Mathematical Analysis Fundamentals

Figure 7.5 Proof of Theorem 7.24.

Note that Theorem 7.24 states only the existence of a solution of the differential Eq. (7.11) if $f$ is continuous. For uniqueness of the solution, we need a stronger condition. This subject will be handled later (see Theorem 9.30).

7.7* Banach Spaces and the Space $C^1(a\text{,}b)$

In this section we are looking to a suitable structure for a subset of $C(a\text{,}b)$, consisting of all differentiable functions with continuous derivatives ...