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Showing 271 - 280 of 297 results for "The wave"
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https://sheffield.ac.uk/media/32006/download?attachmentWe will investigate the calculation of centre of mass through the following Tasks. ... b) Let ρ stand for the mass per unit area of the lamina. ... x=2x=0. ρxyδx. Write down the integral which follows as δx 0:. ... Assume that all the mass of...
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https://sheffield.ac.uk/media/32023/download?attachmentdy. dx= 2x. On integrating, we obtain the general solution. y = x2 C. ... b) Here the second condition is y(1) = 5 so at x = 1. ... Example 2Classify the differential equations specifying the order and type (linear/non-linear). ... Sketch the curves...
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https://sheffield.ac.uk/media/32029/download?attachmenta). Figure 13. The Laplace transform of the shifted function is easily obtained:. ... We can re-organise this integral by making the substitution x = t a. ... Now, using the first shift theorem. L1. {s 1. (s 1)2 1. }= ... estδ(t d) dt = esd. by the...
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https://sheffield.ac.uk/media/32067/download?attachmentThis vector fieldis the direction of the maximum rate of change of φ. ... contours). Figure 16: Grad φ and the steepest ascent direction for a hill. ... c) the derivative of φ at (2, 1,1) in the direction of. ... 2. Find the curl of each of the...
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https://sheffield.ac.uk/media/32084/download?attachmentPrerequisites. Before starting this Section you should. • review the preceding material in thisWorkbook. ... We use Euler’s method to predict and the trapezium method to correct. ... We now correct using. the trapezium method in the form. y1 =...
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https://sheffield.ac.uk/media/32073/download?attachment2x2 6x3 = 2. 11x3 = 11. Solution. The bottom equation implies that x3 = 1. ... 0 11 110 0 1. which is in the required upper triangular form. ... recall Gaussian elimination. • be able to find the inverse of a 2 2 matrix. ... and finally,...
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https://sheffield.ac.uk/media/32061/download?attachmentf(z) = 1 z z2 z3. The circle of convergence is |z| = 1. ... 2. where the coefficients an and bn (for each n) is given by. ... z. Task. Classify the singularities of the function f(z) =2. z 1. ... c) The contour C3 encloses both poles so thatC3. f(z)...
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https://sheffield.ac.uk/media/32090/download?attachmentThe angle, θ, made by r with thehorizontal is a function of time. ... We can consider four special values of θ and the associated valuesof r. ... d) What does this imply about the minimum value of the coefficient offriction? ... a) At what speed...
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https://sheffield.ac.uk/media/32089/download?attachmentWe wish to find the location at which it will splash into theriver. ... r(t) = y(t)j =1. 2gt2j, illustrated in the diagram below. j. ... Note that when integrating vector expressions the arbitrary constant is a constant vector. ... b) Find the...
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https://sheffield.ac.uk/media/32098/download?attachment37.3 The Poisson Distribution 37. 37.4 The Hypergeometric Distribution 53. Learning. ... p (n1! n2! nr!) = n! and so p is given by the formula. ... n(n 1)(n 2). (n r 1) which is the same asn! ... a) Find the probabilities that X takes the values 0,...