I love professors who post their syllabi early

Syllabus for Math 532, Section 001, Fall 2009

• Review of basic linear algebra and constant-coefficient differential equations
• Eigenvalues, eigenvectors and diagonalization
• Jordan canonical forms for non-diagonalizable matrices
• Powers and exponentials of matrices
• Systems of linear, homogeneous ordinary differential equations (ODEs) with constant coefficients
• Linear planar systems of ODEs
• The phase plane: Saddles, nodes, spirals, sources, sinks, etc...
• Stable, unstable and center subspaces

————– FIRST EXAM ————–

• Inhomogeneous systems
• Systems of nonlinear ODEs
• New issues: Existence, uniqueness, and maximal intervals of existence
• Stability of equilibria
• Linearization about hyperbolic equilibrium points, the Hartman-Grobman Theorem
• Stable and unstable manifolds, Stable Manifold Theorem
• Lyapunov functions and non-hyperbolic equilibria

————– SECOND EXAM ————–

• Periodic orbits and the Poincar´e-Bendixon Theorem
• Homoclinic and heteroclinic orbits
• Bifurcation theory: saddle-node, transcritical, pitchfork and Hopf
• Introduction to delay differential equations

I have been swooning over this all day. Needless to say, I can hardly contain my overflowing excitement! I fucking can't wait for this class to begin!!!!