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 6.11, Problem 7P

Use either Stokes' theorem or the divergence theorem to evaluate each of the following integrals in the easiest possible way.

∬ ( curl V ) ⋅ n d σ over any surface whose bounding curve is in the ( x , y ) plane, where V = x − x 2 z i + y z 3 − y 2 j + x 2 y − x z k .

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Chapter 6.11, Problem 6P

Chapter 6.11, Problem 8P

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Let C be the closed, piecewise smooth curve formed by traveling in a straight line between the points (0,0,0), (2, 1,5), (1, 1,3), and back to the origin in that order. Use Stokes' theorem to evaluate the integral. [[(11xyz)dx + ( 11xyz) dx + (6xy) dy + xdz =

Verify the Stokes' Theorem in evaluating F.dr if F(x, y, z) = z² i + 2xj-y³k, where C is the circle x² + y² = 1 in xy-plane with the counterclockwise orientation looking down the positive z-axis.

Let F = Use Stokes' Theorem to evaluate So F. dr, where C is the curve of intersection of the parabolic cylinder z = y² - x and the circular cylinder x² + y² = 1, oriented counterclockwise as viewed from above.

Chapter 6 Solutions

Mathematical Methods in the Physical Sciences

Ch. 6.3 - If A=2ijk,B=2i3j+k,C=j+k, find (AB)C,A(BC),(AB)C,...Ch. 6.3 - For Problems 2 to 6, given A=i+j2k,B=2ij+3k,C=j5k:...Ch. 6.3 - For Problems 2 to 6, given A=i+j2k,B=2ij+3k,C=j5k:...Ch. 6.3 - For Problems 2 to 6, given A=i+j2k,B=2ij+3k,C=j5k:...Ch. 6.3 - For Problems 2 to 6, given A=i+j2k,B=2ij+3k,C=j5k:...Ch. 6.3 - For Problems 2 to 6, given A=i+j2k,B=2ij+3k,C=j5k:...Ch. 6.3 - A force F=2i3j+k acts at the point (1,5,2). Find...Ch. 6.3 - Prob. 8P Ch. 6.3 - Prob. 9P Ch. 6.3 - In Figure 3.5, let r be another vector from O to...

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