Co-Instructors: Tarek Elgindi, James Nolen, Hongkai Zhao
This special-topics course will introduce students to important and fascinating topics in mathematical analysis that have played a fundamental role in many applications. This semester, the course will focus on Fourier analysis and its application to partial differential equations (PDEs) and to imaging. The course will be divided into three modules: (1) Fourier series and analysis (2) PDEs for diffusion and reaction (3) application to Computed Tomography (CT). Prior experience with analysis or differential equations or imaging is not required. The course is designed to build student literacy in mathematics and to expose students to salient ideas before they have taken more advanced analysis courses. Specific topics to be covered in the three modules include: Fourier series and transforms, function spaces, orthogonality, Plancherel theorem; heat equation, linear reaction-diffusion systems, Turing instability and pattern formation; X-ray and Radon transform, Fourier Slice Theorem for Radon transform, filtered back projection for computed tomography (CT).