Advanced Calculus  Fundamentals of Mathematics

Advanced Calculus Fundamentals of Mathematics

Vector calculus is an essential mathematical tool for performing mathematical analysis of physical and natural phenomena. It is employed in advanced applications in the field of engineering and ...
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Real–Valued Functions

Pp. 21-45 (25)

Carlos Polanco


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 theorem.


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