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Precalculus
Sheldon Axler's Precalculus: A Prelude to Calculus, 3rd Edition focuses only on topics that students actually need to succeed in calculus. This book is geared towards courses with intermediate algebra prerequisites and it does not assume that students remember any trigonometry. It covers topics such as inverse functions, logarithms, half-life and exponential growth, area, e, the exponential function, the natural logarithm and trigonometry.
Linear Algebra Done Right
This text for a second course in linear algebra, aimed at math majors and graduates, adopts a novel approach by banishing determinants to the end of the book and focusing on understanding the structure of linear operators on vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. For example, the book presents - without having defined determinants - a clean proof that every linear operator on a finite-dimensional complex vector space has an eigenvalue. The book starts by discussing vector spaces, linear independence, span, basics, and dimension. Students are introduced to inner-product spaces in the first half of the book and shortly thereafter to the finite- dimensional spectral theorem. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. This second edition features new chapters on diagonal matrices, on linear functionals and adjoints, and on the spectral theorem; some sections, such as those on self-adjoint and normal operators, have been entirely rewritten; and hundreds of minor improvements have been made throughout the text.
Measure, Integration & Real Analysis
This open access textbook welcomes students into the fundamental theory of measure, integration, and real analysis. Focusing on an accessible approach, Axler lays the foundations for further study by promoting a deep understanding of key results. Content is carefully curated to suit a single course, or two-semester sequence of courses, creating a versatile entry point for graduate studies in all areas of pure and applied mathematics. Motivated by a brief review of Riemann integration and its deficiencies, the text begins by immersing students in the concepts of measure and integration. Lebesgue measure and abstract measures are developed together, with each providing key insight into the mai...
Harmonic Function Theory
This book is about harmonic functions in Euclidean space. This new edition contains a completely rewritten chapter on spherical harmonics, a new section on extensions of Bochers Theorem, new exercises and proofs, as well as revisions throughout to improve the text. A unique software package supplements the text for readers who wish to explore harmonic function theory on a computer.
Algebra and Trigonometry
Axler Algebra & Trigonometry is written for the two semester course. The text provides students with the skill and understanding needed for their coursework and for participating as an educated citizen in a complex society. Axler Algebra & Trigonometry focuses on depth, not breadth of topics by exploring necessary topics in greater detail. Readers will benefit from the straightforward definitions and plentiful examples of complex concepts. The Student Solutions Manual is integrated at the end of every section. The proximity of the solutions encourages students to go back and read the main text as they are working through the problems and exercises. The inclusion of the manual also saves students money. Axler Algebra & Trigonometry is available with WileyPLUS; an innovative, research-based, online environment for effective teaching and learning. WileyPLUS sold separately from text.
Understanding Analysis
This elementary presentation exposes readers to both the process of rigor and the rewards inherent in taking an axiomatic approach to the study of functions of a real variable. The aim is to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on questions which give analysis its inherent fascination. Each chapter begins with the discussion of some motivating examples and concludes with a series of questions.
Advanced Calculus
With a fresh geometric approach that incorporates more than 250 illustrations, this textbook sets itself apart from all others in advanced calculus. Besides the classical capstones--the change of variables formula, implicit and inverse function theorems, the integral theorems of Gauss and Stokes--the text treats other important topics in differential analysis, such as Morse's lemma and the Poincaré lemma. The ideas behind most topics can be understood with just two or three variables. 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. The g...
College Algebra, Binder Ready Version
College Algebra, First Edition will appeal to those who want to give important topics more in-depth, higher-level coverage. This text offers streamlined approach accompanied with accessible definitions across all chapters to allow for an easy-to-understand read. College Algebra contains prose that is precise, accurate, and easy to read, with straightforward definitions of even the topics that are typically most difficult for students.
Real Mathematical Analysis
Was plane geometry your favourite math course in high school? Did you like proving theorems? Are you sick of memorising integrals? If so, real analysis could be your cup of tea. In contrast to calculus and elementary algebra, it involves neither formula manipulation nor applications to other fields of science. None. It is Pure Mathematics, and it is sure to appeal to the budding pure mathematician. In this new introduction to undergraduate real analysis the author takes a different approach from past studies of the subject, by stressing the importance of pictures in mathematics and hard problems. The exposition is informal and relaxed, with many helpful asides, examples and occasional comments from mathematicians like Dieudonne, Littlewood and Osserman. The author has taught the subject many times over the last 35 years at Berkeley and this book is based on the honours version of this course. The book contains an excellent selection of more than 500 exercises.
Holomorphic Spaces
Expository articles describing the role Hardy spaces, Bergman spaces, Dirichlet spaces, and Hankel and Toeplitz operators play in modern analysis.
