FOURIER SERIES This slide show consists of graphs of various functions together with some of their Fourier Series approximations. When viewing the slides, the following keys are operational: HOME takes you to the first slide in the sequence you selected END takes you to the last slide in the sequence you selected UP ARROW takes you to the previous slide in the sequence you selected F9 immediately quits the program These keys do NOT operate like that while you are reading this document. A. Triangular Wave The function here is x if -ã/2 < x < ã/2 ã - x if ã/2 < x < 3ã/2 and has period 2ã. The first slide shows this function for -2ã < x < 2ã. The next 6 slides show the Fourier series expansion out to terms 1, 2, 3, 4, 5, 6, superimposed on the function. B. Square Wave The function here is -1 if -2 < x < 0 1 if 0 < x < 2 and has period 4. The first slide shows this function for -4 < x < 4. The next 11 slides show the Fourier series expansion out to terms 1, 2, 3, ... , 9, 10, 11, superimposed on the function. Notice Gibbs phenomena. C. Saw Tooth Wave The function here is x if -1 < x < 1 and has period 2. The first slide shows this function for -3 < x < 3. The next 11 slides show the Fourier series expansion out to terms 1, 2, 3, ... , 9, 10, 11, superimposed on the function. Again notice Gibbs phenomena. D. Cosine Expansion of Sine The function is sin x if 0 < x < ã. The first slide shows this function. The next 8 slides show the Fourier cosine series expansion out to terms 1, 2, 3, 4, 5, 6, 7, 8 superimposed on the function. E. Interrupted Square Wave The function here is 0 if -ã < x < -ã/2 -ã/2 if -ã/2 < x < 0 ã/2 if 0 < x < ã/2 0 if ã/2 < x < ã and has period 2ã. The first slide shows this function for -ã < x < ã. The next 13 slides show the Fourier series expansion out to terms 1, 2, 3, ... 11, 12, 13, superimposed on the function. When you have finished reading this document, press Q to quit.