FW Math 321
Homework 5, F 2016/10/14
Problems due beginning of lecture on Thursday 10/20/2016, 9:30am.
Late homework not accepted. No email or web submissions.
You can discuss the homework with other students currently enrolled in Math 321 (no former
stud
Y7 o b)o\
Name . 7 . Math 321 Quiz 1, 2010/1/28
1.(5pts) Given a square ABCD, use vectors to ShOW that the two diagonals are perpen-
dicular.
B 2\= H
A i A? B3: (k+>=<-E+i>
2 _\0b+b.,~v_9i
\
:07
.33: fig ML: 0; in
A N N _\
b; L, N
-\~ Rik
I -,'Z
Name . Math 321 Quiz 8, 2010/4/15
1.(10pts) What is the Taylor series of (1:2)2 about 2 = 0? What is its radius of
convergence?
Q01 2( z)- - 2H); at rm < 1
/ 1+2: V: 0 v" :0 I\ < I
Take clerfva+ives
00 n Y!
(+%)2 M120
(>0 W m-
*3 20!) V1 1?
2
E Nl
2 24!)
Math 321 Quiz 4M October 24, 2011
Name: Evakvvsggbg D \mok
Note: Show all your work. No calculators allowed.
1. Let F: m), 27
dF/dt = mi ds = m, df/ds = m and a = d/dt.
(a) (1 point) Show that v = g.
2
(b) (3 points) Prove that if = dii: )
+ (112/071.
. 3030
Name Math 321 Quiz 4, 2010/2/25
1. (i) (3pts) What does (1 - 2: = 0 tell you about (1"?
do
(ii) (3pts) What does ("i X (1: = 0 tell you about ('1?
2 (16 a d5 (1 a 2 2
(111) (4pts) Suppose a - E = 0 and b- :1; = 0. What does 8201 x b) = 0 tell you a
Math 321 Quiz 8M November 28, 2011
Name: EVCMASQLQS D \mau
Note: Show all your work. No calculators allowed.
1. (3 points) Let p(f) = p0 pg(2 . F),'where p0, p and g are constants.
Compute fspdS, Where S is a closed surface and is the outside
unit normal
P2 0 A
Name . (j . Math 321 Quiz 2, 2010/2/4
1. Let fi be a unit vector and let 6 be any vector.
1) (3pm) Find (in.
iii) (2pts) Find (in and (ii if 73 is any nonzero vector (i.e. not necessary a unit vector).
3. = 3;? "A a fox x?
/ if? QJ. - (a )
51
. 3030
1. Let Q be an orthogonal transformation matrix.
i) (3pts) Find the (i,j)-entry of QQT.
T .= M '. T .
(QQ )U' 9&0 )9
Name Math 321 Quiz 3, 2010/2/11
ii) (3pts) Find the (i,j)-entry of QTQ.
T ' T x
(Q Q)U _ (Q )g'k Q13
1" QM Q 5'
iii) (2pts) What ar
Math 321 Quiz 7 November 2123, 2011
Name: EV ouncgzLOS \W\ow
Note: Show all your work. No calculators allowed.
1._(3 points) Consider the vector eld 17107) = f(7")f, Where 7" = [7"].
Compute f0 F - df, Where C is a curve from a point A to a point B. Is
th
_Math 321 Quiz 2W . September 28, 2011
Name: E Vaneio 5 \3 \moq
Note: Show all your work. No calculators allowed.
1. (3 points) Find vector equations for the line passing through the two
points with position vectors F1, 715 and the plane through the thr
So
Math 321 Quiz 1M September 19, 2011
Name: Evawgakos Bwrxou
Note: Show all your work. N o calculators allowed.
1., (3 points) Let (i, I; be two vectors. Show that the following identity is
true:
lax 312 +(ci-5)2=|612U3I2
\ELXCH ; \3:\ $\% A
53% : \ac\
Math 321 , Quiz 6M November 14; 2011
Name: ; \r GKNGPXDS h \M 0 UK
Note: Show all your work. No calculators allowed.
1
1. ' a = -
(3 pomts) Compute Vf, Where f (F) l2 X 77"
\iXT-W : \~3,\E\s\v\%: r swe: :6
a va
3 V 2X3 cfw_7" E)
1, 019 6
:57 V 9 :. _ A
Math 321 _ _ Quiz 8W November 30, 2011
Name: E \/ cm 36193 b _\mvo :1-
Note: Show all your work. No Calculators allowed.
1. (3 points) Let p(f) = p0 pg(2 - 7"), Where p0, p and g are Constants.
Compute fspdS, where S is a closed surface and 713 is the o
Math 321 Quiz 5W November 2, 2011
Name: EVQVQSxOS D \mqu
Note: Show all your work. No calculators allowed.
1. (3 points) A curve is parametrized in cartesian coordinates as 7" =
a: ; + y 57, + h(:r, y) 63;, where h is a differentiable function. Compute
vi
Part of Hints for Hw 9
Math 321
By Lei Li
Some easy problems
1. a). (0 2, 0 2, 0 z 4)
b). dV = dddz
c). 256
3
2. a).
b). 3
25
3
1.5
R
R 2
R
#2. For area, use dSr Area = S R2 sin dd = 0 d 0 R2 sin d = 4R2
R
R R R 2
R
Volume: V = ball r2 sin drdd = 0 dr 0 d
Part of Hints for Hw 13
Math 321
By Lei Li
1.5
1. Use the ratio test. Center is 1/2. Radius is 1. Then the domain of convergence is a disk
with radius one centered at 1/2
P
P
2. #4: The series is
(z 2 )n =
(1)n z 2n . Radius of convergence is 1.
n=0
#5:
1
FW Math 321
Homework 6, F 2016/10/21
Problems due beginning of lecture on Thursday 10/27/2016, 9:30am.
Late homework not accepted. No email or web submissions.
You can discuss the homework with other students currently enrolled in Math 321 (no former
stud
FW Math 321
Homework 4, F 2016/9/30
Problems due beginning of lecture on Thursday 10/6/2016, 9:30am.
Late homework not accepted. No email or web submissions.
You can discuss the homework with other students currently enrolled in Math 321 (no former
studen
FW Math 321
Homework 8, F 2016/11/4
Problems due beginning of lecture on Thursday 11/10/2016, 9:30am.
Late homework not accepted. No email or web submissions.
You can discuss the homework with other students currently enrolled in Math 321 (no former
stude
FW Math 321
Homework 3, F 2016/9/23
Problems due beginning of lecture on Thursday 9/29/2016, 9:30am.
Late homework not accepted. No email or web submissions.
You can discuss the homework with other students currently enrolled in Math 321 (no former
studen
FW Math 321
Homework 6, F 2016/10/28
Problems due beginning of lecture on Thursday 11/3/2016, 9:30am.
Late homework not accepted. No email or web submissions.
You can discuss the homework with other students currently enrolled in Math 321 (no former
stude
Part of anwsers to Hw 1
Math 321
Without specific declaration, the scalar set is always R, i.e. the set of all real numbers. The
problems with are for the ones who like math.
Section 1.1 #3:
Idea: Denote the set V . For any f, g V , we need to show that f
Some Hints for Hw 14
Math 321
By Lei Li
3.2
1. #4 The series is
P
(1)n z 2n . You can see that it has singularities at i. The
n=0
2.
3.
4.
5.
distance between the center and i is just the radius of convergence.
2i dn1
#7: use the Taylor series or the gene
Part of Hints for Hw 10
Math 321
By Lei Li
Some easy problems
1. c). Here, I just calculate the Jacobian:
x x x
r
(x, y, z)
y y y
J=
= r
z z z
(r, , )
r
sin cos
sin sin
cos
= r cos cos r cos sin r sin
r sin sin r sin cos
0
= r2 sin
2.
Part of Hints for Hw 10
Math 321
By Lei Li
One important concept problem
b). d~r ~ex = (dx~ex + dy~ey ) ~ex = dx. In the cases, dx = x0 (t)dt and dx = x0 (y)dy. Similar
for dy
c). Just use the relationship n
= t ~ez
3.4
1. You would get 2Area(A). Area of
Part of Hints for to Hw 3
Math 321
Section 1.6
P
2.(a). The final answer is ai . I dont want to write the corresponding
notation here.
However, if you are trying to understand Einsteins convention, you should do this.
(c). To overcome this difficulty, we
Part of anwsers to Hw 2
Math 321
The problems with are for the ones who like math.
3
P
Section 1.4 #1: ~ej w
~=
wi ji = wj
i=1
#4:
3 P
3
P
vi wj~ai ~aj
i=1 j=1
#5: (i) ai (ii) a1 b1 + a2 b2 + a3 b3 (iii) 3
rn rn
n
P 2 P 2
P
xi
yi
Extra (a). Component form
Part of Hints for to Hw 5
Math 321
Exercises in 1.10
1. ~v = (etan t 1, 12 t t2 + 1 + 21 ln(t + t2 + 1), 2(t2t+1) + 12 arctan t).
~ is
2. This problem is harder than I thought. First of all show that ~vk (parallel to B)
always zero and thus the particle i
Math 321 Quiz 1 (G)
301/302 Feb. 7, 2012
Your Name:
Instructions: This is the quiz for 301/302. (Yes, at last, Ill normalize the quiz scores such
that the sections on Tuesday and the sections on Thursday have the same average quiz
score.) You have 15 minu
Math 321 , Quiz 3W October 19, 2011
Name: EVQWeXOS D (hog
Note: Show all your work. N o calculators allowed.
1. (a) (1.5 point) Give the implicit cartesian equation of a hyperbola in
the cry-plane, having its two vertices on the :r-axis. Make a sketCh.
I Math 321: Midterm Exam 1
20 February 2013
Name: ,. 2? a EU 9
Instructions:
9 This exam consists of 5 pages, including this one. If pages are missing, let the examiner
know right away.
0 Do not unstaple the pages.
0 Attempt all FOUR (4) questions.
a Show
Math 321 ' Quiz 2M September 26, 2011
Name: EVGAKSQXOS Dwo oux
Note: Show all your work. No calculators allowed.
1. (3 points) Find vector equations for the line passing through the two
points with position vectors F1, F2 and the plane through the three
Math 321 Quiz 4W . October 26, 2011
Name: Evansejkos ngou.
Note: Show all your work. No calculators allowed.
1. Let F=F(t), 17: (r/dt 20$, ds = 1m, df/ds = mi and a = d/dt.
(a) (1 point) Show that v = g;
(b) (3 points) Prove that d =-;dg;) +(U2H) 7%.