Math 21D Homework
Classical Homework Assignments
These problems are NOT required for submission. Even though these problems are optional, you are responsible for knowing how to solve all of them and are highly encouraged to try as many as possible.
Solutions are provided by Dr. Kouba.
NOTE: All of the numbers here refer to 12th Edition of our textbook (NOT the 13th Edition). I've provided copies of the problem sets for reference.
HW#1: Section 15.1 (pg 858): # 5, 6, 12 ... Solutions
HW#2: Section 15.2 (pg 865): # 19, 21, 23-26, 28, (Setup but don't evaluate the integrals for the next 6 problems) 33, 35, 37, 38 (Change e^x to e^y), 40, 42, 47-49, 52, 54, (Setup both orders of integration but don't evaluate the integrals for the next 2 problems) 55, 56, (Setup but don't evaluate integrals for the next 7 problems) 57, 59-63, 69, 72, 77, 79 ... Worksheet 1 ... Solutions
HW#3: Section 15.3 (pg 870): # (Setup but don't evaluate integrals for the first 9 problems) (Setup integrals using both vertical and horizontal cross-sections for first 3 problems) 2, 3, 6, 7, 13, 15-18, 19a, 21 (Change region R to region bounded by:y=2x, y=0, x=2), 22 (Change function to 1/(x+1)y and change region R to region described by: 0 <= x <=1, e^x <= y <= e) ... Solutions
HW#4: Section 15.4 (pg 875): # 9, 10, 13, 14, 17, 18, 28-30, (Setup but don't evaluate integrals for the next problem) 32, 33, 36, 37, 41a, 44, 46 ... Solutions
HW#5: Section 15.5 (pg 877): # 7, 8, 11, 16, 17, 19, 20, (Setup but don't evaluate integrals for the next 10 problems) 21, 23-25, 27, 29, 33, 34, 36, 38, 41, 42 ... Solutions
HW#6: Section 15.6 (pg 891): # (Setup but don't evaluate integrals) 1, 3, 6-8, 12-14, 16, 19 ... Solutions
HW#7: Section 15.6 (pg 891): # 21, 22 (Find the moment of inertia about a.) the x-axis and b.) the origin only.), 23 (Assume that the density at point (x,y,z) is x+y+z+2. Find the moment of inertia about the y-axis and center of mass only.), 25a (Assume that the density at point (x,y,z) is e^-(x^2+y^2+z^2).), 29, 31abc (On part c. find the moment of inertia about the z-axis and the moment of inertia about the origin only.), 33 ... Solutions
HW#8: Section 15.7 (pg 901): # 1, 6, 8, 10, (Setup but don't evaluate integrals for the next 15 problems) 11-13, 14 (Evaluate this one), 16, 18, 19, 43, 44, 47, 53, 56, 63, 68 ... Solutions
HW#9: Section 15.7 (pg 901): # 21, 24, 26, 27, 30, (Setup but don't evaluate integrals for the next 18 problems. Use spherical coordinates on all problems except 41ab.) 31-35, 37, 38, 40ab, 41abc, 42b (Assume density at point P=(x,y,z) is z), 46, 52, 56, 65, 70 (Find x bar only) ... Solutions
HW#10: Section 15.8 (pg 913) (SKIPPED UNTIL END OF QUARTER IF TIME PERMITS): # 1, 4, 6, 8-10, 12, 14, 17a, 18, 22, 24 ... Solutions
HW#11: Section 13.1 (pg 731): # 1, 3, 4, 6, 8, 10, 12, 13, 15, 17, 19, 22, 23de, 24, 25, 25, 34 ... Solutions
HW#12: Section 13.2 (pg 738): # 1, 4, 6, 15, 19-23, 34, 36 ... Solutions
HW#13: Section 13.3 (pg 745): # 1, 3, 6, 7, 9, (For problems 12-14 write time t as a function of arc length s and write position vector function r bar as a a function of s.) 12-14, 17, 19, 20 ... Solutions
HW#14: Section 13.4 (pg 751): # 2-5, 9, 11, 13, 14, 17, 19, 21, 22 ... Solutions
HW#15: Section 16.1 (pg. 923): # 1-8, 10-13, 15-18, 27, 30, 33, 34 (Find y bar only.), 35a , 37, 39 (Assume that density at point P=(x,y,z) is z+1. Find moment of inertia about the z-axis, moment of inertia about the origin, the z bar coordinate for center of mass, and the z bar coordinate for centroid.) ... Solutions
HW#16: Section 16.2 (pg 935): # 1, 3-6, 7abc, 12abc, 19, 21, 23, 25-28, 39 (Do not plot horizontal and vertical components.), 40 (Do not plot horizontal and vertical components.), 43 ... Solutions
HW#17: Section 16.2 (pg 935): # 29a, 30, 32, 33, 35ab, 36, 47, 50, 51, 53 ... Solutions
HW#18: Section 16.3 (pg 947): # 1-10, 13, 14, 16, 17, 19, 20, 24, 25, 37 ... Solutions
HW#19: Section 16.4 (pg 958): # 1, 2, 4, 5, 7, 8, 14-17, 19-25, 30, 33, 34, 37 ... Solutions
HW#20: Section 16.5 (pg 969): # 1, 4, 5, 7, 9, 11, 14a, 17, 20, 24, 37, 39, 41, 42, 43 (Assume that c=3.), 48 ... Solutions
HW#21: Section 16.6 (pg 979): # 1, 4, 8, 19, 21, 23, 24, 25, 9 (Assume that a=1.), 11, 13, 39-41, 34-37, 43 (Find x bar only. Find z bar first and use symmetry of region to conclude that x bar = y bar = z bar.), 45 (Find z bar only and the moment of inertia.) ... Solutions
HW#22: Section 16.7 (pg 988): # 1, 3, 6, 7, 8, 13, 15, 17 ... Solutions
HW#23: Section 16.8 (pg 999): # 5, 6c, 7, 8, 14, 16, 26 ... Solutions