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Problem Set 5

Page history last edited by sidjaggi 13 years, 4 months ago

ERG2011A Advanced Engineering Mathematics (Syllabus A),
Problem Set 5
Kreyszig 9th edition - Chapters 5.1 - 5.5


1. (Taylor series)

 

The Taylor series expansion for Formula is


                                                      Formula


Compute the Taylor series of the following functions


Formula


2. (Power series solutions)

 

Kreyszig 9th Edition Problem set 5.1, problems 1 to 5, 5.2, problems 16, 18, 21, 23.
Solve the below ODE by using power series method.


Formula


Find a power series solution in power of Formula. (Show the details of your works.)


Formula

 

3. (Radius of convergence)

 

Kreyszig 9th Edition Problem set 5.2, problems 1, 3, 5, 6, 11, 12, 13, 15
Determine the radius of convergence. (Show the details.)


Formula


This is often convenient or necessary in the power series method. Shift the index so that the power under the summation sign is Formula. Check by writing the first few terms explicitly. Also determine the radius of convergence Formula.


Formula


4. (Legendre's equation) (ADVANCED TOPICS QUESTION)

 

Rederive the solution of Legendre's equation discussed in class


                                                      Formula


for integral Formula. Read the corresponding section in the textbook or worksheet. Problem set 5.3, problems 4, 14(d). Noting that Formula and Formula, use 14(d) to compute Formula for Formula, and compare with equation (11') on page 180.

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