Mathematical Methods in the Physical Sciences
3rd Edition
ISBN: 9780471198260
Author: Mary L. Boas
Publisher: Wiley, John & Sons, Incorporated
expand_more
expand_more
format_list_bulleted
Videos
Textbook Question
Chapter 7.9, Problem 4P
The functions in Problems 1 to 3 are neither even nor odd. Write each of them as the sum of an even function and an odd function.
Using what you know about even and odd functions, prove the first part of (5.2).
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Please answer exercise 11.2.10 and 11.4.1 stepwise
To help consumers in purchasing a laptop computef, Consumer Reports calculates an overall
test score for each computer tested based upon rating factors such as ergonomics, portability,
performance, display, and battery life. Higher overall scores indicate better test results. The
following data show the average retail price and the overall score for ten 13-inch models
(Consumer Reports website, October 25, 2012).
Price
Overall
Brand & Model
Score
Samsung Ultrabook NP900X3C-A01US
1250
83
Apple MacBook Air MC965LL/A
1300
83
Apple MacBook Air MD231LL/A
1200
82
HP ENVY 13-2050nr Spectre XT
950
79
Sony VAIO SVS13112FXB
800
77
Acer Aspire S5-391-9880 Ultrabook
1200
74
Apple MacBook Pro MD101LL/A
1200
74
Apple MacBook Pro MD313LL/A
1000
73
Dell Inspiron 113Z-6591SLV
700
67
600
63
Samsung NP535U3C-A01US
a. Develop a scatter diagram with price as the independent variable.
b. What does the scatter diagram developed in part (a) indicate about the relationship
between the two variables?
c. Use the…
Please answer exercises 11.4.8 and 11.4.10 Stepwise
Chapter 7 Solutions
Mathematical Methods in the Physical Sciences
Ch. 7.2 - In Problems 1 to 6 find the amplitude, period,...Ch. 7.2 - In Problems 1 to 6 find the amplitude, period,...Ch. 7.2 - In Problems 1 to 6 find the amplitude, period,...Ch. 7.2 - In Problems 1 to 6 find the amplitude, period,...Ch. 7.2 - In Problems 1 to 6 find the amplitude, period,...Ch. 7.2 - In Problems 1 to 6 find the amplitude, period,...Ch. 7.2 - In Problems 7 to 10 you are given a complex...Ch. 7.2 - In Problems 7 to 10 you are given a complex...Ch. 7.2 - In Problems 7 to 10 you are given a complex...Ch. 7.2 - In Problems 7 to 10 you are given a complex...
Ch. 7.2 - The charge q on a capacitor in a simple a-c...Ch. 7.2 - RepeatProblem11:(a)ifq=Re4e30it;(b)ifq=Im4e30it.Ch. 7.2 - A simple pendulum consists of a point mass m...Ch. 7.2 - The displacements x of two simple pendulums (see...Ch. 7.2 - As in Problem 14, the displacements x of two...Ch. 7.2 - As in Problem 14, let the displacements be...Ch. 7.2 - Show that equation (2.10) for a wave can be...Ch. 7.2 - In Problems 18 to 20, find the amplitude, period,...Ch. 7.2 - In Problems 18 to 20, find the amplitude, period,...Ch. 7.2 - In Problems 18 to 20, find the amplitude, period,...Ch. 7.2 - Write the equation for a sinusoidal wave of...Ch. 7.2 - Do Problem 21 for a wave of amplitude 4, period 6,...Ch. 7.2 - Write an equation for a sinusoidal sound wave of...Ch. 7.2 - The velocity of sound in sea water is about...Ch. 7.2 - Write an equation for a sinusoidal radio wave of...Ch. 7.3 - For each of the following combinations of a...Ch. 7.3 - For each of the following combinations of a...Ch. 7.3 - For each of the following combinations of a...Ch. 7.3 - For each of the following combinations of a...Ch. 7.3 - Using the definition (end of Section 2) of a...Ch. 7.3 - In Problems 6 and 7, use a trigonometry formula to...Ch. 7.3 - In Problems 6 and 7, use a trigonometry formula to...Ch. 7.3 - A periodic modulated (AM) radio signal has the...Ch. 7.4 - Show that if f(x) has period p, the average value...Ch. 7.4 - (a) Prove that 0/2sin2xdx=0/2cos2xdx by making the...Ch. 7.4 - In Problems 3 to 12, find the average value of the...Ch. 7.4 - In Problems 3 to 12, find the average value of the...Ch. 7.4 - In Problems 3 to 12, find the average value of the...Ch. 7.4 - In Problems 3 to 12, find the average value of the...Ch. 7.4 - In Problems 3 to 12, find the average value of the...Ch. 7.4 - In Problems 3 to 12, find the average value of the...Ch. 7.4 - In Problems 3 to 12, find the average value of the...Ch. 7.4 - In Problems 3 to 12, find the average value of the...Ch. 7.4 - In Problems 3 to 12, find the average value of the...Ch. 7.4 - In Problems 3 to 12, find the average value of the...Ch. 7.4 - Using (4.3) and equations similar to (4.5) to...Ch. 7.4 - Use the results of Problem 13 to evaluate the...Ch. 7.4 - Use the results of Problem 13 to evaluate the...Ch. 7.4 - Use the results of Problem 13 to evaluate the...Ch. 7.5 - In each of the following problems you are given a...Ch. 7.5 - In each of the following problems you are given a...Ch. 7.5 - In each of the following problems you are given a...Ch. 7.5 - In each of the following problems you are given a...Ch. 7.5 - In each of the following problems you are given a...Ch. 7.5 - In each of the following problems you are given a...Ch. 7.5 - In each of the following problems you are given a...Ch. 7.5 - In each of the following problems you are given a...Ch. 7.5 - In each of the following problems you are given a...Ch. 7.5 - In each of the following problems you are given a...Ch. 7.5 - In each of the following problems you are given a...Ch. 7.5 - Show that in (5.2) the average values of...Ch. 7.5 - Write out the details of the derivation of...Ch. 7.6 - For each of the periodic functions in Problems 5.1...Ch. 7.6 - For each of the periodic functions in Problems 5.1...Ch. 7.6 - For each of the periodic functions in Problems 5.1...Ch. 7.6 - For each of the periodic functions in Problems 5.1...Ch. 7.6 - For each of the periodic functions in Problems 5.1...Ch. 7.6 - For each of the periodic functions in Problems 5.1...Ch. 7.6 - For each of the periodic functions in Problems 5.1...Ch. 7.6 - For each of the periodic functions in Problems 5.1...Ch. 7.6 - For each of the periodic functions in Problems 5.1...Ch. 7.6 - For each of the periodic functions in Problems 5.1...Ch. 7.6 - For each of the periodic functions in Problems 5.1...Ch. 7.6 - Use a computer to produce graphs like Fig. 6.2...Ch. 7.6 - Repeat the example using the same Fourier series...Ch. 7.6 - Use Problem 5.7 to show that oddn1/n2=2/8. Try...Ch. 7.6 - UseProblem5.11toshowthat1221+1421+1621+=12.Ch. 7.7 - Expand the same functions as in Problems 5.1 to...Ch. 7.7 - Expand the same functions as in Problems 5.1 to...Ch. 7.7 - Expand the same functions as in Problems 5.1 to...Ch. 7.7 - Expand the same functions as in Problems 5.1 to...Ch. 7.7 - Expand the same functions as in Problems 5.1 to...Ch. 7.7 - Expand the same functions as in Problems 5.1 to...Ch. 7.7 - Expand the same functions as in Problems 5.1 to...Ch. 7.7 - Expand the same functions as in Problems 5.1 to...Ch. 7.7 - Expand the same functions as in Problems 5.1 to...Ch. 7.7 - Expand the same functions as in Problems 5.1 to...Ch. 7.7 - Expand the same functions as in Problems 5.1 to...Ch. 7.7 - Show that if a real f(x) is expanded in a complex...Ch. 7.7 - If f(x)=12a0+1ancosnx+1bnsinnx=cneinx, use Eulers...Ch. 7.8 - In Problems 5.1 to 5.9, define each function by...Ch. 7.8 - In Problems 5.1 to 5.9, define each function by...Ch. 7.8 - In Problems 5.1 to 5.9, define each function by...Ch. 7.8 - In Problems 5.1 to 5.9, define each function by...Ch. 7.8 - In Problems 5.1 to 5.9, define each function by...Ch. 7.8 - In Problems 5.1 to 5.9, define each function by...Ch. 7.8 - In Problems 5.1 to 5.9, define each function by...Ch. 7.8 - In Problems 5.1 to 5.9, define each function by...Ch. 7.8 - In Problems 5.1 to 5.9, define each function by...Ch. 7.8 - (a) Sketch several periods of the function f(x) of...Ch. 7.8 - In Problems 11 to 14, parts (a) and (b), you are...Ch. 7.8 - In Problems 11 to 14, parts (a) and (b), you are...Ch. 7.8 - In Problems 11 to 14, parts (a) and (b), you are...Ch. 7.8 - In Problems 11 to 14, parts (a) and (b), you are...Ch. 7.8 - Sketch (or computer plot) each of the following...Ch. 7.8 - Each of the following functions is given over one...Ch. 7.8 - Each of the following functions is given over one...Ch. 7.8 - Each of the following functions is given over one...Ch. 7.8 - Each of the following functions is given over one...Ch. 7.8 - Each of the following functions is given over one...Ch. 7.8 - Write out the details of the derivation of the...Ch. 7.9 - The functions in Problems 1 to 3 are neither even...Ch. 7.9 - The functions in Problems 1 to 3 are neither even...Ch. 7.9 - The functions in Problems 1 to 3 are neither even...Ch. 7.9 - The functions in Problems 1 to 3 are neither even...Ch. 7.9 - Each of the functions in Problems 5 to 12 is given...Ch. 7.9 - Each of the functions in Problems 5 to 12 is given...Ch. 7.9 - Each of the functions in Problems 5 to 12 is given...Ch. 7.9 - Each of the functions in Problems 5 to 12 is given...Ch. 7.9 - Each of the functions in Problems 5 to 12 is given...Ch. 7.9 - Each of the functions in Problems 5 to 12 is given...Ch. 7.9 - Each of the functions in Problems 5 to 12 is given...Ch. 7.9 - Each of the functions in Problems 5 to 12 is given...Ch. 7.9 - Give algebraic proofs of (9.3). Hint: Write...Ch. 7.9 - Give algebraic proofs that for even and odd...Ch. 7.9 - Given f(x)=x for 0x1, sketch the even function fc...Ch. 7.9 - Let f(x)=sin2x,0x. Sketch (or computer plot) the...Ch. 7.9 - In Problems 17 to 22 you are given f(x) on an...Ch. 7.9 - In Problems 17 to 22 you are given f(x) on an...Ch. 7.9 - In Problems 17 to 22 you are given f(x) on an...Ch. 7.9 - In Problems 17 to 22 you are given f(x) on an...Ch. 7.9 - In Problems 17 to 22 you are given f(x) on an...Ch. 7.9 - In Problems 17 to 22 you are given f(x) on an...Ch. 7.9 - If a violin string is plucked (pulled aside and...Ch. 7.9 - If, in Problem 23, the string is stopped at the...Ch. 7.9 - Suppose that f(x) and its derivative f(x) are both...Ch. 7.9 - In Problems 26 and 27, find the indicated Fourier...Ch. 7.9 - In Problems 26 and 27, find the indicated Fourier...Ch. 7.10 - In Problems 1 to 3, the graphs sketched represent...Ch. 7.10 - In Problems 1 to 3, the graphs sketched represent...Ch. 7.10 - In Problems 1 to 3, the graphs sketched represent...Ch. 7.10 - In Problems 4 to 10, the sketches show several...Ch. 7.10 - In Problems 4 to 10, the sketches show several...Ch. 7.10 - In Problems 4 to 10, the sketches show several...Ch. 7.10 - In Problems 4 to 10, the sketches show several...Ch. 7.10 - In Problems 4 to 10, the sketches show several...Ch. 7.10 - In Problems 4 to 10, the sketches show several...Ch. 7.10 - In Problems 4 to 10, the sketches show several...Ch. 7.11 - Prove (11.4) for a function of period 2l expanded...Ch. 7.11 - Prove that if f(x)=i=cneinx, then the average...Ch. 7.11 - If f(x) is complex, we usually want the average of...Ch. 7.11 - When a current I flows through a resistance R, the...Ch. 7.11 - Use Parsevals theorem and the results of the...Ch. 7.11 - Use Parsevals theorem and the results of the...Ch. 7.11 - Use Parsevals theorem and the results of the...Ch. 7.11 - Use Parsevals theorem and the results of the...Ch. 7.11 - Use Parsevals theorem and the results of the...Ch. 7.11 - A general form of Parsevals theorem says that if...Ch. 7.11 - Let f(x) on (0,2l) satisfy f(2lx)=f(x), that is,...Ch. 7.12 - Following a method similar to that used in...Ch. 7.12 - Do Example 1 above by using a cosine transform...Ch. 7.12 - In Problems 3 to 12, find the exponential Fourier...Ch. 7.12 - In Problems 3 to 12, find the exponential Fourier...Ch. 7.12 - In Problems 3 to 12, find the exponential Fourier...Ch. 7.12 - In Problems 3 to 12, find the exponential Fourier...Ch. 7.12 - In Problems 3 to 12, find the exponential Fourier...Ch. 7.12 - In Problems 3 to 12, find the exponential Fourier...Ch. 7.12 - In Problems 3 to 12, find the exponential Fourier...Ch. 7.12 - In Problems 3 to 12, find the exponential Fourier...Ch. 7.12 - In Problems 3 to 12, find the exponential Fourier...Ch. 7.12 - In Problems 3 to 12, find the exponential Fourier...Ch. 7.12 - In Problems 13 to 16, find the Fourier cosine...Ch. 7.12 - In Problems 13 to 16, find the Fourier cosine...Ch. 7.12 - In Problems 13 to 16, find the Fourier cosine...Ch. 7.12 - In Problems 13 to 16, find the Fourier cosine...Ch. 7.12 - In Problems 17 to 20, find the Fourier sine...Ch. 7.12 - In Problems 17 to 20, find the Fourier sine...Ch. 7.12 - In Problems 17 to 20, find the Fourier sine...Ch. 7.12 - In Problems 17 to 20, find the Fourier sine...Ch. 7.12 - Find the Fourier transform of f(x)=ex2/22. Hint:...Ch. 7.12 - The function j1()=(cossin)/ is of interest in...Ch. 7.12 - Using Problem 17, show that...Ch. 7.12 - (a) Find the exponential Fourier transform of...Ch. 7.12 - (a) Represent as an exponential Fourier transform...Ch. 7.12 - Using Problem 15, show that 01cos2d=2.Ch. 7.12 - Represent each of the following functions (a) by a...Ch. 7.12 - Represent each of the following functions (a) by a...Ch. 7.12 - Represent each of the following functions (a) by a...Ch. 7.12 - Represent each of the following functions (a) by a...Ch. 7.12 - Verify Parsevals theorem (12.24) for the special...Ch. 7.12 - Verify Parsevals theorem (12.24) for the special...Ch. 7.12 - Verify Parsevals theorem (12.24) for the special...Ch. 7.12 - Show that if (12.2) is written with the factor 1/2...Ch. 7.12 - Starting with the symmetrized integrals as in...Ch. 7.12 - Normalize f(x) in Problem 21; that is find the...Ch. 7.13 - The displacement (from equilibrium) of a particle...Ch. 7.13 - The symbol [x] means the greatest integer less...Ch. 7.13 - We have said that Fourier series can represent...Ch. 7.13 - The diagram shows a relaxation oscillator. The...Ch. 7.13 - Consider one arch of f(x)=sinx. Show that the...Ch. 7.13 - Let f(t)=eit on (,). Expand f(t) in a complex...Ch. 7.13 - Given f(x)=x on (,), expand f(x) in an appropriate...Ch. 7.13 - From facts you know, find in your head the average...Ch. 7.13 - Given f(x)= x,0x1, 2,1x2. (a) Sketch at least...Ch. 7.13 - (a) Sketch at least three periods of the graph of...Ch. 7.13 - Find the three Fourier series in Problems 9 and...Ch. 7.13 - What would be the apparent frequency of a sound...Ch. 7.13 - (a) Given f(x)=(x)/2 on (0,), find the sine series...Ch. 7.13 - (a) Find the Fourier series of period 2 for...Ch. 7.13 - Given f(x)=1,2x0,1,0x2, find the exponential...Ch. 7.13 - Given f(x)=x,0x1,2x,1x2,0,x2, find the cosine...Ch. 7.13 - Show that the Fourier sine transform of x1/2 is...Ch. 7.13 - Let f(x) and g() be a pair of Fourier transforms....Ch. 7.13 - Find the form of Parsevals theorem ( 12.24) for...Ch. 7.13 - Find the exponential Fourier transform of...Ch. 7.13 - Define a function h(x)=k=f(x+2k), assuming that...Ch. 7.13 - Use Poissons formula (Problem 21b) and Problem 20...Ch. 7.13 - Use Parsevals theorem and Problem 12.11 to...
Additional Math Textbook Solutions
Find more solutions based on key concepts
CHECK POINT 1 In a survey on musical tastes, respondents were asked: Do you listed to classical music? Do you l...
Thinking Mathematically (6th Edition)
The equivalent expression of x(y+z) by using the commutative property.
Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
Symmetry in graphs State whether the functions represented by graphs A, B, and C in the figure are even, odd, o...
Calculus: Early Transcendentals (2nd Edition)
Assessment 71A Write each of the following as a sum in expanded place value form. a. 0.023 b. 206.06 c. 312.010...
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
CLT Shapes (Example 4) One of the histograms is a histogram of a sample (from a population with a skewed distri...
Introductory Statistics
Evaluate for the vector field along the curve from (4, 2) to (1, –1).
University Calculus: Early Transcendentals (4th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- Please answer exercises 11.4.4 and 11.4.5 Stepwisearrow_forwardData on advertising expenditures and revenue (in thousands of dollars) for the Four Sea- sons Restaurant follow, Advertising Expenditures Revenue 124 19 32 44 6 40 10 52 14 20 53 54 a. Let x equal advertising expenditures and y equal revenue. Use the method of least squares to develop a straight line approximation of the relationship between the two variables. b. Test whether revenue and advertising expenditures are related at a .05 level of significance. - C. Prepare a residual plot of yŷ versus ŷ. Use the result from part (a) to obtain the values of ŷ. d. What conclusions can you draw from residual analysis? Should this model be used, or should we look for a better one?arrow_forwardPlease answer exercises 11.2.7 and 11.2.8 Stepwisearrow_forward
- In a manufacturing process the assembly line speed (feet per minute) was thought to af- fect the number of defective parts found during the inspection process. To test this theory, managers devised a situation in which the same batch of parts was inspected visually at a variety of line speeds. They collected the following data. Line Speed 20 Number of Defective Parts Found 21 20 19 40 *** 40 15 30 16 60 14 17 a. Develop the estimated regression equation that relates line speed to the number of defective parts found. b. At a .05 level of significance, determine whether line speed and number of defective parts found are related. C. Did the estimated regression equation provide a good fit to the data? d. Develop a 95% confidence interval to predict the mean number of defective parts for a line speed of 50 feet per minute.arrow_forwardPlease answer exercise 11.4.11 Stepwisearrow_forwardIn exercise 12, the following data on x = average daily hotel room rate and y = amount spent on entertainment (The Wall Street Journal, August 18, 2011) lead to the estimated regression equation ŷ = 17.49 + 1.0334x. For these data SSE = 1541.4. - Room Rate Entertainment City ($) ($) Boston 148 161 Denver 96 105 Nashville 91 101 New Orleans 110 142 Phoenix 90 100 San Diego 102 120 San Francisco 136 167 San Jose 90 140 Tampa 82 98 a. Predict the amount spent on entertainment for a particular city that has a daily room rate of $89. b. Develop a 95% confidence interval for the mean amount spent on entertainment for C. all cities that have a daily room rate of $89. The average room rate in Chicago is $128. Develop a 95% prediction interval for the amount spent on entertainment in Chicago.arrow_forward
- Please answer exercises 11.4.6 and 11.4.7 Stepwisearrow_forwardAn important application of regression analysis in accounting is in the estimation of cost. By collecting data on volume and cost and using the least squares method to develop an estimated regression equation relating volume and cost, an accountant can estimate the cost associated with a particular manufacturing volume. Consider the following sample of production volumes and total cost data for a manufacturing operation. Production Volume (units) 400 Total Cost ($) 450 550 600 700 750 4000 5000 5400 5900 6400 7000 a. Use these data to develop an estimated regression equation that could be used to predict the total cost for a given production volume. b. What is the variable cost per unit produced? c. Compute the coefficient of determination. What percentage of the variation in total cost can be explained by production volume? d. The company's production schedule shows 500 units must be produced next month. Predict the total cost for this operation?arrow_forwardPlease answer exercises 11.4.2 and 11.4.3 Stepwisearrow_forward
- Please answer exercise 11.2.5 and 11.2.6 stepwisearrow_forwardFind two unit vectors orthogonal to both given vectors. (7, -7, 7), (0, 2, 2) (smaller i-value) (larger i-value) Need Help? Read It Master Itarrow_forward(a) Let P be a point not on the line L that passes through the points Q and R. Show that the distance d from the point P to the line L is |a × b| |a| d where a QR and b QR and b = QP. = This answer has not been graded yet. (b) Use the formula in part (a) to find the distance from the point P(1, 1, 1) to the line through Q(0, 7, 6) and R(-1, 2, 6).arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell
Trigonometry (MindTap Course List)TrigonometryISBN:9781305652224Author:Charles P. McKeague, Mark D. TurnerPublisher:Cengage Learning
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Algebra for College StudentsAlgebraISBN:9781285195780Author:Jerome E. Kaufmann, Karen L. SchwittersPublisher:Cengage Learning
Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt
Algebra: Structure And Method, Book 1
Algebra
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:McDougal Littell
Trigonometry (MindTap Course List)
Trigonometry
ISBN:9781305652224
Author:Charles P. McKeague, Mark D. Turner
Publisher:Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Algebra for College Students
Algebra
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Cengage Learning
Big Ideas Math A Bridge To Success Algebra 1: Stu...
Algebra
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:Houghton Mifflin Harcourt
Derivatives of Trigonometric Functions - Product Rule Quotient & Chain Rule - Calculus Tutorial; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=_niP0JaOgHY;License: Standard YouTube License, CC-BY