v(x. y)= (ar² + 3y². yy), (x,y) € R², where a, 3, 7 are nonzero real numbers. (i) Let C be a circle of radius R> 0 centered at (a,b) R2 such that the distance from (a, b) to (0,0) is greater than R. Compute the index of e around C. (ii) Let C be any closed curve in R2 not enclosing (0,0) inside. Compute the index of e around C. (iii) In either case (i) or (ii), show that v(x, y) = 0 indeed has no solution inside C and explain your finding in view of your results in (i) and (ii). (Hint: It may be hard to compute (i) directly. However, you may study what happens when you shrink R down to zero. You need to justify why you can do so.)
v(x. y)= (ar² + 3y². yy), (x,y) € R², where a, 3, 7 are nonzero real numbers. (i) Let C be a circle of radius R> 0 centered at (a,b) R2 such that the distance from (a, b) to (0,0) is greater than R. Compute the index of e around C. (ii) Let C be any closed curve in R2 not enclosing (0,0) inside. Compute the index of e around C. (iii) In either case (i) or (ii), show that v(x, y) = 0 indeed has no solution inside C and explain your finding in view of your results in (i) and (ii). (Hint: It may be hard to compute (i) directly. However, you may study what happens when you shrink R down to zero. You need to justify why you can do so.)
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
Pls send me solution fast within 10 min and i will rate instantly for sure!!!
Solution must be in typed form!!
Transcribed Image Text:v(x, y) = (ar² + 3y², yy), (x,y) = R²,
where a, 5, 7 are nonzero real numbers.
(i) Let C be a circle of radius R> 0 centered at (a,b) € R2 such that the distance from (a, b) to (0,0)
is greater than R. Compute the index of v around C.
(ii) Let C be any closed curve in R² not enclosing (0,0) inside. Compute the index of v around C.
(iii) In either case (i) or (ii), show that
v(x, y) = 0
indeed has no solution inside C and explain your finding in view of your results in (i) and (ii).
(Hint: It may be hard to compute (i) directly. However, you may study what happens when you shrink
R down to zero. You need to justify why you can do so.)
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 4 steps with 119 images
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,
