ABSTRACT
This first part of this chapter presents the implicit function theorem in its scalar form. Throughout the chapter related topics are developed such as a study on vectorial functions which includes the implicit function theorem in its vectorial form and the inverse function theorem. The final section develops some basic concepts on differential geometry. Topics such as arc length and curvature are presented in details. The chapter ends with the statement and proof of a well known Gauss theorem concerning the curvature for a surface in ℝ3.
