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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.
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
Department of Mathematics Faculty of Sciences Universidad Nacional Autónoma de México México City México.