Other Old Math 317 Final Exam Questions
1) Consider the vector eld
F(x, y, z) = (2xyz, x2 z, x2 y + 2z)
describing a force.
a) Show that F is conservative.
b) Find the work done by F in moving an object along the line segment beginning at (1, 1, 1) and en
This examination has 11 pages including this cover
The University of British Columbia
Sessional Examination December 2005
Mathematics 217
Multivariable and Vector Calculus
Time: 2 1 hours
2
Closed book examination
Name
Signature
UBC Student Number
Special
This examination has 10 pages including this cover
The University of British Columbia
Final Examination 12 December 2006
Mathematics 217
Multivariable and Vector Calculus
Closed book examination
Name
Time: 150 minutes
Signature
UBC Student Number
Special
Be sure that this examination has 10 pages including this cover
The University of British Columbia
Sessional Examinations - December 2003
Mathematics 217
Vector Calculus
Closed book examination
Print NaJne _____________ Signature
Student Number Instr
MATH 200 Winter 2009 Solutions
1.
(i) To use implicit dierentiation, we rst need to get our function F (x, y, z) satisfying F (x, y, z) = k for some constant k. The obvious choice here (although not
z
z
the only possibility) is F (x, y, z) = z 4 xy 2 z 2
V = (t2 + 2xy) + (t y 2 + x + z) +
i
j
tk
u v w
+
+
= 2y 2y
x y
z
= 0
(x, y, z, t) = (1, 2, 3, 4)
x
ax
u
u
u
u
+u
+v
+w
t
x
y
z
= 2t + t2 + 2xy (2y) + t y 2 + x + z (2x) +
t (0)
= 2 4 + 42 + 2 1 2 (2 2) + 4 22 + 1 + 3 (2 1) + 0
= 8 + 20 4 + 4 2
= 96 2
s
Suggested Problems from
Mathematics Text
Week # 5
The following is a list of extra problems from the text for
you to try:
16.1: 117(as needed), 2932, 35
16.7: 9, 11, 13, 17, 19, 2132 as needed,
39, 43, 47
Suggested Problems from
Mathematics Text
Week #5 1
The following is a list of extra problems from the text for
you to try:
15.1: # 1, 9
15.2: # 3 21 (as needed to get the idea), 29, 35, 37
15.3: # 5, 9, 11, 13, 17, 21, 25, 39, 57
15.4: # 1, 5, 9, 11, 13,
Suggested Problems from
Mathematics Text
Week 41 2
The following is a list of extra problems from the text for
you to try:
15.5: 1, 5, 11, 15
Chapter 12 review: concepts, TF quiz, 127 (as needed)
12.6: 1, 3, 5, 9, 11, 13212347
15.7: 521 (as needed), 25, 2
Suggested Problems from
Mathematics Text
Week # 3
The following is a list of extra problems from the text for
you to try:
14.1: #15, 19
14.3: #5, 9, 21, 33, 53, 57, 83
14.4: # 1, 3, 5, 21, 35, 37, 41
14.5: #5, 11, 25, 35, 45
14.6: #5, 11, 19, 23, 29, 33,
Mech 222 Quiz 2 2011W
Solutions to Thermodynamics Questions
1. (14 Marks) Explain 4 important ideas about temperature T and total energy E. Use a
complete sentence for each idea (i.e., 2x4=8 sentences total). Equations or simple sketches
are welcome but n