Math 554: Linear Analysis and Partial Differential Equations 


Eigenfunction of the Laplacian on an Lshaped region. (The Mathworks.) 
Course outlineWe develop a modern framework for linear partial differential equations. Then we apply it to secondorder elliptic, parabolic, and (briefly) hyperbolic equations, such as the kind of potential, diffusion and wave equations that arise in nonhomogeneous media. The course will be valuable to students of differential equations, analysis, probability, and differential geometry.We cover the following topics:
PrerequisitesA strong grasp of basic real analysis (Math 447 or equivalent), and fluency with multivariable calculus are essential. Some measure theory (Math 540) would be very helpful, as would familiarity with partial differential equations (such as Math 442, or preferably Math 553).If you have inquiries or concerns, please contact me by email at laugesen@illinois.edu. 