A proof of Parseval's theorem for trigonometric Fourier series is outlined.

We show how to use index notation and sum over row and column indices to perform matrix multiplication. The Einstein summation convention is introduced.

The complex Fourier coefficients are calculated for the function e^t with period 2 pi.

In this recording use the inverse function rule for differentiation to find the derivate of the inverse sine of x. This example includes discussion of the importance of looking at the graph of such a function, to see whether it is increasing or decreasing.

In this recording use the inverse function rule for differentiation to find the derivate of the inverse sine of x. This example includes discussion of the importance of looking at the graph of such a function, to see whether it is increasing or decreasing.

We show how to use index notation and sum over row and column indices to perform matrix multiplication. The Einstein summation convention is introduced.

The complex Fourier coefficients are calculated for the function e^t with period 2 pi.

Parseval's theorem is used to achieve a bonus result for the sum of the series of reciprocal fourth powers of odd integers.

Parseval's theorem is used to achieve a bonus result for the sum of the series of reciprocal fourth powers of odd integers.

Further use of Fourier series to find the sum of a series involving alternating signed reciprocals of odd integers.