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The video aims to represent a complex periodic function, like a square wave, as an infinite sum of simpler sinusoidal components. This decomposition is highly useful because many differential equations are much easier to solve when the inputs are sines and cosines, and it serves as the foundation for signal processing.

Conditions: The target function is periodic.; The proposed representation uses sines and cosines with different periods or frequencies.

The video aims to represent a complex periodic function, like a square wave, as an infinite sum of simpler sinusoidal components. This decomposition is highly useful because many differential equations are much easier to solve when the inputs are sines and cosines, and it serves as the foundation for signal processing.

Conditions: The target function is periodic.; The proposed representation uses sines and cosines with different periods or frequencies.

The period of the square wave is $2\pi$ seconds per cycle, and its frequency is $\frac{1}{2\pi}$ cycles per second (or hertz). Frequency is defined as the reciprocal of the period.

Conditions: The function is periodic.; The horizontal axis represents time in seconds.

The period of the square wave is $2\pi$ seconds per cycle, and its frequency is $\frac{1}{2\pi}$ cycles per second (or hertz). Frequency is defined as the reciprocal of the period.

Conditions: The function is periodic.; The horizontal axis represents time in seconds.