M3337  Advanced Math
Homework 2, due 2/3
1. Evaluate the line integrals
C
F dr,
where
(a) F = (xy, 1 x2 y 2), where C is the quarter circle from (2,0) to (0,2) with
4
center at the origin.
(b) Same F as in (a) but with C the straight line segment from (2
rlx
e,
A
f,
,
=

4
= /L 5,inM)
h
/L
h
I
D
b
t
~ (
i +
5 , , ~ ( e,
(
3
+
 ~ J s L (
L
1 E  Y ~ ~=s cfw_
t
?
12

5
C
a
.4
eI
 I r n ~ l ~ > q0
.t
Q
4
P,
4
k 5 u .
S,n&
/l/L
T/L
(
5
i
.
+
1
v
0
c a r 3 ~ r t G Ak
u
=
I,

[G

, J~JL
4
+ t i ) G S
M3337  Advanced Math
Homework 5, due 2/24
1. Use the Stokess theorem to nd the line integrals
C
u dr
for the following vector eld and curves:
(a) u = (y, xz 3 , zy 3 ); C: x2 + y 2 = 4, z = 3
(b) u = (ez , ez sin y, ez cos y); C: edge of surface S formed
M3337  Advanced Math
Homework 4, due 2/17
1. Find the directional derivative of f (x, y, z) = xe2yz at the point P (3, 0, 2) in the
2
direction of u = ( 2 , 3 , 1 ).
3
3
2. Find the potential of the conservative vector eld u = (3x2 + 2xy, x2 , 2z).
3. Us
M3337  Advanced Math
Homework 3, due 2/10
1. Evaluate
S
f (x, y)dS,
where f (x, y) = x4 + y 4 and S: r(u, v) = (5 cos u, 5 sin u, v) with 0 u and
0.2 v 0.2.
2. Evaluate
f ndS,
S
where
(a) f = (x2 , ey , 1), S: x + y + z = 1, x 0, y 0, z 0.
(b) f = (sinh(
M3337  Advanced Math
Homework 1, due 1/27
1. Find all three angles of the triangle with vertices at A(0, 0, 0), B(4, 2, 1),
C(1, 2, 4).
2. Find the work done by the force F = (2, 6, 6) N as it moves a mass of
m = 40 kg between the points A : (3, 4, 0) an
Practice First Exam for Math 3337
Sept. 27, 2016
I pledge that I do not give or receive help on this exam.
Signature:
Name: (please print)
Note: Please write down your answer to each problem step by step. Omitting necessary intermediate steps may result i
Answer sheet: Practice First Exam for Math 3337
Sept. 27, 2016
Problem 1. Let
f (x, y, z) = xy 2 ez ,
(a)
Find f
Answer:
and
F (x, y, z) = hxy, yz, zxi .
div( F )
f = y 2 ez , 2xyez , xy 2 ez .
div( F ) = y + z + x.
(b)
Find curl( F )
Answer:
e
e
e
1
2
3
Syllabus for MATH 3337:
Advanced Mathematics for Science and Engineering
Fall 2016
Instructor:
Dr. Yunkai Zhou
(yzhou@smu.edu,
Time & Location:
11:00 12:20 pm, Clements Hall 126
Office hours:
Tuesday & Thursday, 3:306:00pm,
Clements Hall 133
x82512)
Textb
Math 1303
Name:
_
Quiz #3 (Sec. 1.6 1.7)
You must show all work on this page. Partial credit will be given for work that is appropriate to the problem.
22 x3+10=48
1. Solve for x:
2. Solve for x: (x + 5)2 + 3 = (x 2)2
3. Solve for x:
4 x 8 9 11
4. Solve
Exam 3: Least Squres Fitting, Numerical Integration, and Root Finding
MATH 3315 / CSE 3365 : 801C Spring Semester 2007 Total points: 100 Thursday 26 April
The SMU honor code applies. Don't forget to write and sign your name. An answer should include