Using Green's theorem, evaluate Fir)-drcounterclockwise around the boundary curve C of the region R, where 1. F=Bry. ). R the rectangle with vertices (0, 0). (3, 0). (3, 2). (0, 2)
Using Green's theorem, evaluate Fir)-drcounterclockwise around the boundary curve C of the region R, where 1. F=Bry. ). R the rectangle with vertices (0, 0). (3, 0). (3, 2). (0, 2)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question

Transcribed Image Text:PROBLEM SET 10.4
1-12 EVALUATION OF LINE INTEGRALS
BY GREEN'S THEOREM
13-16
INTEGRAL OF THE NORMAL DERIVATIVE
Using (9), evaluate
ds counterclockwise over the
Using Green's theorem, evaluate Fir) dr counterclockwise
around the boundary curve C of the region R, where
boundary curve C of the region R.
13. w sinh x, R the triangle with vertices (0, 0). (2, 0),
(2, 1)
14. w =x + y. C: + y = 1. Confirm the answer by
direct integration.
15. w 2 In (x + y+xy. R: 1Sys 5 -.x20
16. w = xy + xy"., R: x +ys 4. y2 0
1. F-y . R the rectangle with vertices (0, 0).
(3, 0). (3. 2). (0. 2)
2. F = [y sin x. 2r cos y). R the square with vertices
(0,0%. (.0), m 까 (0. m
3. F [-y. , Cthe circle x+ y 25
4. F = [-e. . R the triangle with vertices (0, 0).
(2. 0). (2. 1)
5. F le 1 R the triangle with vertices (0, 0).
(1. 1), (1, 2)
6. F [x cosh y. sinh y). R: xS y S x. Sketch R.
7. F = [? + y. - y). R: 1sys2 -. Sketch
COs
17. CAS EXPERIMENT. Apply (4) to figures of your
choice whose area can also be obtained by another
method and compare the results.
18. (Laplace's equation) Show that for a solution w(x, y)
of Laplace's equation Vw = 0 in a region R with
boundary curve C and outer unit normal vector n,
R.
8. F [e cos y.-e sin yl. R the semidisk
dx dy
(10)
9. F = grad (r cos cay), R the region in Prob. 7
10. F= [r In y. ye R the rectangle with vertices (0, 1).
(3, 1). (3, 2). (0. 2)
11. F= [2r- 3y. x+ 5y), R: 16+ 25ys 400, y 20
12. F = -th), R: 1s+ s 4, x2 0,
y 2x. Sketch R.
ds.
%3D
19. Show that w = 2e cos y satisfies Laplace's equation
w = 0 and, using (10), integrate w(awlon)
counterclockwise around the boundary curve C of the
square 0 SxS 2,0 sys2.
Expert Solution

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps

Recommended textbooks for you

Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated

Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY

Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated

Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY

Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,

