**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 is

Compute the Taylor series of the following functions

**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.

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

**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.)

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

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

Rederive the solution of Legendre's equation discussed in class

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

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