MA 528 Practice Problems for Final Exam
Problem 1:
Let F = [x cosh(y ), x2 sinh(y )]. Using Greens theorem, evaluate
F dr
C
around the boundary curve of the region R, where R : x2 y x.
Problem 2:
Evaluate the integral
curl(F ) n dA
S
directly for F = [z 2
MA 528 PRACTICE PROBLEMS
1. Find the directional derivative of f (x, y ) = 5 4x2 3y at (x, y ) towards the origin
a. 8x 3
b.
8x2 3y
8x 3
c.
64x2 + 9
x2 + y 2
d. 8x2 + 3y
e.
8x2 + 3y
x2 + y 2
.
2. Find a vector pointing in the direction in which f (x, y,
MA 52800 Spring 2012
Midterm 2
April 4, 2012
Faculty: B. Kaufmann
Name:
Signature:
Student ID Number:
Section (choose one):
PTR live class in Potter
ONC distance learning
EPE engineering professional education
Directions: Work on as many of the problems b
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AA XT C @r P F x ~ Cr Q G XT FT QX iC V VF rC F x s Ar X Xr xv s F
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Syllabus
MA 52800 Advanced Mathematics for Engineers and Physicists II
Spring 2013
Instructor: Prof. E. Birgit Kaufmann
Office: Math 748
Telephone: (765) 494-3173
E-Mail: ebkaufma@math.purdue.edu
Office Hours: M 11:30-12:20 pm
Th 1:30-2:20 pm
Lectures: MW