[ Solutions to problems 1 2 3 4 5 | Lecture 6 | Home | Instructor ]

# Lecture 6: Exercises

• 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.