It provides a transition from elementary calculus to advanced courses in real and complex function theory and introduces the reader to some of the abstract thinking that pervades modern analysis.

    In writing the book James Stewart asked himself: What is essential for a three-semester calculus course for scientists and engineers? Stewart's ESSENTIAL CALCULUS offers a concise approach to teaching calculus that focuses on major concepts and supports those concepts with precise definitions, patient explanations, and carefully graded problems. Essential Calculus is only 850 pages-two-thirds the size of Stewart's other calculus texts (CALCULUS, Fifth Edition and CALCULUS, EARLY TRANSCENDENTALS, Fifth Edition)-and yet it contains almost all of the same topics. The author achieved this relative brevity mainly by condensing the exposition and by putting some of the features on the website, www.StewartCalculus.com. Despite the reduced size of the book, there is still a modern flavor: Conceptual understanding and technology are not neglected, though they are not as prominent as in Stewart's other books. ESSENTIAL CALCULUS has been written with the same attention to detail, eye for innovation, and meticulous accuracy that have made Stewart's textbooks the best-selling calculus texts in the world.

    His aim is to present calculus as the first real encounter with mathematics: it is the place to learn how logical reasoning combined with fundamental concepts can be developed into a rigorous mathematical theory rather than a bunch of tools and techniques learned by rote. Since analysis is a subject students traditionally find difficult to grasp, Spivak provides leisurely explanations, a profusion of examples, a wide range of exercises and plenty of illustrations in an easy-going approach that enlightens difficult concepts and rewards effort. Calculus will continue to be regarded as a modern classic, ideal for honours students and mathematics majors, who seek an alternative to doorstop textbooks on calculus, and the more formidable introductions to real analysis.

    The Big Bang Cosmology is explored, looking at its observational successes in explaining the expansion of the Universe, the existence and properties of the cosmic microwave background, and the origin of light elements in the universe. Properties of the very early Universe are also covered, including the motivation for a rapid period of expansion known as cosmological inflation. The third edition brings this established undergraduate textbook up-to-date with the rapidly evolving observational situation. This fully revised edition of a bestseller takes an approach which is grounded in physics with a logical flow of chapters leading the reader from basic ideas of the expansion described by the Friedman equations to some of the more advanced ideas about the early universe. It also incorporates up-to-date results from the Planck mission, which imaged the anisotropies of the Cosmic Microwave Background radiation over the whole sky. The Advanced Topic sections present subjects with more detailed mathematical approaches to give greater depth to discussions. Student problems with hints for solving them and numerical answers are embedded in the chapters to facilitate the reader's understanding and learning. Cosmology is now part of the core in many degree programs. This current, clear and concise introductory text is relevant to a wide range of astronomy programs worldwide and is essential reading for undergraduates and Masters students, as well as anyone starting research in cosmology.

    Sipser's candid, crystal-clear style allows students at every level to understand and enjoy this field. His innovative "proof idea" sections explain profound concepts in plain English. The new edition incorporates many improvements students and professors have suggested over the years, and offers updated, classroom-tested problem sets at the end of each chapter.

    I also hope that it will serve as a useful reference too for the many workers engaged in one type of solid state research activity or another, who may be without formal training in the subject.

    Its techniques are widely applied in engineering, science, finance, and commerce. This book is designed for a short course on machine learning. It is a short course, not a hurried course. From over a decade of teaching this material, we have distilled what we believe to be the core topics that every student of the subject should know. We chose the title `learning from data' that faithfully describes what the subject is about, and made it a point to cover the topics in a story-like fashion. Our hope is that the reader can learn all the fundamentals of the subject by reading the book cover to cover. ---- Learning from data has distinct theoretical and practical tracks. In this book, we balance the theoretical and the practical, the mathematical and the heuristic. Our criterion for inclusion is relevance. Theory that establishes the conceptual framework for learning is included, and so are heuristics that impact the performance of real learning systems. ---- Learning from data is a very dynamic field. Some of the hot techniques and theories at times become just fads, and others gain traction and become part of the field. What we have emphasized in this book are the necessary fundamentals that give any student of learning from data a solid foundation, and enable him or her to venture out and explore further techniques and theories, or perhaps to contribute their own. ---- The authors are professors at California Institute of Technology (Caltech), Rensselaer Polytechnic Institute (RPI), and National Taiwan University (NTU), where this book is the main text for their popular courses on machine learning. The authors also consult extensively with financial and commercial companies on machine learning applications, and have led winning teams in machine learning competitions.

    The framework of probabilistic graphical models, presented in this book, provides a general approach for this task. The approach is model-based, allowing interpretable models to be constructed and then manipulated by reasoning algorithms. These models can also be learned automatically from data, allowing the approach to be used in cases where manually constructing a model is difficult or even impossible. Because uncertainty is an inescapable aspect of most real-world applications, the book focuses on probabilistic models, which make the uncertainty explicit and provide models that are more faithful to reality.Probabilistic Graphical Models discusses a variety of models, spanning Bayesian networks, undirected Markov networks, discrete and continuous models, and extensions to deal with dynamical systems and relational data. For each class of models, the text describes the three fundamental cornerstones: representation, inference, and learning, presenting both basic concepts and advanced techniques. Finally, the book considers the use of the proposed framework for causal reasoning and decision making under uncertainty. The main text in each chapter provides the detailed technical development of the key ideas. Most chapters also include boxes with additional material: skill boxes, which describe techniques; case study boxes, which discuss empirical cases related to the approach described in the text, including applications in computer vision, robotics, natural language understanding, and computational biology; and concept boxes, which present significant concepts drawn from the material in the chapter. Instructors (and readers) can group chapters in various combinations, from core topics to more technically advanced material, to suit their particular needs.

    Indispensable reference for graduates and undergraduates.

    Book is unique in its emphasis on the frequency approach and its use in the solution of problems. Contents include: Fundamentals and Algorithms; Polynomial Approximation — Classical Theory; Fourier Approximation — Modern Theory; and Exponential Approximation.

    However, these activities can be viewed as two facets of the same field, and together they have undergone substantial development over the past ten years. In particular, Bayesian methods have grown from a specialist niche to become mainstream, while graphical models have emerged as a general framework for describing and applying probabilistic models. Also, the practical applicability of Bayesian methods has been greatly enhanced through the development of a range of approximate inference algorithms such as variational Bayes and expectation propagation. Similarly, new models based on kernels have had a significant impact on both algorithms and applications. This new textbook reflects these recent developments while providing a comprehensive introduction to the fields of pattern recognition and machine learning. It is aimed at advanced undergraduates or first-year PhD students, as well as researchers and practitioners, and assumes no previous knowledge of pattern recognition or machine learning concepts. Knowledge of multivariate calculus and basic linear algebra is required, and some familiarity with probabilities would be helpful though not essential as the book includes a self-contained introduction to basic probability theory.

    In this book, a wealth of exercises are provided throughout each section, designed to reinforce learning and the logical comprehension of topics. The use of real data is incorporated much more extensively than in any other book on the market. Consist of strong coverage of computer-based methods, especially in the coverage of analysis of variance and regression. This text stresses mastery of methods most often used in medical research, with specific reference to actual medical literature and actual medical research. The approach minimizes mathematical formulation, yet gives complete explanations of all important concepts. Every new concept is systematically developed through completely worked-out examples from current medical research problems. Computer output is used to illustrate concepts when appropriate.

    No graduate student of quantum theory should leave it unread"--W.C Schieve, University of Texas

    The author paves the way for readers to discover for themselves what entropy is, how it changes, and most importantly, why it always changes in one direction in a spontaneous process.

    This new edition simplifies many of the steps involved in analysis by using the computer application Excel. Over 100 detailed example problems illustrate important fluid mechanics concepts: Approximately 1300 end-of-chapter problems are arranged by difficulty level and include many problems that are designed to be solved using Excel. The CD for the book includes: A Brief Review of Microsoft Excel and numerous Excel files for the example problems and for use in solving problems. The new edition includes an expanded discussion of pipe networks, and a new section on oblique shocks and expansion waves.