This book details how applied mathematics involves predictions, interpretations, analysis, and mathematical modeling to solve real-world 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.

This textbook covers the essentials of atmospheric radiation at a level appropriate to advanced undergraduates and first-year graduate students. It was... written specifically to be readable and technically accessible to students having no prior background in the subject area and who may or may not intend to continue with more advanced study of radiation or remote sensing. The author emphasizes physical insight, first and foremost, but backed by the essential mathematical relationships. The second edition adds new exercises, improved figures, a table of symbols, and discussions of new topics, such as the Poynting vector and the energy balance within the atmosphere. The book web page includes additional resources for courses taught using this book, including downloadable/printable PDF figures as well as solutions to most problems (for instructors of recognized courses only).

This textbook is written for meteorology majors who require an initial introduction to the physical properties of the atmosphere and to the essential... principles and real-world applications of atmospheric thermodynamics. These topics are supplemented by a sampling of techniques and technologies related to atmospheric measurements and observations. A unique tutorial, included as an appendix, teaches students how to attack physical problems symbolically, deferring numerical calculations until the final step in the solution. The author's objectives include not only covering the traditional core subject matter of an undergraduate thermodynamics course but also facilitating students transition from a purely abstract understanding of calculus and physics concepts to the confident application of both to the science of meteorology.

A self-contained introduction to probability, exchangeability and Bayes’ rule provides a theoretical understanding of the applied material. Numerous... examples with R-code that can be run "as-is" allow the reader to perform the data analyses themselves. The development of Monte Carlo and Markov chain Monte Carlo methods in the context of data analysis examples provides motivation for these computational methods.

A self-contained introduction to probability, exchangeability and Bayes’ rule provides a theoretical understanding of the applied material. Numerous... examples with R-code that can be run "as-is" allow the reader to perform the data analyses themselves. The development of Monte Carlo and Markov chain Monte Carlo methods in the context of data analysis examples provides motivation for these computational methods.

Designed for readers with a background in basic algebra, this best-selling introduction to statistics for business and economics emphasizes... inference—with extensive coverage of data collection and analysis as needed to evaluate the reported results of statistical studies and make good business decisions. It stresses the development of statistical thinking, the assessment of credibility and value of the inferences made from data—both by those who consume and those who produce them—and features numerous case studies, examples, and exercises—all drawing on real business situations and recent economic events. Statistics, Data, and Statistical Thinking. Methods for Describing Sets of Data. Probability. Random Variables and Probability Distributions. Inferences Based on a Single Sample: Estimation with Confidence Intervals. Inferences Based on a Single Sample: Tests of Hypothesis. Comparing Population Means. Comparing Population Proportions. Simple Linear Regression. Introduction to Multiple Regression. Basic Methods for Quality Improvement. For anyone interested in statistics for business and economics.

This fifth edition of Lang's book covers all the topics traditionally taught in the first-year calculus sequence. Divided into five parts, each section... of A FIRST COURSE IN CALCULUS contains examples and applications relating to the topic covered. In addition, the rear of the book contains detailed solutions to a large number of the exercises, allowing them to be used as worked-out examples -- one of the main improvements over previous editions.

A First Course in Chaotic Dynamical Systems: Theory and Experiment is the first book to introduce modern topics in dynamical systems at the... undergraduate level. Accessible to readers with only a background in calculus, the book integrates both theory and computer experiments into its coverage of contemporary ideas in dynamics. It is designed as a gradual introduction to the basic mathematical ideas behind such topics as chaos, fractals, Newton’s method, symbolic dynamics, the Julia set, and the Mandelbrot set, and includes biographies of some of the leading researchers in the field of dynamical systems. Mathematical and computer experiments are integrated throughout the text to help illustrate the meaning of the theorems presented.Chaotic Dynamical Systems Software, Labs 1–6 is a supplementary laboratory software package, available separately, that allows a more intuitive understanding of the mathematics behind dynamical systems theory. Combined with A First Course in Chaotic Dynamical Systems, it leads to a rich understanding of this emerging field.

Algebraic coding theory is a new and rapidly developing subject, popular for its many practical applications and for its fascinatingly rich mathematical... structure. This book provides an elementary yet rigorous introduction to the theory of error-correcting codes. Based on courses given by the author over several years to advanced undergraduates and first-year graduated students, this guide includes a large number of exercises, all with solutions, making the book highly suitable for individual study.

Jon Lee focuses on key mathematical ideas leading to useful models and algorithms, rather than on data structures and implementation details, in this... introductory graduate-level text for students of operations research, mathematics, and computer science. The viewpoint is polyhedral, and Lee also uses matroids as a unifying idea. Topics include linear and integer programming, polytopes, matroids and matroid optimization, shortest paths, and network flows. Problems and exercises are included throughout as well as references for further study.

The new Second Edition of A First Course in Complex Analysis with Applications is a truly accessible introduction to the fundamental principles and... applications of complex analysis. Designed for the undergraduate student with a calculus background but no prior experience with complex variables, this text discusses theory of the most relevant mathematical topics in a student-friendly manor. With Zill's clear and straightforward writing style, concepts are introduced through numerous examples and clear illustrations. Students are guided and supported through numerous proofs providing them with a higher level of mathematical insight and maturity. Each chapter contains a separate section on the applications of complex variables, providing students with the opportunity to develop a practical and clear understanding of complex analysis.

Computers and computation are extremely important components of physics and should be integral parts of a physicist s education. Furthermore,... computation physics is reshaping the way calculations are made in all areas of physics. Intended for the physics and engineering students who have completed the introductory physics course, A First Course in Computational Physics, Second Edition covers the different types of computational problems using MATLAB with exercises developed around problems of physical interest. opics such as root finding, Newton-Cotes integration, and ordinary differential equations are included and presented in the context of physics problems. A few topics rarely seen at this level such as computerized tomography, are also included. Within each chapter, the student is led from relatively elementary problems and simple numerical approaches through derivations of more complex and sophisticated methods, often culminating in the solution to problems of significant difficulty. The goal is to demonstrate how numerical methods are used to solve the problems that physicists face.