Find the one-dimensional Greens function for the interval

Chapter 7, Problem 1

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QUESTION:

Find the one-dimensional Green’s function for the interval. The three properties defining it can be restated as follows.

 (i) It solves  for  (“harmonic”).

 (ii) .

 (iii) is continuous at  and  is harmonic at .

Questions & Answers

QUESTION:

Find the one-dimensional Green’s function for the interval. The three properties defining it can be restated as follows.

 (i) It solves  for  (“harmonic”).

 (ii) .

 (iii) is continuous at  and  is harmonic at .

ANSWER:

Step 1 of 3

Green's Function: The Green's Function for any half space  is given by:

                                           

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