Advanced Calculus - Fundamentals of Mathematics

Real–Valued Functions

Author(s): Carlos Polanco

Pp: 21-45 (25)

DOI: 10.2174/9789811415081119010008

* (Excluding Mailing and Handling)


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.

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