Book description
This book details how applied mathematics involves predictions, interpretations, analysis, and mathematical modeling to solve realworld problems. Due to the broad range of applications, mathematical concepts and techniques and reviewed throughout, especially those in linear algebra, matrix analysis, and differential equations. Some classical definitions and results from analysis are also discussed and used. Some applications (postscript fonts, information retrieval, etc.) are presented at the end of a chapter as an immediate application of the theory just covered, while those applications that are discussed in more detail (ranking web pages, compression, etc.) are presented in dedicated chapters. Acollection of mathematical models of a slightly different nature, such as basic discrete mathematics and optimization, is also provided. Clear proofs of the main theorems ultimately help to make the statements of the theorems more understandable, and a multitude of examples follow important theorems and concepts. In addition, the author builds material from scratch and thoroughly covers the theory needed to explain the applications in full detail, while not overwhelming readers with unneccessary topics or discussions. In terms of exercises, the author continuously refers to the real numbers and results in calculus when introducing a new topic so readers can grasp the concept of the otherwise intimidating expressions. By doing this, the author is able to focus on the concepts rather than the rigor. The quality, quantity, and varying level of difficulty of the exercises provides instructors more classroom flexibility. Topical coverage includes linear algebra; ranking web pages; matrix factorizations; least squares; image compression; ordinary differential equations; dynamical systems; and mathematical models.
Table of contents
 Cover Page
 Title Page
 Copyright
 Dedication
 Contents
 PREFACE

CHAPTER 1: BASICS OF LINEAR ALGEBRA
 1.1 NOTATION AND TERMINOLOGY
 1.2 VECTOR AND MATRIX NORMS
 1.3 DOT PRODUCT AND ORTHOGONALITY
 1.4 SPECIAL MATRICES
 1.5 VECTOR SPACES
 1.6 LINEAR INDEPENDENCE AND BASIS
 1.7 ORTHOGONALIZATION AND DIRECT SUMS
 1.8 COLUMN SPACE, ROW SPACE, AND NULL SPACE
 1.9 ORTHOGONAL PROJECTIONS
 1.10 EIGENVALUES AND EIGENVECTORS
 1.11 SIMILARITY
 1.12 BEZIER CURVES AND POSTSCRIPT FONTS
 1.13 FINAL REMARKS AND FURTHER READING
 CHAPTER 2: RANKING WEB PAGES
 CHAPTER 3: MATRIX FACTORIZATIONS
 CHAPTER 4: LEAST SQUARES
 CHAPTER 5: IMAGE COMPRESSION
 CHAPTER 6: ORDINARY DIFFERENTIAL EQUATIONS
 CHAPTER 7: DYNAMICAL SYSTEMS
 CHAPTER 8: MATHEMATICAL MODELS
 REFERENCES
 INDEX
Product information
 Title: A First Course in Applied Mathematics
 Author(s):
 Release date: April 2012
 Publisher(s): Wiley
 ISBN: 9781118229620
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