Features an introduction to advanced calculus and highlights its inherent concepts from linear algebra
Advanced Calculus reflects the unifying role of linear algebra in an effort to smooth readers' transition to advanced mathematics. The book fosters the development of complete theorem-proving skills through abundant exercises while also promoting a sound approach to the study. The traditional theorems of elementary differential and integral calculus are rigorously established, presenting the foundations of calculus in a way that reorients thinking toward modern analysis.
Following an introduction dedicated to writing proofs, the book is divided into three parts:
Part One explores foundational one-variable calculus topics from the viewpoint of linear spaces, norms, completeness, and linear functionals.
Part Two covers Fourier series and Stieltjes integration, which are advanced one-variable topics.
Part Three is dedicated to multivariable advanced calculus, including inverse and implicit function theorems and Jacobian theorems for multiple integrals.
Numerous exercises guide readers through the creation of their own proofs, and they also put newly learned methods into practice. In addition, a "Test Yourself" section at the end of each chapter consists of short questions that reinforce the understanding of basic concepts and theorems. The answers to these questions and other selected exercises can be found at the end of the book along with an appendix that outlines key terms and symbols from set theory.
Guiding readers from the study of the topology of the real line to the beginning theorems and concepts of graduate analysis, Advanced Calculus is an ideal text for courses in advanced calculus and introductory analysis at the upper-undergraduate and beginning-graduate levels. It also serves as a valuable reference for engineers, scientists, and mathematicians.
An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course ...
Chapter 11: Uniform continuity is now defined in terms of differences of sequences as it was for functions of a single variable. What was Section 1 1.3 in the first edition is now split into two sections. Section 11.3 is devoted to ...
An excellent undergraduate text examines sets and structures, limit and continuity in En, measure and integration, differentiable mappings, sequences and series, applications of improper integrals, more.
The book incorporates modern computational tools to give visualization real power. Using 2D and 3D graphics, the book offers new insights into fundamental elements of the calculus of differentiable maps.
This book is a high-level introduction to vector calculus based solidly on differential forms.
60068-8 THE THIRTEEN BOOKS OF EUCLID'S ELEMENTS , translated with introduction and commentary by Sir Thomas L. Heath . Definitive edition . Textual and linguistic notes , mathematical analysis . 2,500 years of critical commentary .
Classic text offers exceptionally precise coverage of partial differentiation, vectors, differential geometry, Stieltjes integral, infinite series, gamma function, Fourier series, Laplace transform, much more.
Advanced Calculus of Several Variables provides a conceptual treatment of multivariable calculus. This book emphasizes the interplay of geometry, analysis through linear algebra, and approximation of nonlinear mappings by linear ones.
Intended for students who have already completed a one-year course in elementary calculus, this two-part treatment advances from functions of one variable to those of several variables. Solutions. 1971 edition.
Starting with an abstract treatment of vector spaces and linear transforms, this introduction presents a corresponding theory of integration and concludes with applications to analytic functions of complex variables. 1959 edition.