it should influence marketing decisions. Political Factors The actions
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Numerical Simulation of Marangoni-Driven Boundary Layer Flow Over a Flat Plate with an Imposed Temperature Distribution Abstract: A numerical algorithm is presented for studying Marangoni convection flow over a flat plate with an imposed temperature distribution. Plate temperature varies with x in the following prescribed manner: where A and k are constants. By means of similarity transformation‚ the original nonlinear partial differential equations of flow are transformed to a pair of nonlinear
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ECSE 443- introduction to Numerical Methods in EE Practice Problem Set – Chapter 4 (Note: This problem set is for extra practice. It is not for credit‚ and not to be handed in) Question 1: Suppose that in a study‚ several measurements were made to determine a particular quantity for different values of . The collected data are summarized in the following table: 1.0000 5.8823 1.5000 2.0000 2.5000 3.0000 3.5000 4.0000 4.5000 5.0000 5.5000 6.0000 8.8823 17.8821 11.8822 14.8826 26.8825 24.8822
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