Mathematical Methods in the Physical Sciences
3rd Edition
ISBN: 9780471198260
Author: Mary L. Boas
Publisher: Wiley, John & Sons, Incorporated
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Chapter 13.10, Problem 2MP
Solve Problem 1 if
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Students have asked these similar questions
1.
(i)
(ii)
which are not.
What does it mean to say that a set ECR2 is closed?
[1 Mark]
Identify which of the following subsets of R2 are closed and
(a)
A = [-1, 1] × (1, 3)
(b)
B = [-1, 1] x {1,3}
(c)
C = {(1/n², 1/n2) ER2 | n EN}
Provide a sketch and a brief explanation to each of your answers.
[6 Marks]
(iii) Give an example of a closed set which does not have interior
points.
[3 Marks]
Function: y=xsinx
Interval: [ 0 ; π ]
Requirements:
Draw the graphical form of the function.
Show the coordinate axes (x and y).
Choose the scale yourself and show it in the flowchart.
Create a flowchart based on the algorithm.
Write the program code in Python.
Additional requirements:
Each stage must be clearly shown in the flowchart.
The program must plot the graph and save it in PNG format.
Write the code in a modular way (functions and main section should be separate).
Expected results:
The graph of y=xsinx will be plotted in the interval [ 0 ; π ].
The algorithm and flowchart will be understandable and complete.
When you test the code, a graph file in PNG format will be created.
A company specializing in lubrication products for vintage motors produce two
blended oils, Smaza and Nefkov. They make a profit of K5,000.00 per litre of
Smaza and K4,000.00 per litre of Nefkov. A litre of Smaza requires 0.4 litres of
heavy oil and 0.6 litres of light oil. A litre of Nefkov requires 0.8 litres of heavy oil
and 0.2 litres of light oil. The company has 100 litres of heavy oil and 80 litres of
light oil. How many litres of each product should they make to maximize profits
and what level of profit will they obtain? Show all your workings.
Chapter 13 Solutions
Mathematical Methods in the Physical Sciences
Ch. 13.1 - Assume from electrostatics the equations E=/0 and...Ch. 13.1 - Show that the expression u=sin(xvt) describing a...Ch. 13.1 - Assume from electrodynamics the following...Ch. 13.1 - Obtain the heat flow equation (1.3) as follows:...Ch. 13.2 - After you find the series solution of a problem,...Ch. 13.2 - T=0,0x10,100,10x20. Solve the semi-infinite plate...Ch. 13.2 - Solve the semi-infinite plate problem if the...Ch. 13.2 - Solve the semi-infinite plate problem if the...Ch. 13.2 - Show that the solutions of (2.5) can also be...Ch. 13.2 - Show that the series in (2.12) can be summed to...
Ch. 13.2 - Solve Problem 3 if the plate is cut off at height...Ch. 13.2 - Find the steady-state temperature distribution in...Ch. 13.2 - Solve Problem 2 if the plate is cut off at height...Ch. 13.2 - Find the steady-state temperature distribution in...Ch. 13.2 - Find the steady-state temperature distribution in...Ch. 13.2 - Find the temperature distribution in a rectangular...Ch. 13.2 - Find the steady-state temperature distribution in...Ch. 13.2 - In the rectangular plate problem, we have so far...Ch. 13.2 - Consider a finite plate, 10cm by 30cm, with two...Ch. 13.2 - Show that there is only one function u which...Ch. 13.3 - Verify the coefficients in equation (3.14).Ch. 13.3 - A bar 10 cm long with insulated sides is initially...Ch. 13.3 - In the initial steady state of an infinite slab of...Ch. 13.3 - At t=0, two flat slabs each 5cm thick, one at 0...Ch. 13.3 - Prob. 5PCh. 13.3 - Show that the following problem is easily solved...Ch. 13.3 - A bar of length l with insulated sides has its...Ch. 13.3 - A bar of length 2 is initially at 0. From t=0 on,...Ch. 13.3 - Solve Problem 8 if, for t0, the x=0 end of the bar...Ch. 13.3 - Separate the wave equation (1.4) into a space...Ch. 13.3 - Solve the particle in a box problem to find (x,t)...Ch. 13.3 - Do Problem 11 if (x,0)=sin2x on (0,1).Ch. 13.4 - Complete the plucked string problem to get...Ch. 13.4 - A string of length l has a zero initial velocity...Ch. 13.4 - Solve Problem 2 if the initial displacement is:Ch. 13.4 - Solve Problem 2 if the initial displacement is :Ch. 13.4 - A string of length l is initially stretched...Ch. 13.4 - Do Problem 5 if the initial velocity V(x)=(y/t)t=0...Ch. 13.4 - Solve Problem 5 if the initial velocity is:Ch. 13.4 - Solve Problem 5 if the initial velocity is...Ch. 13.4 - In each of the Problems 1 to 8,find the frequency...Ch. 13.4 - Verify that, if k=nT, then the sum of the two...Ch. 13.4 - Verify (4.16) and find a similar formula for a...Ch. 13.4 - In Sections 2, 3, 4, we have solved a number of...Ch. 13.4 - Do Problem 12 for f(x)=1cos2x on (0,).Ch. 13.4 - Do Problem 12 for f(x)=xx3 on (0, 1).Ch. 13.5 - Compute numerically the coefficients (5.16) of the...Ch. 13.5 - Find the steady-state temperature distribution in...Ch. 13.5 - Find the steady-state temperature distribution in...Ch. 13.5 - A flat circular plate of radius a is initially at...Ch. 13.5 - Do Problem 4 if the initial temperature...Ch. 13.5 - Consider Problem 4 if the initial temperature...Ch. 13.5 - Find the steady-state temperature distribution in...Ch. 13.5 - Water at 100 is flowing through a long pipe of...Ch. 13.5 - Find the steady-state distribution of temperature...Ch. 13.5 - A cube is originally at 100. From t=0 on, the...Ch. 13.5 - The following two R(r) equations arise in various...Ch. 13.5 - Separate Laplaces equation in two dimensions in...Ch. 13.5 - Find the steady-state distribution of temperature...Ch. 13.5 - Find the steady state temperature distribution in...Ch. 13.5 - Solve Problem 14 if the temperatures of the two...Ch. 13.6 - Continue Figure 6.1 to show the fundamental modes...Ch. 13.6 - Prob. 2PCh. 13.6 - Separate the wave equation in two-dimensional...Ch. 13.6 - Find the characteristic frequencies for sound...Ch. 13.6 - A square membrane of side l is distorted into the...Ch. 13.6 - Let V=0 in the Schrödinger equation (3.22) and...Ch. 13.6 - In your Problem 6 solutions, find some examples of...Ch. 13.6 - Do Problem 6 in polar coordinates to find the...Ch. 13.7 - Find the steady-state temperature distribution...Ch. 13.7 - Find the steady-state temperature distribution...Ch. 13.7 - Find the steady-state temperature distribution...Ch. 13.7 - Find the steady-state temperature distribution...Ch. 13.7 - Find the steady-state temperature distribution...Ch. 13.7 - Find the steady-state temperature distribution...Ch. 13.7 - Find the steady-state temperature distribution...Ch. 13.7 - Find the steady-state temperature distribution...Ch. 13.7 - Find the steady-state temperature distribution...Ch. 13.7 - Find the steady-state temperature distribution...Ch. 13.7 - Find the steady-state temperature distribution...Ch. 13.7 - Do Problem 11 if the curved surface is held at...Ch. 13.7 - Find the electrostatic potential outside a...Ch. 13.7 - Find the steady-state temperature distribution in...Ch. 13.7 - A sphere initially at 0 has its surface kept at...Ch. 13.7 - Separate the wave equation in spherical...Ch. 13.7 - Do Problem 6.6 in 3 dimensional rectangular...Ch. 13.7 - Prob. 18PCh. 13.7 - Find the eigenfunctions and energy eigenvalues for...Ch. 13.7 - Write the Schrödinger equation (3.22) if is a...Ch. 13.7 - Prob. 21PCh. 13.7 - Find the energy eigenvalues and eigen functions...Ch. 13.8 - Show that the gravitational potential V=Gm/r...Ch. 13.8 - Using the formulas of Chapter 12, Section 5, sum...Ch. 13.8 - Do the problem in Example 1 for the case of a...Ch. 13.8 - Prob. 4PCh. 13.8 - Find the method of images for problem 4.Ch. 13.8 - Substitute (8.25) into (8.22) and use (8.23) and...Ch. 13.8 - Verify that the Green function in (8.29) is zero...Ch. 13.8 - Show that the Green function (8.28) which is zero...Ch. 13.8 - Show that our results can be extended to find the...Ch. 13.9 - Verify that (9.15) follows from (9.14). Hint: Use...Ch. 13.9 - A metal plate covering the first quadrant has the...Ch. 13.9 - Consider the heat flow problem of Section 3. Solve...Ch. 13.9 - A semi-infinite bar is initially at temperature...Ch. 13.9 - Prob. 5PCh. 13.9 - Continue the problem of Example 2 in the following...Ch. 13.9 - Continue with Problem 4 as in Problem 6.Ch. 13.10 - Find the steady-state temperature distribution in...Ch. 13.10 - Solve Problem 1 if T=0 for x=0,x=1,y=0, and T=1x...Ch. 13.10 - Solve Problem 1 if the sides x=0 and x=1 are...Ch. 13.10 - Find the steady-state temperature distribution in...Ch. 13.10 - A bar of length l is initially at 0. From t=0 on,...Ch. 13.10 - Do Problem 5 if the x=0 end is insulated and the...Ch. 13.10 - Solve Problem 2 if the sides x=0 and x=1 are...Ch. 13.10 - A slab of thickness 10cm has its two faces at 10...Ch. 13.10 - A string of length l has initial displacement...Ch. 13.10 - Solve Problem 5.7 if half the curved surface of...Ch. 13.10 - The series in Problem 5.12 can be summed (see...Ch. 13.10 - A plate in the shape of a quarter circle has...Ch. 13.10 - Sum the series in Problem 12 to get...Ch. 13.10 - A long cylinder has been cut into quarter...Ch. 13.10 - Repeat Problems 12 and 13 for a plate in the shape...Ch. 13.10 - Consider the normal modes of vibration for a...Ch. 13.10 - Sketch some of the normal modes of vibration for a...Ch. 13.10 - Repeat Problem 17 for a membrane in the shape of a...Ch. 13.10 - Prob. 19MPCh. 13.10 - Use Problem 7.16 to find the characteristic...Ch. 13.10 - The surface temperature of a sphere of radius 1 is...Ch. 13.10 - Find the interior temperature in a hemisphere if...Ch. 13.10 - Find the steady-state temperature in the region...Ch. 13.10 - Find the general solution for the steady-state...Ch. 13.10 - The Klein-Gordon equation is 2u=1/v22u/t2+2u. This...Ch. 13.10 - Prob. 26MPCh. 13.10 - Do Problem 26 for a rectangular membrane.Ch. 13.10 - Find the steady-state temperature in a...
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