This rigorous textbook is intended for a year-long analysis or
advanced calculus course for advanced undergraduate or beginning
graduate students. Starting with detailed, slow-paced proofs that
allow students to acquire facility in reading and writing proofs,
it clearly and concisely explains the basics of differentiation and
integration of functions of one and several variables, and covers
the theorems of Green, Gauss, and Stokes. Minimal prerequisites are
assumed, and relevant linear algebra topics are reviewed right
before they are needed, making the material accessible to students
from diverse backgrounds. Abstract topics are preceded by concrete
examples to facilitate understanding, for example, before
introducing differential forms, the text examines low-dimensional
examples. The meaning and importance of results are thoroughly
discussed, and numerous exercises of varying difficulty give
students ample opportunity to test and improve their knowledge of
this difficult yet vital subject.
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