Constructive reverse investigations into differential equations

We study Picard’s Theorem and Peano’s Theorem from a constructive reverse perspective. This means that we have to change our focus from global properties to local properties. We also extend the theory of pointwise continuously differentiable functions to include Rolle’s Theorem, the Mean Value Theorem, and the full Fundamental Theorem of Calculus. 2000 Mathematics Subject Classification 03F60, 26E40 (primary); 03F55 (secondary)