Student Solution Manual To Accompany The 4th Edition Of Vector Calculus Linear Algebra And Differential Forms A Unified Approach

Contains worked-out solutions to odd exercises in "Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach," by John H. Hubbard, professor of mathematics at Cornell University, and Barbara Burke Hubbard

This text covers most of the standard topics in multivariate calculus and part of a standard first course in linear algebra. It focuses on underlying ideas, integrates theory and applications, offers a host of pedagogical aids, and features coverage of differential forms and an emphasis on numerical methods to prepare students for modern applications of mathematics. *Covers important material that is usually omitted. *Presents more difficult and longer proofs (e.g. Proofs of the Kantorovitch theorem, the implicit function theorem) in an appendix. *Makes a careful distinction between vectors and points. *Features an innovative approach to the implicit function theorem and inverse function theorem using Newton's method. *Always emphasizes the underlying meaning - what is really going on (generally, with a geometric interpretation) - eg. The chain rule is a composition of linear transformations; the point of the implicit function theorem is to guarantee that under certain circumstances, non-linear equations have solutions. *Integrates theory and applications. *Begins most chapters with a treatment of a linear problem and then shows how the 7 methods apply to corresponding non-linear p

This manual contains completely worked-out solutions for all the odd-numbered exercises in the text.

A rigorous introduction to calculus in vector spaces The concepts and theorems of advanced calculus combined with related computational methods are essential to understanding nearly all areas of quantitative science. Analysis in Vector Spaces presents the central results of this classic subject through rigorous arguments, discussions, and examples. The book aims to cultivate not only knowledge of the major theoretical results, but also the geometric intuition needed for both mathematical problem-solving and modeling in the formal sciences. The authors begin with an outline of key concepts, terminology, and notation and also provide a basic introduction to set theory, the properties of real numbers, and a review of linear algebra. An elegant approach to eigenvector problems and the spectral theorem sets the stage for later results on volume and integration. Subsequent chapters present the major results of differential and integral calculus of several variables as well as the theory of manifolds. Additional topical coverage includes: Sets and functions Real numbers Vector functions Normed vector spaces First- and higher-order derivatives Diffeomorphisms and manifolds Multiple integrals Integration on manifolds Stokes' theorem Basic point set topology Numerous examples and exercises are provided in each chapter to reinforce new concepts and to illustrate how results can be applied to additional problems. Furthermore, proofs and examples are presented in a clear style that emphasizes the underlying intuitive ideas. Counterexamples are provided throughout the book to warn against possible mistakes, and extensive appendices outline the construction of real numbers, include a fundamental result about dimension, and present general results about determinants. Assuming only a fundamental understanding of linear algebra and single variable calculus, Analysis in Vector Spaces is an excellent book for a second course in analysis for mathematics, physics, computer science, and engineering majors at the undergraduate and graduate levels. It also serves as a valuable reference for further study in any discipline that requires a firm understanding of mathematical techniques and concepts.