Mathematical Methods in the Physical Sciences

3rd Edition

ISBN: 9780471198260

Author: Mary L. Boas

Publisher: Wiley, John & Sons, Incorporated

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Textbook Question

Chapter 14.6, Problem 24P

Find the residues of the following functions at the indicated points. Try to select the easiest of the methods outlined above. Check your results by computer.

1 − cos 2 z z 3 at z = 0

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Chapter 14.6, Problem 23P

Chapter 14.6, Problem 25P

Students have asked these similar questions

A classmate is building a mathematical model for the temperature in his home during the summer. He explains that, without air conditioning, his home is hottest at 3:00 p.m. His model considers temperature, T, in degrees Fahrenheit, as a function of the number of hours since 6:00 a.m., h. He produces the equation, T (h) = -12 cos( (h – 1)) + 75. Why might his equation be invalid for this situation? O The period of 12 hours indicates that two highs occur throughout the day. O The maximum temperature for the function doesn't occur at 3:00 p.m. in the model. The amplitude must be incorrect. O The sine function is more accurate in modeling these temperatures. O The maximum temperature for the function doesn't occur at 3:00 p.m. in the model. The horizontal shift must be incorrect.

Q1. Sketch the graph of y = 2 cos(x – n) or odd , then show if the function is even

Compare the phase shift and amplitude of y=-cos(x-180∘) and y=-2sin(x-90∘). Which of the following choices is the correct comparison? a The cosine function has a phase shift that is 12 that of the sine function and in the same direction; the amplitude of the cosine function is 2 times that of the sine function. b The cosine function has a phase shift that is 12 that of the sine function and in the opposite direction; the amplitude of the cosine function is 12 that of the sine function. c The cosine function has a phase shift that is 2 times larger than the phase shift of the sine function and in the same direction; the amplitude of the cosine function is 12 that of the sine function. d The cosine function has a phase shift that is 2 times larger than that of the sine function and in the opposite direction; the amplitude of the cosine function is 2 times that of the sine function.

Chapter 14 Solutions

Mathematical Methods in the Physical Sciences

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