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5. Find all analytic functions f such that Ref + Im f = ry.

5. Find all analytic functions f such that Ref + Im f = ry.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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5. Find all analytic functions f such that Ref + Im f = xy. 6. Suppose that u is a harmonic function and that vis a harmonic conjugate of u. Show that ди ди Ә Ju ди +u 21 ( 1 - ) - 57 ( дх дх дг ду дх
Transcribed Image Text:5. Find all analytic functions f such that Ref + Im f = xy. 6. Suppose that u is a harmonic function and that vis a harmonic conjugate of u. Show that ди ди Ә Ju ди +u 21 ( 1 - ) - 57 ( дх дх дг ду дх
ev B) ANALYTIC AND HARMONIC FUNCTIONS 4. a) v = 3x²y-y³+y²+y-z²+C, CER, b) v = 2xy + C, CER, c) v = -cosh a cos y + C, CER f(2)=(2²+C), CER. 8. f(z)= az+bz², a,b € C. d) v = e(y siny-rcos y) + C, CER, e) v = n(2² + y²) + C, CER 1 9. f(z) = 2³+iaz² + bz+ic, a, b, c € R. 10. f(2)= ae+ib, a € C, bER.
Transcribed Image Text:ev B) ANALYTIC AND HARMONIC FUNCTIONS 4. a) v = 3x²y-y³+y²+y-z²+C, CER, b) v = 2xy + C, CER, c) v = -cosh a cos y + C, CER f(2)=(2²+C), CER. 8. f(z)= az+bz², a,b € C. d) v = e(y siny-rcos y) + C, CER, e) v = n(2² + y²) + C, CER 1 9. f(z) = 2³+iaz² + bz+ic, a, b, c € R. 10. f(2)= ae+ib, a € C, bER.
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