Experiments with Fourier Series

Part 1: Synthesis of Periodic Functions

We begin by experimenting with the construction of complex periodic functions out of the simple trigonometric building blocks, sine and cosine.

1. In your worksheet, create a complicated periodic function, starting from a constant function, by adding one at a time the given trigonometric terms of orders 1, 2, 3, 4.
2. Continue the construction by adding your own order-five term.
3. Describe briefly how the graphs change as higher-order terms are added.