Lecture
This lecture on Fourier series begins with the detailed correction of a test, focusing on calculating Fourier coefficients for a periodic function. The instructor emphasizes the importance of drawing the function's graph to simplify calculations. The lecture then transitions to the Laplace transform, demonstrating how to find the transform of functions like sine and cosine efficiently using tables and properties. Through step-by-step explanations, the instructor covers convolution products, convergence criteria, and recursive formulas for exponential functions. The session concludes with a thorough explanation of the convolution of exponential functions and the application of the Laplace transform to derive complex formulas.