
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
Textbook Question
Chapter 7.11, Problem 1P
Prove (11.4) for a function of period 2l expanded in a sine-cosine series.
Expert Solution & Answer

Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Prove that
1) | RxX (T) | << = (R₁ " + R$)
2) find Laplalse trans.
of Normal dis:
3) Prove thy t
/Rx (z) | < | Rx (0)\
4) show that evary
algebra is algebra
or not.
=
5 37
A 4 8 0.5
06
9
For each of the time series, construct a line chart of the data and identify the characteristics of the time series (that is, random, stationary, trend, seasonal, or cyclical).
Month Number (Thousands)Dec 1991 65.60Jan 1992 71.60Feb 1992 78.80Mar 1992 111.60Apr 1992 107.60May 1992 115.20Jun 1992 117.80Jul 1992 106.20Aug 1992 109.90Sep 1992 106.00Oct 1992 111.80Nov 1992 84.50Dec 1992 78.60Jan 1993 70.50Feb 1993 74.60Mar 1993 95.50Apr 1993 117.80May 1993 120.90Jun 1993 128.50Jul 1993 115.30Aug 1993 121.80Sep 1993 118.50Oct 1993 123.30Nov 1993 102.30Dec 1993 98.70Jan 1994 76.20Feb 1994 83.50Mar 1994 134.30Apr 1994 137.60May 1994 148.80Jun 1994 136.40Jul 1994 127.80Aug 1994 139.80Sep 1994 130.10Oct 1994 130.60Nov 1994 113.40Dec 1994 98.50Jan 1995 84.50Feb 1995 81.60Mar 1995 103.80Apr 1995 116.90May 1995 130.50Jun 1995 123.40Jul 1995 129.10Aug 1995…
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
In hypothesis testing, the common level of significance is =0.05. Some might argue for a level of significance ...
Basic Business Statistics, Student Value Edition
the area of given figure.
Pre-Algebra Student Edition
Solve each formula for the given letter . [2.3] What percent of 60 is 42? [2.4]
Elementary and Intermediate Algebra: Concepts and Applications (7th Edition)
In Exercises 5-36, express all probabilities as fractions.
23. Combination Lock The typical combination lock us...
Elementary Statistics
Finding Polar Areas
Find the areas of the regions in Exercises 1–8.
3. Inside the oval limaçon r = 4 + 2 cos θ....
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
- For each of the time series, construct a line chart of the data and identify the characteristics of the time series (that is, random, stationary, trend, seasonal, or cyclical). Year Month Units1 Nov 42,1611 Dec 44,1862 Jan 42,2272 Feb 45,4222 Mar 54,0752 Apr 50,9262 May 53,5722 Jun 54,9202 Jul 54,4492 Aug 56,0792 Sep 52,1772 Oct 50,0872 Nov 48,5132 Dec 49,2783 Jan 48,1343 Feb 54,8873 Mar 61,0643 Apr 53,3503 May 59,4673 Jun 59,3703 Jul 55,0883 Aug 59,3493 Sep 54,4723 Oct 53,164arrow_forwardConsider the table of values below. x y 2 64 3 48 4 36 5 27 Fill in the right side of the equation y= with an expression that makes each ordered pari (x,y) in the table a solution to the equation.arrow_forwardsolving for xarrow_forward
- Consider the table of values below. x y 2 63 3 70 4 77 5 84 Fill in the right side of the equation y= with an expression that makes each ordered pari (x,y) in the table a solution to the equation.arrow_forwardfind the value of each variablearrow_forwardConsider the following system of equations, Ax=b : x+2y+3z - w = 2 2x4z2w = 3 -x+6y+17z7w = 0 -9x-2y+13z7w = -14 a. Find the solution to the system. Write it as a parametric equation. You can use a computer to do the row reduction. b. What is a geometric description of the solution? Explain how you know. c. Write the solution in vector form? d. What is the solution to the homogeneous system, Ax=0?arrow_forward
- 2. Find a matrix A with the following qualities a. A is 3 x 3. b. The matrix A is not lower triangular and is not upper triangular. c. At least one value in each row is not a 1, 2,-1, -2, or 0 d. A is invertible.arrow_forwardFind the exact area inside r=2sin(2\theta ) and outside r=\sqrt(3)arrow_forwardHigh Cholesterol: A group of eight individuals with high cholesterol levels were given a new drug that was designed to lower cholesterol levels. Cholesterol levels, in milligrams per deciliter, were measured before and after treatment for each individual, with the following results: Individual Before 1 2 3 4 5 6 7 8 237 282 278 297 243 228 298 269 After 200 208 178 212 174 201 189 185 Part: 0/2 Part 1 of 2 (a) Construct a 99.9% confidence interval for the mean reduction in cholesterol level. Let a represent the cholesterol level before treatment minus the cholesterol level after. Use tables to find the critical value and round the answers to at least one decimal place.arrow_forward
- Please could you explain how to do integration by parts for this question in detail pleasearrow_forwardThere were 426 books sold in one week. The number of biology books sold was 5 times that of the number of psychology books. How many books each were sold?arrow_forwardI worked out the answers for most of this, and provided the answers in the tables that follow. But for the total cost table, I need help working out the values for 10%, 11%, and 12%. A pharmaceutical company produces the drug NasaMist from four chemicals. Today, the company must produce 1000 pounds of the drug. The three active ingredients in NasaMist are A, B, and C. By weight, at least 8% of NasaMist must consist of A, at least 4% of B, and at least 2% of C. The cost per pound of each chemical and the amount of each active ingredient in one pound of each chemical are given in the data at the bottom. It is necessary that at least 100 pounds of chemical 2 and at least 450 pounds of chemical 3 be used. a. Determine the cheapest way of producing today’s batch of NasaMist. If needed, round your answers to one decimal digit. Production plan Weight (lbs) Chemical 1 257.1 Chemical 2 100 Chemical 3 450 Chemical 4 192.9 b. Use SolverTable to see how much the percentage of…arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCollege Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage

College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Power Series; Author: Professor Dave Explains;https://www.youtube.com/watch?v=OxVBT83x8oc;License: Standard YouTube License, CC-BY
Power Series & Intervals of Convergence; Author: Dr. Trefor Bazett;https://www.youtube.com/watch?v=XHoRBh4hQNU;License: Standard YouTube License, CC-BY