This undergraduate textbook is based on lectures given by the author on the differential and
integral calculus of functions of several real variables. The book has a modern approach and
includes topics such as: -The p-norms on vector space and their equivalence -The Weierstrass
and Stone-Weierstrass approximation theorems -The differential as a linear functional
Jacobians Hessians and Taylor's theorem in several variables -The Implicit Function Theorem
for a system of equations proved via Banach's Fixed Point Theorem -Applications to Ordinary
Differential Equations -Line integrals and an introduction to surface integralsThis book
features numerous examples detailed proofs as well as exercises at the end of sections. Many
of the exercises have detailed solutions making the book suitable for self-study. Several Real
Variables will be useful for undergraduate students in mathematics who have completed first
courses in linear algebra and analysis of one real variable.
