Mathematical Methods in the Physical Sciences
Mathematical Methods in the Physical Sciences
3rd Edition
ISBN: 9780471198260
Author: Mary L. Boas
Publisher: Wiley, John & Sons, Incorporated
bartleby

Concept explainers

Cylinders
A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.
Cones
A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is dr…
bartleby

Videos

Textbook Question
Book Icon
Chapter 7.2, Problem 24P

The velocity of sound in sea water is about 1530 m / sec . Write an equation for a sinusoidal sound wave in the ocean, of amplitude 1 and frequency 1000 hertz.

Expert Solution & Answer
Check Mark

Want to see the full answer?

Check out a sample textbook solution
Blurred answer
Previous
Chapter 7.2, Problem 23P
Next
Chapter 7.2, Problem 25P
Students have asked these similar questions
Numerically estimate the value of limx→2+x3−83x−9, rounded correctly to one decimal place. In the provided table below, you must enter your answers rounded exactly to the correct number of decimals, based on the Numerical Conventions for MATH1044 (see lecture notes 1.3 Actions  page 3). If there are more rows provided in the table than you need, enter NA for those output values in the table that should not be used. x→2+ x3−83x−9   2.1     2.01     2.001     2.0001     2.00001     2.000001
e Grade Breakdown x Dashboard | Big Spring HX Dashboard | Big Spring H x Home | Lesson | Assessm cds.caolacourses.edisonlearning.com/lessons/assessmentplayer Co bigspringsd.org bookmarks Prodigy New Tab my video Brielynn... Algebra 2 Part 1-Exam-EDCP.MA003.A D Question 6 D ? 10 17°F Mostly sunny BSMS Home Significant Events in... Classes 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 Solve using row operations: x-3y= -4; 2x - y = 7 Use the paperclip button below to attach files. Student can enter max 2000 characters BISU DAIAAA X2 X2 T ② Type here Q Search e I ✓ Paragra O
Martinez Auto Supplies has retail stores located in eight cities in California. The price they charge for a particular product in each city are vary because of differing competitive conditions. For instance, the price they charge for a case of a popular brand of motor oil in each city follows. Also shown are the number of cases that Martinez Auto sold last quarter in each city. City Price ($) Sales (cases) Bakersfield 34.99 501 Los Angeles 38.99 1425 Modesto 36.00 294 Oakland 33.59 882 Sacramento 40.99 715 San Diego 38.59 1088 San Francisco 39.59 1644 San Jose 37.99 819 Compute the average sales price per case for this product during the last quarter? Round your answer to two decimal places.

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
To find the prime factorization of number

Pre-Algebra Student Edition

The Ratio Test Use the Ratio Test to determine whether the following series converge. 11. k=1k24k

Calculus: Early Transcendentals (2nd Edition)

The 16 sequences in the sample space S.

Probability And Statistical Inference (10th Edition)

The null hypothesis, alternative hypothesis, test statistic, P-value and state the conclusion. To test: Whether...

Elementary Statistics

Replace the Cartesian equations in Exercises 53–66 with equivalent polar equations. x2 + y2 = 4

University Calculus: Early Transcendentals (4th Edition)

Fill in each blank so that the resulting statement is true. An equation that expresses a relationship between t...

Algebra and Trigonometry (6th Edition)

Knowledge Booster
Background pattern image
Math
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
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
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
Text book image
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Text book image
Mathematics For Machine Technology
Advanced Math
ISBN:9781337798310
Author:Peterson, John.
Publisher:Cengage Learning,
Text book image
College Algebra
Algebra
ISBN:9781337282291
Author:Ron Larson
Publisher:Cengage Learning
Text book image
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Text book image
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
SEE MORE TEXTBOOKS
The surface area and volume of cone, cylinder, prism and pyramid; Author: AtHome Tuition;https://www.youtube.com/watch?v=SlaQmaJCOt8;License: Standard YouTube License, CC-BY