Fourier Analysis and Applications

3 Units

Introduction to the mathematical aspects of Fourier analysis and synthesis. Accessible to upper level undergraduates and graduate students in the sciences and engineering. Periodic functions. Fourier series. Convergence theorems. The classical sine and cosine series. General orthogonal systems. Multiple Fourier series. Applications. Fourier integrals and Fourier Transforms. L1 and L2 theory. Inversion theorems. Classical sine and cosine transforms. Multiple Fourier Transform. Spherical symmetry. Other important transforms and representation systems including wavelets. Applications. We will also use some elements of measure theory, those will be reviewed/introduced in the beginning of the semester. Recommended Preparation: MATH 307 and MATH 321 . Prereq: Graduate student standing or MATH 224 .