Mathematics 723 Advanced Differential Equations Spring 1997

Class Notes and Homework:

• The Gronwall Inequality. A version of the Gronwall inequality that estimates the difference between solutions to two differential equations in terms of the difference between their initial conditions and how how much the two equations differ.

• Examples and problems relating to the general existence theorem and Gronwall's Inequality.

• The inverse function theorem. A proof, in the from of exercises with detailed hints, of the classical inverse function and the inverse function theorem for Lipschitz maps between Banach spaces.

• The inverse function theorem.

• A Special case of the Grobman-Hartman Theorem.