This chapter focuses on the characterisation of a real-valued function, its
graphs, and level surfaces; its limits, continuity, and differentiation. The operators
here reviewed are gradient, directional derivatives, and the polynomial approximation
to a function named Taylor´s theorem. All of them will be extensively used
in the following chapters.
Keywords: Composition, Continuity, Differentiation, Directional derivatives,
Domain of function, Gradient, Graph function, Hospital’s Rule, Image of function,
Level surfaces, Limits, Partial derivatives, Real-valued functions, Taylor’s
theorem.