All Matches

Solution Library

Expert Answer

Textbooks

Search Textbook questions, tutors and Books

Oops, something went wrong!

Change your search query and then try again

Result Not Found

Books FREE
Tutors
Study Help
Ask a Question

Search
Sign In
Register

study help
mathematics
advanced engineering mathematics

Questions and Answers of Advanced Engineering Mathematics

Find the isotherms for the square and grid in Prob. 13 if u = sin1/4 πx on the horizontal and -sin1/4πy on the vertical edges. Try to sketch some isotherms.Data from Prob. 13For the square 0 ≤ x
How many initial conditions did we prescribe for the wave equation? For the heat equation?
Solve (1)–(3) by Crank–Nicolson with r = 1 (5 steps), where:f(x) = 5x if 0 ≤ x < 0.25, f(x) = 1.25(1 - x) if 0.25 ≤ x ≤ 1, h = 0.2
Do 10 steps. Compare as indicated. Show details.y' = 1 + y2, y(0) = 0, h = 0.1
Solve the Laplace equation in the region and for the boundary values shown in Fig. 463, using the indicated grid. (The sloping portion of the boundary is y = 4.5 - x.) u=0- y 3 2 1 0 0 P₁ 12 P₁
How did we approximate the Laplace and Poisson equations?
For the square 0 ≤ x ≤ 4, 0 ≤ y ≤ 4 let the boundary temperatures be on the horizontal and 50°C on the vertical edges. Find the temperatures at the interior points of a square grid with h =
When and how did we use finite differences? Give as many details as you can remember without looking into the text.
Do 10 steps. Compare as indicated. Show details.y' = xy2 = 0, y(0) = 1, h = 0.1.Compare with Prob. 7. Apply the error estimate (10) to y10. Data from Prob. 7Do 10 steps. Solve exactly. Compute
Solve Prob. 9 by (9) with h = 0.2, 2 steps. Compare with exact values obtained from the series in (2 terms) with suitable coefficients.Data from Prob. 9Solve Prob. 8 with f(x) = x if 0 ≤ x ≤ 0.2,
Why did we have to treat the main types of PDEs in separate sections? Make a list of types of problems and numeric methods.
Find the potential in Fig. 457 using(a) The coarse grid.(b) The fine grid 5 × 3 and Gauss elimination. In (b), use symmetry; take u = 0 as boundary value at the two points at which the potential has
How do we extend Runge–Kutta to systems of ODEs?
Do 10 steps. Solve exactly. Compute the error. Show details.Do Prob. 7 using Euler’s method with h = 0.1 and compare the accuracy.Data from Prob. 7Do 10 steps. Solve exactly. Compute the error.
Solve by the classical RK.The system in Prob. 1Data from Prob. 1Solve by the Euler’s method. Graph the solution in the y1y2-plane. Calculate the errors.y'1 = 2y1 - 4y2, y'2 = y1 - 3y2, y1(0) = 3,
Solve Prob. 8 with f(x) = x if 0 ≤ x ≤ 0.2, f(x) = 0.25(1 - x) if 0.2 < x ≤ 1, the other data being as before.Data from Prob. 8In a laterally insulated bar of length 1 let the initial
Solve the initial value problem by Adams–Moulton (7a), (7b), 10 steps with 1 correction per step. Solve exactly and compute the error. Use RK where no starting values are giveny' = 3x2(1 + y), y(0)
What is automatic step size control? When is it needed? How is it done in practice?
For the grid in Fig. 456 compute the potential at the four internal points by Gauss and by 5 Gauss?Seidel steps with starting values 100, 100, 100, 100 (showing the details of your work) if the
Compute u in Prob. 5 for t = 0.1 and x = 0.1, 0.2, · · ·, 0.9, using the formula in Prob. 8, and compare the values.Data from Prob. 8Compute approximate values in Prob. 7, using a finer grid (h =
What is a predictor–corrector method? Give an important example.
Do 10 steps. Solve exactly. Compute the error. Show details.y' - xy2 = 0, y(0) = 1, h = 0.1
Solve by the classical RK.The ODE in Prob. 5. By what factor did the error decrease?Data from Prob. 5Solve by the Euler’s method. Graph the solution in the y1y2-plane. Calculate the errors.y" - y =
The accuracy of the explicit method depends on r(≤1/2). Illustrate this for Prob. 6, choosing r = 1/2 (and h = 0.2 as before). Do 4 steps. Compare the values for and 0.08 with the 3S-values in
Solve the initial value problem by Adams–Moulton (7a), (7b), 10 steps with 1 correction per step. Solve exactly and compute the error. Use RK where no starting values are giveny' = 3y - 12y2, y(0)
Solve Prob. 4 when un = 110 on the upper edge and u = 110 on the other edges.Data from Prob. 4Solve the mixed boundary value problem for the Laplace equation ∇2u = 0 in the rectangle in Fig.
What does it mean that a method is not self-starting? How do we overcome this problem?
For the grid in Fig. 456 compute the potential at the four internal points by Gauss and by 5 Gauss?Seidel steps with starting values 100, 100, 100, 100 (showing the details of your work) if the
If the string governed by the wave equation (1) starts from its equilibrium position with initial velocity g(x) = sin πx, what is its displacement at time t = 0.4 and x = 0.2, 0.4, 0.6, 0.8? (Use
What are one-step methods? Multistep methods? The underlying ideas? Give examples.
Do 10 steps. Solve exactly. Compute the error. Show details.y' = y, y(0) = 1, h = 0.1
Solve by the Euler’s method. Graph the solution in the y1y2-plane. Calculate the errors.y" - y = x, y(0) = 1, y'(0) = -2, h = 0.1, 5 steps
Using (5) with h = 1 and k = 0.5, solve the heat problem (1)–(3) to find the temperature at t = 2 in a laterally insulated bar of length 10 ft and initial temperature f(x) = x(1 - 0.1x).
Solve the initial value problem by Adams–Moulton (7a), (7b), 10 steps with 1 correction per step. Solve exactly and compute the error. Use RK where no starting values are givenDo Prob. 3 by RK, 5
What is adaptive integration? How does its idea extend to Runge–Kutta?
For the grid in Fig. 456 compute the potential at the four internal points by Gauss and by 5 Gauss?Seidel steps with starting values 100, 100, 100, 100 (showing the details of your work) if the
Illustrate the starting procedure when both f and g are not identically zero, say, f(x) = 1 - cos 2πx, g(x) = x(1 - x), h = k = 0.1, 2 time steps.
Why did we compute auxiliary values in each Runge–Kutta step? How many?
Do 10 steps. Solve exactly. Compute the error. Show details.y' = (y - x)2, y(0) = 0, h = 0.1
Solve by the Euler’s method. Graph the solution in the y1y2-plane. Calculate the errors.y" + 1/4y = 0, y(0) = 1, y'(0) = 0, h = 0.2, 5 steps
Solve the initial value problem by Adams–Moulton (7a), (7b), 10 steps with 1 correction per step. Solve exactly and compute the error. Use RK where no starting values are giveny' = 1 + y2, y(0) =
What are the local and the global orders of a method? Give examples.
Conclude from the boundary values in Example 1 that u21 = u11 and u22 = u12. Show that this leads to a system of two equations and solve it.
Using the present method, solve (1)–(4) with h = k = 0.2 for the given initial deflection and initial velocity 0 on the given t-interval.f(x) = 0.2(x - x2), 0 ≤ t ≤ 2
Derive the difference approximation (4) of the heat equation.
How did we obtain numeric methods from the Taylor series?
Do 10 steps. Solve exactly. Compute the error. Show details.y' + 0.2y = 0, y(0) = 5, h = 0.2
Solve by the Euler’s method. Graph the solution in the y1y2-plane. Calculate the errors.y'1 = 2y1 - 4y2, y'2 = y1 - 3y2, y1(0) = 3, y2(0) = 0, h = 0.1, 10 steps
Show that the heat equation u∼t∼ = c2u∼xx, 0 ≤ x∼ ≤ L, can be transformed to the “nondimensional” standard form ut = uxx, 0 ≤ x ≤ 1, by setting x = x∼/L, t = c2t∼/L2, u =
Solve the initial value problem by Adams–Moulton (7a), (7b), 10 steps with 1 correction per step. Solve exactly and compute the error. Use RK where no starting values are giveny' = y, y(0) = 1, h =
Check the values for the Poisson equation at the end of Example 1 by solving (3) by Gauss elimination.
Explain the Euler and improved Euler methods in geometrical terms. Why did we consider these methods?
Using the present method, solve (1)–(4) with h = k = 0.2 for the given initial deflection and initial velocity 0 on the given t-interval.f(x) = x if 0 = x < 1/5, f(x) = 1/4(1 - x) if 1/5 ≤ x
Find and graph three circular disks that must contain all the eigenvalues of the matrix:Of the coefficients in Prob. 14Data from Prob. 14Solve 3x2 - 6x3
Find and graph three circular disks that must contain all the eigenvalues of the matrix: In Prob. 19 Data from Prob. 19 Compute the inverse of: 15 20 10 20 35 15 10 15 90
Fit and graph:A quadratic parabola to the data in Prob. 34.Data from Prob. 34Fit and graph:A straight line to (1, 0), (0, 2), (1, 2), (2, 3), (3, 3)
Compute the condition number (corresponding to the l∞-vector norm) of the coefficient matrix:In Prob. 21Data from Prob. 21Do 3 steps without scaling, starting from [1 1 1]T.4x1 -
Compute the condition number (corresponding to the l?-vector norm) of the coefficient matrix: In Prob. 18 Data from Prob. 18 Compute the inverse of: 2.0 1.6 0.3 0.1 4.4 -4.3 3.3 0.5 2.8
Compute the condition number (corresponding to the l?-vector norm) of the coefficient matrix: In Prob. 19 Data from Prob. 19 Compute the inverse of: 15 20 10 20 35 15 10 15 90
Compute the matrix norm corresponding to the l∞-vector norm for the coefficient matrix:In Prob. 22Data from Prob. 22Do 3 steps without scaling, starting from [1 1 1]T.0.2x1 + 4.0x2 -
Compute the matrix norm corresponding to the l∞-vector norm for the coefficient matrix:In Prob. 21Data from Prob. 21Do 3 steps without scaling, starting from [1 1 1]T.4x1 - x2
Compute the matrix norm corresponding to the l∞-vector norm for the coefficient matrix:In Prob. 17Data from Prob. 17Solve 42x1 + 74x2 + 36x3 = 96-46x1 - 12x2 -
Compute the matrix norm corresponding to the l∞-vector norm for the coefficient matrix:In Prob. 15Data from Prob. 15Solve 8x2 -
What is the consumer’s risk in Prob. 12 if we want the RQL to be 12%? Use c = 9 from the answer of Prob. 12.Data from Prob. 12If in a sampling plan for large lots of spark plugs, the sample size is
Lots of kitchen knives are inspected by a sampling plan that uses a sample of size 20 and the acceptance number c = 1. What is the probability of accepting a lot with 1%, 2%, 10% defectives (knives
Why are interval estimates generally more useful than point estimates?
If we have several samples from the same population, do they have the same sample distribution function? The same mean and variance?
Make a list of methods in this section, each with the distribution needed in testing.
Show that in Prob. 1, the requirement of the significance level α = 0.3% leads to LCL = μ - 3σ/√n and UCL = μ + 3σ/√n, and find the corresponding numeric values.Data from Prob. 1Suppose a
Find and graph the sample regression line of y on x and the given data as points on the same axes. Show the details of your work. x = Revolutions per minute, y = Power of a Diesel engine [hp] y 400
Can we develop statistical methods without using probability theory? Apply the methods without using a sample?
Test μ = 0 assuming μ > 0, normality and using the sample 0, 1, -1, 3, -8, 6, 1 (deviations of the azimuth [multiples of 0.01 radian] in some revolution of a satellite). Choose α = 5%.
How will the probabilities in Prob. 1 with n = 20 change (up or down) if we decrease c to zero? First guess.Data from Prob. 1Lots of kitchen knives are inspected by a sampling plan that uses a sample
Derive the maximum likelihood estimator for μ. Apply it to the sample (10, 25, 26, 17, 10, 4), giving numbers of minutes with 0–10, 11–20, 21–30, 31–40, 41–50, more than 50 fliers per
If 100 flips of a coin result in 40 heads and 60 tails, can we assert on the 5% level that the coin is fair?
Are oil filters of type A better than type B filters if in 11 trials, A gave cleaner oil than B in 7 cases, B gave cleaner oil than A in 1 case, whereas in 3 of the trials the results for A and B
By what factor does the length of the interval in Prob. 2 change if we double the sample size?Data from Prob. 2Find a 95% confidence interval for the mean of a normal population with standard
What is the idea of the maximum likelihood method? Why do we say “likelihood” rather than “probability”?
Find and graph the sample regression line of y on x and the given data as points on the same axes. Show the details of your work. x = Brinell hardness, y = Tensile strength [in 1000 psi (pounds per
Couldn’t we make the error of interval estimation zero simply by choosing the confidence level 1?
Do the same test as in Prob. 4, using a result by K. Pearson, who obtained 6019 heads in 12,000 trials.Data from Prob. 4In one of his classical experiments Buffon obtained 2048 heads in tossing a
How should we change the sample size in controlling the mean of a normal population if we want UCL - LCL to decrease to half its original value?
Lots of copper pipes are inspected according to a sample plan that uses sample size 25 and acceptance number 1. Graph the OC curve of the plan, using the Poisson approximation. Find the producer’s
Derive a maximum likelihood estimate for p.
Can you claim, on a 5% level, that a die is fair if 60 trials give 1,· · ·, 6 with absolute frequencies 10, 13, 9, 11, 9, 8?
Do the computations in Prob. 4 without the use of the DeMoivre–Laplace limit theorem.Data from Prob. 4Does a process of producing stainless steel pipes of length 20 ft for nuclear reactors need
What sample size would be needed for obtaining 95% a confidence interval (3) of length 2σ? Of length σ?
What is testing? Why do we test? What are the errors involved?
Find and graph the sample regression line of y on x and the given data as points on the same axes. Show the details of your work. x = Voltage [V], y = Current [A]. Also find the resistance R [?]. X
When did we use the t-distribution? The F-distribution?
How does the result in Prob. 6 change if we use a smaller sample, say, of size 5, the other data (x̅ = 58.05, α = 5%, etc.) remaining as before?Data from Prob. 6Assuming normality and known
Graph the ranges of the samples in Prob. 6 on a control chart for ranges. Data from Prob. 6 Graph the means of the following 10 samples (thickness of gaskets, coded values) on a control chart for
Suppose that in Prob. 6 we made 3 times 4 trials and A happened 2, 3, 2 times, respectively. Estimate p.Data from Prob. 6Extend Prob. 5 as follows. Suppose that m times n trials were made and in the
If a service station had served 60, 49, 56, 46, 68, 39 cars from Monday through Friday between 1 P.M. and 2 P.M., can one claim on 5% a level that the differences are due to randomness? First guess.
Assuming normality, solve Prob. 6 by a suitable test. Data from Prob. 6 Thirty new employees were grouped into 15 pairs of similar intelligence and experience and were then instructed in data
Find a 95% confidence interval for the percentage of cars on a certain highway that have poorly adjusted brakes, using a random sample of 800 cars stopped at a roadblock on that highway, 126 of which
What is the chi-square (χ2) test? Give a sample example from memory.
Find and graph the sample regression line of y on x and the given data as points on the same axes. Show the details of your work. x = Temperature [?F], y = Conductivity [Btu/(hr ? ft ? ?F)]. Also
What are one-sided and two-sided tests? Give typical examples.
What is the rejection region in Prob. 6 in the case of a two-sided test with α = 5%?Data from Prob 6Assuming normality and known variance σ2 = 9, test the hypothesis μ = 60.0 against the

Showing 1700 - 1800 of 3884

First
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
Last

Get In Touch

About Us
Contact Us
Career
Jobs
FAQ
Campus Ambassador

Company Info

Security
Copyrights
Privacy Policy
Terms & Condition
SolutionInn Fee
Scholarship

Services

Sitemap
Fun
Definitions
Become Tutor
Study Help Categories
Recent Questions
Expert Questions

Copyright © 2024 SolutionInn All Rights Reserved.

Get the SolutionInn - Study Help App