Differential Eigensystems Mathematica Version 11 extends its symbolic and numerical differential equation-solving capabilities to include finding eigenvalues and eigenfunctions over regions. Given a possibly coupled partial differential equation (PDE), a region specification, and, optionally, boundary conditions, the eigensolvers find corresponding eigenvalues and eigenfunctions of the PDE operator over the given domain. This functionality will enable you to gain a deeper understanding of your physics and engineering designs. Key Features Find symbolic eigenvalues and eigenfunctions over regions. » Find numeric eigenvalues and eigenfunctions over regions. » Find eigenvalues and eigenfunctions of PDEs with arbitrary-order time derivative. Specify and solve eigenvalue problems in one, two, and three dimensions. Specify and solve constrained or unconstrained eigenvalue problems. » Freely formulate coupled PDEs for multi-physics eigenvalue analysis. » Specify domains using the full geometric region framework. » Use automatically generated meshes with curved boundaries for numeric eigenvalue computations. » Related Examples A Laplacian's Eigenvalues & Eigenfunctions » Solve the Eigenproblem of a Constrained Laplacian » Find the Spectrum of a Schrödinger Operator » Probe the Eigenproblem of a Wave Operator » Analyze a Sturm–Liouville Operator with an Asymmetric Potential » Study a Sturm–Liouville System with Antiperiodic Boundary Conditions » Investigate a Laplace Equation on a Torus » Compute Eigenfunctions for a Clamped Membrane » Compute Eigenfunctions in an L-shaped Region » Analyze the Acoustic Eigenmodes of a Car » Compute the Spectrum on a Koch Snowflake » Find Eigenvalues That Lie in an Interval » Find Aharonov–Bohm Eigenvalues » Eigenfunctions of a 3D Laplacian » Eigenmodes in a Knot » A Crankshaft's Eigenvalues and Eigenfunctions » Find a 1D Laplacian's Symbolic Eigenfunctions » Compute Symbolic Eigenvalues » Model Small Oscillations in a CO Molecule » Generate an Eigenfunction Expansion » Calculate Exact Eigenfunctions for the Laplacian in a Rectangle » Obtain a Clamped Triangular Membrane's Symbolic Eigenfunctions » Compute the Exact Eigenmodes of the Heat Equation » Create a Gallery of Eigenfunctions for the Laplacian in a Ball »
