Partial Differential Equations: Theorems, Proofs, and Python Implementations (Computational Mathematics Library)

Twenty-four dense chapters take you from the method of characteristics through microlocal analysis and the Navier-Stokes equations, supplying every theorem and proof you expect at the graduate level and illustrating every major idea in live code.What You Will Find Inside• High-demand analytic foundations – Multi-index calculus, Sobolev spaces, variational methods – Maximum principles, elliptic regularity, spectral theory• Essential classical models – Heat equation energy methods with Python semigroup solvers – Wave equation finite propagation visualised in Jupyter notebooks – Conservation laws, shocks, and entropy conditions with NumPy demonstrations• Modern high-interest topics – Fourier and Littlewood-Paley analysis for dispersive PDE (Strichartz code included) – Pseudo-differential operators and symbolic calculus – Microlocal propagation of singularities – Fluid dynamics and the Navier-Stokes regularity problem• Geometry and interfaces – Elliptic and parabolic equations on manifolds – Mean curvature and Ricci flows – Free boundary problems and phase transitions Read more