Analysis in Vector Spaces
()
About this ebook
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.
Related to Analysis in Vector Spaces
Related ebooks
Introductory Calculus: With Analytic Geometry and Linear Algebra Rating: 4 out of 5 stars4/5Numerical Sound Synthesis: Finite Difference Schemes and Simulation in Musical Acoustics Rating: 0 out of 5 stars0 ratingsEssentials of Math Methods for Physicists Rating: 5 out of 5 stars5/5A Matrix Handbook for Statisticians Rating: 0 out of 5 stars0 ratingsGreen's Functions and Boundary Value Problems Rating: 0 out of 5 stars0 ratingsA Rational Finite Element Basis Rating: 0 out of 5 stars0 ratingsIntroduction to Calculus Rating: 5 out of 5 stars5/5Manifold Theory: An Introduction for Mathematical Physicists Rating: 0 out of 5 stars0 ratingsThe Mathematical Theory of Coding Rating: 1 out of 5 stars1/5A First Course in Applied Mathematics Rating: 0 out of 5 stars0 ratingsWavelet Theory: An Elementary Approach with Applications Rating: 0 out of 5 stars0 ratingsFundamentals of Matrix Computations Rating: 0 out of 5 stars0 ratingsBasic Real and Abstract Analysis Rating: 0 out of 5 stars0 ratingsModeling with Data: Tools and Techniques for Scientific Computing Rating: 3 out of 5 stars3/5College Algebra and Trigonometry Rating: 2 out of 5 stars2/5Algebraic Curves over a Finite Field Rating: 5 out of 5 stars5/5Finite Elements for Analysis and Design: Computational Mathematics and Applications Series Rating: 5 out of 5 stars5/5The Theory of Measures and Integration Rating: 0 out of 5 stars0 ratingsLinear Statistical Models Rating: 0 out of 5 stars0 ratingsLinear Models in Statistics Rating: 0 out of 5 stars0 ratingsMethods of Numerical Integration Rating: 2 out of 5 stars2/5Calculus: Introductory Theory and Applications in Physical and Life Science Rating: 1 out of 5 stars1/5Multivariable Calculus with Linear Algebra and Series Rating: 0 out of 5 stars0 ratingsMultiparameter eigenvalue problems Rating: 0 out of 5 stars0 ratingsVector Analysis and Cartesian Tensors Rating: 4 out of 5 stars4/5An Introduction to Numerical Analysis for Electrical and Computer Engineers Rating: 0 out of 5 stars0 ratingsAn Invitation to Modern Number Theory Rating: 0 out of 5 stars0 ratingsMathematical Tools for Applied Multivariate Analysis Rating: 5 out of 5 stars5/5Coupled-Oscillator Based Active-Array Antennas Rating: 0 out of 5 stars0 ratings
Mathematics For You
Basic Math & Pre-Algebra For Dummies Rating: 4 out of 5 stars4/5Calculus For Dummies Rating: 4 out of 5 stars4/5Mental Math Secrets - How To Be a Human Calculator Rating: 5 out of 5 stars5/5Algebra I Workbook For Dummies Rating: 3 out of 5 stars3/5Geometry For Dummies Rating: 5 out of 5 stars5/5Algebra - The Very Basics Rating: 5 out of 5 stars5/5Pre-Calculus For Dummies Rating: 5 out of 5 stars5/5Introducing Game Theory: A Graphic Guide Rating: 4 out of 5 stars4/5Precalculus: A Self-Teaching Guide Rating: 4 out of 5 stars4/5The Everything Guide to Algebra: A Step-by-Step Guide to the Basics of Algebra - in Plain English! Rating: 4 out of 5 stars4/5Quantum Physics for Beginners Rating: 4 out of 5 stars4/5The Everything Everyday Math Book: From Tipping to Taxes, All the Real-World, Everyday Math Skills You Need Rating: 5 out of 5 stars5/5Relativity: The special and the general theory Rating: 5 out of 5 stars5/5The Little Book of Mathematical Principles, Theories & Things Rating: 3 out of 5 stars3/5ACT Math & Science Prep: Includes 500+ Practice Questions Rating: 3 out of 5 stars3/5Calculus Made Easy Rating: 4 out of 5 stars4/5Practice Makes Perfect Algebra II Review and Workbook, Second Edition Rating: 4 out of 5 stars4/5The Golden Ratio: The Divine Beauty of Mathematics Rating: 5 out of 5 stars5/5The Thirteen Books of the Elements, Vol. 1 Rating: 0 out of 5 stars0 ratingsIs God a Mathematician? Rating: 4 out of 5 stars4/5Game Theory: A Simple Introduction Rating: 4 out of 5 stars4/5My Best Mathematical and Logic Puzzles Rating: 5 out of 5 stars5/5The Math of Life and Death: 7 Mathematical Principles That Shape Our Lives Rating: 4 out of 5 stars4/5The Number Devil: A Mathematical Adventure Rating: 4 out of 5 stars4/5Real Estate by the Numbers: A Complete Reference Guide to Deal Analysis Rating: 0 out of 5 stars0 ratings
Reviews for Analysis in Vector Spaces
0 ratings0 reviews