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This book presents the basic concepts of calculus and its relevance to real-world problems, covering the standard topics in their conventional order. By focusing on applications, it allows readers to view mathematics in a practical and relevant setting. Organized into 12 chapters, this book includes numerous interesting, relevant and up-to date applications that are drawn from the fields of business, economics, social and behavioural sciences, life sciences, physical sciences, and other fields of general interest. It also features MATLAB, which is used to solve a number of problems. The book is ideal as a first course in calculus for mathematics and engineering students. It is also useful for students of other sciences who are interested in learning calculus.
Drawing on their decades of teaching experience, William Briggs and Lyle Cochran have created a calculus text that carries the teacher's voice beyond the classroom. That voice evident in the narrative, the figures, and the questions interspersed in the narrative is a master teacher leading readers to deeper levels of understanding. The authors appeal to readers' geometric intuition to introduce fundamental concepts and lay the foundation for the more rigorous development that follows. Comprehensive exercise sets have received praise for their creativity, quality, and scope. This book is an expanded version of Calculus: Early Transcendentals by the same authors, with an entire chapter devoted to differential equations, additional sections on other topics, and additional exercises in most sections.
This book gives a practical overview of Fractional Calculus as it relates to Signal Processing
For a three-semester or four-quarter calculus course covering single variable and multivariable calculus for mathematics, engineering, and science majors. Briggs/Cochran is the most successful new calculus series published in the last two decades. The authors' decades of teaching experience resulted in a text that reflects how students generally use a textbook-i.e., they start in the exercises and refer back to the narrative for help as needed. The text therefore builds from a foundation of meticulously crafted exercise sets, then draws students into the narrative through writing that reflects the voice of the instructor, examples that are stepped out and thoughtfully annotated, and figures that are designed to teach rather than simply supplement the narrative. The authors appeal to students' geometric intuition to introduce fundamental concepts, laying a foundation for the rigorous development that follows. To further support student learning, the MyMathLab course features an eBook with 700 Interactive Figures that can be manipulated to shed light on key concepts. In addition, the Instructor's Resource Guide and Test Bank features quizzes, test items, lecture support, guided projects, and more. This book is an expanded version of Calculus: Early Transcendentals by the same authors, with an entire chapter devoted to differential equations, additional sections on other topics, and additional exercises in most sections. See the "Features" section for more details.
Focusing on the "why's" of mathematics rather than the "how's," the unique approach of this text will appeal to a wide range of readers, from those taking a first course in calculus to those seeking deeper insights or needing a transition from calculus to analysis. The author takes care to supply strong motivations for abstract concepts, thereby helping beginners overcome the intimidation often felt when first confronting abstraction. While emphasizing the "why's," the book does not entirely neglect the "how's" and provides sufficient exposure to the techniques through numerous exercises, with answers supplied in the back of the book.
Applied Calculus For Scientists And Engineers Is An Invitation To An Intellectual Journey Into A Discipline That Has Profoundly Influenced The Development Of Western Civilization For More Than Three Hundred Years. The Author Takes A Functional Pedagogical Approach Through The Use Of A Dialogue-Based Writing Style That Is Uniquely Suited To Make Transparent The Essential Problem-Solving Strategies. As The Text Follows Simplicio And Sophie In Their Struggle To Understand The Teacher's Explanations, Students Will Find That Many Of Their Own Difficulties Are Adequately Addressed And Elegantly Resolved. The Text Is Centered On The Idea That Good Teaching Must Bring Knowledge To Life. True To This Premise, The Author Has Taken Great Care To Present All Mathematical Subjects Within The Context Of Stimulating Applications That Cover A Wide Range Of Topics In Science And Engineering. Also Included Are Engaging Discussions Of The Historical And Philosophical Background That Gave The Discipline Of Calculus Its Present Shape. Indeed, It Is The Central Focus On Applications Combined With A Commitment To Very High Standards Of Expository Writing That Sets This Book Apart From The Competition.
Expanded coverage of essential math, including integral equations, calculus of variations, tensor analysis, and special integrals Math Refresher for Scientists and Engineers, Third Edition is specifically designed as a self-study guide to help busy professionals and students in science and engineering quickly refresh and improve the math skills needed to perform their jobs and advance their careers. The book focuses on practical applications and exercises that readers are likely to face in their professional environments. All the basic math skills needed to manage contemporary technology problems are addressed and presented in a clear, lucid style that readers familiar with previous editions have come to appreciate and value. The book begins with basic concepts in college algebra and trigonometry, and then moves on to explore more advanced concepts in calculus, linear algebra (including matrices), differential equations, probability, and statistics. This Third Edition has been greatly expanded to reflect the needs of today's professionals. New material includes: * A chapter on integral equations * A chapter on calculus of variations * A chapter on tensor analysis * A section on time series * A section on partial fractions * Many new exercises and solutions Collectively, the chapters teach most of the basic math skills needed by scientists and engineers. The wide range of topics covered in one title is unique. All chapters provide a review of important principles and methods. Examples, exercises, and applications are used liberally throughout to engage the readers and assist them in applying their new math skills to actual problems. Solutions to exercises are provided in an appendix. Whether to brush up on professional skills or prepare for exams, readers will find this self-study guide enables them to quickly master the math they need. It can additionally be used as a textbook for advanced-level undergraduates in physics and engineering.
Convenient access to information from every area of mathematics: Fourier transforms, Z transforms, linear and nonlinear programming, calculus of variations, random-process theory, special functions, combinatorial analysis, game theory, much more.
This book can be used as either a primary text or a supplemental reference for courses in applied mathematics. Its core chapters are devoted to linear algebra, calculus, and ordinary differential equations. Additional topics include partial differential equations and approximation methods. Each chapter features an ample selection of solved problems. These problems were chosen to illustrate not only how to solve various algebraic and differential equations but also how to interpret the solutions in order to gain insight into the behavior of the system modeled by the equation. In addition to the worked-out problems, numerous examples and exercises appear throughout the text.
This textbook provides a rigorous approach to tensor manifolds in several aspects relevant for Engineers and Physicists working in industry or academia. With a thorough, comprehensive, and unified presentation, this book offers insights into several topics of tensor analysis, which covers all aspects of n-dimensional spaces. The main purpose of this book is to give a self-contained yet simple, correct and comprehensive mathematical explanation of tensor calculus for undergraduate and graduate students and for professionals. In addition to many worked problems, this book features a selection of examples, solved step by step. Although no emphasis is placed on special and particular problems of Engineering or Physics, the text covers the fundamentals of these fields of science. The book makes a brief introduction into the basic concept of the tensorial formalism so as to allow the reader to make a quick and easy review of the essential topics that enable having the grounds for the subsequent themes, without needing to resort to other bibliographical sources on tensors. Chapter 1 deals with Fundamental Concepts about tensors and chapter 2 is devoted to the study of covariant, absolute and contravariant derivatives. The chapters 3 and 4 are dedicated to the Integral Theorems and Differential Operators, respectively. Chapter 5 deals with Riemann Spaces, and finally the chapter 6 presents a concise study of the Parallelism of Vectors. It also shows how to solve various problems of several particular manifolds.