The graceful role of analysis in underpinning calculus is often lost to their separation in the
curriculum. This book entwines the two subjects providing a conceptual approach to
multivariable calculus closely supported by the structure and reasoning of analysis. The
setting is Euclidean space with the material on differentiation culminating in the inverse and
implicit function theorems and the material on integration culminating in the general
fundamental theorem of integral calculus. More in-depth than most calculus books but less
technical than a typical analysis introduction Calculus and Analysis in Euclidean Space offers
a rich blend of content to students outside the traditional mathematics major while also
providing transitional preparation for those who will continue on in the subject. The writing
in this book aims to convey the intent of ideas early in discussion. The narrative proceeds
through figures formulas and text guiding the reader to do mathematics resourcefully by
marshaling the skills of geometric intuition (the visual cortex being quickly instinctive)
algebraic manipulation (symbol-patterns being precise and robust) incisive use of natural
language (slogans that encapsulate central ideas enabling a large-scale grasp of the subject).
Thinking in these ways renders mathematics coherent inevitable and fluid. The prerequisite is
single-variable calculus including familiarity with the foundational theorems and some
experience with proofs.
