Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Example: 10.9 Write down all possible Laurent expansions of the function ƒ(2) = (z−1)(z-2) around the point zo 3. = First of all we can use partial fractions to write f(2)=2²2-Å· The function has poles at z = 1,2 so the regions of interest are |z3| < 1, 1 < |z − 3| < 2 and |z − 3| > 2. This will give three different Laurent expansions. We can write 2 2 2-2 2 3+1 2Σ(-1)^(z − 3)"

Example: 10.9 Write down all possible Laurent expansions of the function ƒ(2) = (z−1)(z-2) around the point zo 3. = First of all we can use partial fractions to write f(2)=2²2-Å· The function has poles at z = 1,2 so the regions of interest are |z3| < 1, 1 < |z − 3| < 2 and |z − 3| > 2. This will give three different Laurent expansions. We can write 2 2 2-2 2 3+1 2Σ(-1)^(z − 3)"

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
See similar textbooks
icon
Related questions
Question

How did they get that partial fraction. When I did it I got fractions. 

Done Rangle 1.4: La fall, Wis the Laurent expansion BT is analytic. It is the posible to proses L in this ring. Ikl, le ce partial fue deption, we bod Note that it came the c of the Laurent series be Example 10. bet atbWitte Latent expanden aroud. We wet to peal of X of 2-2 with post exposats it is tic in the hel-2 <2 In order to see fillon Lorne noin in this asulas, w festa partial fraction depodtis sa wake -1-(7) which cover ke-21. Tha A AL(A) which conges for< 1., that is, |-> 1. Putting the which is wild ke 1-2 Zeroes and Poles We can clasly the ladeal deketin of alytic actions Sup that) wanadal duty. Thes 1 do il pr Lai 00) lepole af onder the anglaive power in the pracipal part la 2 E21 scalad a szuple pola (1) analgicky the principal part contala 70-l Examples Example 10.6: The best has a movable dar Example 10.7: The reaction fiz) – 4 baxa cible pole at (¹4) S Examples Example 16. The form) layak 2-344148 abeme La We can write Examples 10.a Wise ees of were latest caperolase of Examples as moestid si akal, by malige" is powers of 1/0 which is covererke (2-3 c il tuo principal part of the For the other fraction, we can AARD which is 3) Examples AAAAA which is cover-11 Fox-ci war that For 14-32 mm a will ge the ------ Fly, -3>2wtar --- ----- ---- 10 of 12 complex10_ce1b37448f28a25c7b4bd42caa064028 Example: 10.9 Write down all possible Laurent expansions of the function f(z) : = 3. (z−1)(z–2) around the point zo = First of all we can use partial fractions to write ƒ(z) : = 2 2-2 The function has poles at z = 1,2 so the regions of interest are |z − 3| < 1, 1 < |z − 3| < 2 and |z − 3| > 2. This will give three different Laurent expansions. We can write ਜਣੇ = 2 a 2 z−3+1 (-1)" (z − 3)" 2 1 2-2 2-1
Transcribed Image Text:Done Rangle 1.4: La fall, Wis the Laurent expansion BT is analytic. It is the posible to proses L in this ring. Ikl, le ce partial fue deption, we bod Note that it came the c of the Laurent series be Example 10. bet atbWitte Latent expanden aroud. We wet to peal of X of 2-2 with post exposats it is tic in the hel-2 <2 In order to see fillon Lorne noin in this asulas, w festa partial fraction depodtis sa wake -1-(7) which cover ke-21. Tha A AL(A) which conges for< 1., that is, |-> 1. Putting the which is wild ke 1-2 Zeroes and Poles We can clasly the ladeal deketin of alytic actions Sup that) wanadal duty. Thes 1 do il pr Lai 00) lepole af onder the anglaive power in the pracipal part la 2 E21 scalad a szuple pola (1) analgicky the principal part contala 70-l Examples Example 10.6: The best has a movable dar Example 10.7: The reaction fiz) – 4 baxa cible pole at (¹4) S Examples Example 16. The form) layak 2-344148 abeme La We can write Examples 10.a Wise ees of were latest caperolase of Examples as moestid si akal, by malige" is powers of 1/0 which is covererke (2-3 c il tuo principal part of the For the other fraction, we can AARD which is 3) Examples AAAAA which is cover-11 Fox-ci war that For 14-32 mm a will ge the ------ Fly, -3>2wtar --- ----- ---- 10 of 12 complex10_ce1b37448f28a25c7b4bd42caa064028 Example: 10.9 Write down all possible Laurent expansions of the function f(z) : = 3. (z−1)(z–2) around the point zo = First of all we can use partial fractions to write ƒ(z) : = 2 2-2 The function has poles at z = 1,2 so the regions of interest are |z − 3| < 1, 1 < |z − 3| < 2 and |z − 3| > 2. This will give three different Laurent expansions. We can write ਜਣੇ = 2 a 2 z−3+1 (-1)" (z − 3)" 2 1 2-2 2-1
3) | f(2) (B) 1-2 18(2) = 2 2A + B = AZ-2)+B(z-1) 20:3 12-1/22) + Z-2 A2-2A+BZ-B- - 24-B=O→ -2A+H-A=o 21 A=L (A+B=1-2B=#1-A - 1 - = =-=-=-=-=-=- 3 0 구 1 1-7-3) _+ 21 13 21 32-2 A® ① ++칼(토) 글 치료께 기 3 2-1 ㅎ ㅎㅇ 4
Transcribed Image Text:3) | f(2) (B) 1-2 18(2) = 2 2A + B = AZ-2)+B(z-1) 20:3 12-1/22) + Z-2 A2-2A+BZ-B- - 24-B=O→ -2A+H-A=o 21 A=L (A+B=1-2B=#1-A - 1 - = =-=-=-=-=-=- 3 0 구 1 1-7-3) _+ 21 13 21 32-2 A® ① ++칼(토) 글 치료께 기 3 2-1 ㅎ ㅎㅇ 4
Expert Solution
steps

Step by step

Solved in 3 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
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…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS