Fourier Analysis for Physicists

My professor wanted me to master these topics from Fourier Analysis. I need a resource where these topics are discussed in brief. Although i know many of the topics in the list, i prefer a good resource to brush up my rusty knowledge and learn what i don’t know. The topics are:

• Fourier series: sin and cos as a basis set; calculating coefficients; complex basis; convergence, Gibbs phenomenon
• Fourier transform: limiting process; uncertainty principle; application to Fraunhofer diffraction
• Dirac delta function: Sifting property; Fourier representation
• Convolution; Correlations; Parseval’s theorem; power spectrum
• Sampling; Nyquist theorem; data compression
• Solving Ordinary Differential Equations with Fourier methods; driven damped oscillators
• Green’s functions for 2nd order ODEs; comparison with Fourier methods
• Partial Differential Equations: wave equation; diffusion equation; Fourier solution
• Partial Differential Equations: solution by separation of variables
• PDEs and curvilinear coordinates; Bessel functions; Sturm-Liouville theory: complete basis set of functions