[ Solutions to problems 1 2
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# Lecture 7: Exercises

### Suggestions for further reading

- Delta function: Arfken (chap. 8.7)
- Fourier transformation: Arfken (chap. 15)

### Questions for Review

- What is the Delta function? How can it be visualized?
- What are the properties of the Delta function? How is it related to
the Heaviside step function?
- How is the Fourier transform defined?
- How do you recover the original function from its Fourier transform?
What is the inversion theorem?
- Remember the most important properties of the Fourier transform. In
particular,
- linearity
- Fourier transform of f(ax+b)
- consequences of symmetries (Fourier transform of real functions, even/odd
functions)
- convolution theorem
- Fourier transform of derivatives
- Parseval equation

- What is the Fourier transform of the Delta function?
- What is the Fourier transform of 1?

### Problems