Multivariable Calculus for Engineering Students:
HOMEWORK PAGE
Mathematics 69.204, Section B, Fall, 1998.
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Homework
Fourier Series
FS package: p537 #13, 15, 19, 21
p543 #1, 3, 5
p554 #1, 3, 7
Polar Coordinates
Sec 10.3: # 7, 9, 12, 15, 25
Sec 10.5: # 11, 12, 16
Cylindrical and Spherical Coordinates
Sec 12.5: # 1, 3, 8
Sec 12.8: # 25, 29, 31, 33, 45, 47, 49
Functions of Several Variales
Sec 13.4: # 1 - 23 (odd)
Sec 13.4: # 31 - 40 (odd)
Sec 13.5: # 1-28 (odd)
Sec 13.7: # 1-18 (odd)
Sec 13.8: #1-20 (odd)
Sec 13.9: # 3, 5, 7, 11, 13, 15
Sec 13.10: # 1-16 (odd)
Multiple Integrals
Sec 14.2: # 13, 19, 23
Sec 14.3: # 3, 5, 11, 19
Sec 14.4 # 3, 9, 15
Sec 14.5 # 1, 3, 5, 13
Sec 14.6 # 3, 5, 7, 15
Sec 14.7 # 5, 7, 15
Sec 14.8 # 3, 7
TEST 4
1 Question on Iterated integrals (the interchange of the order of integration in a double integral)
1 Question on Double integrals and polar coordinates
1 Question on a triple integral in spherical coordinates
Chapter 15
Sec 15.1 # 15-24 (odd)
Sec 15.2 # 1-10 (odd)
Sec 15.3 #1-15 (odd)
Answers to B5 and B6 of the Sample Final Examination
B5. f is an odd function so all an = 0. The bn are given as usual since f is function of period 2L. This gives bn=(2k/nPi)(1+(-1)n-1), for each n >= 1. The series is a pure Fourier sine series.
B6. f(x,y) = xe2y+y+C, where C is a constant.