f (x, y) ~ bo + b1,0(x − 1)+b0,1(y−2)+ b2,0 (x - 1)² + b₁,1(x − 1)(y-2) + bo,2(y − 2)² +…...
f (x, y) ~ bo + b1,0(x − 1)+b0,1(y−2)+ b2,0 (x - 1)² + b₁,1(x − 1)(y-2) + bo,2(y − 2)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:Suppose you want to find an approximate representation for a function z =
f(x, y) that is valid near x = 1, y = 2. Namely, you want to have
f (x, y) ~ bo + b1,0(x − 1) + bo,1(y−2)+
b2,0(x − 1)² + b₁,1(x − 1)(y − 2) + bo,2(y − 2)² +....
a. Use the ideas from the beginning of this chapter to find the coefficients.
b. What are the four coefficients for the third order terms that have the form
(x - 1)³, (x - 1)²(y − 2), (x − 1)(y-2)², (y-2)³?
c. How many coefficients are needed for the fourth order terms?
d. Find the Taylor series approximation up to order two near x = 0, y = л of
f(x, y) = ex cos(y).
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