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Description of  Numerical Exploration of Fourier Transform and Fourier Series: The Power Spectrum of Driven Damped Oscillators (Synthesis Lectures on Mathematics & Statistics)

3031346637 pdf This book presents practical demonstrations of numerically calculating or obtaining Fourier Transform. In particular, the authors demonstrate how to obtain frequencies that are present in numerical data and utilizes Mathematica to illustrate the calculations. This book also contains numerical solution of differential equation of driven damped oscillator using 4th order Runge-Kutta method. Numerical solutions are compared with analytical solutions, and the behaviors of mechanical system are also depicted by plotting velocity versus displacement rather than displaying displacement as a function of time. This book is useful to physical science and engineering professionals who often need to obtain frequencies present in numerical data using the discrete Fourier transform.This book: Aids readers to numerically calculate or obtain frequencies that are present in numerical dataAids readers to numerically calculate or obtain frequencies that are present in numerical dataExplores the use of the discrete Fourier transform and demonstrates practical numerical calculationExplores the use of the discrete Fourier transform and demonstrates practical numerical calculationUtilizes 4th order Runge-Kutta method and Mathematica for the numerical solution of differential equationUtilizes 4th order Runge-Kutta method and Mathematica for the numerical solution of differential equation