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# Lecture
6:
Exercises

### Suggestions for further reading

- Euler-Moivre equation: Arfken (chap. 6.1)
- Fourier expansion: Arfken (chap. 14)

### Questions for Review

- How are trigonometric functions and the exponential function
related? How do you prove this relationship?
- Using the Euler-Moivre equation, how can you represent
arbitrary complex numbers?
- How can you use the Euler-Moivre equation to obtain
addition theorems for trigonometric functions?
- What is a Fourier expansion? What are the basis functions
in which you expand? Are there several possibilities?
- To what kind of functions does the Fourier expansion apply?
- What are the orthogonality relations for trigonometric
functions?
- What is the meaning of the Kronecker symbol?
- How do you calculate the coefficients of the Fourier expansion?
- What can you say about the Fourier coefficients of even/odd
functions?
- Give a heuristic argument why periodic functions should have
a Fourier expansion.

### Problems