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Advanced Calculus: An Introduction to Classical Analysis
by Louis BrandA course in analysis that focuses on the functions of a real variable, this text is geared toward upper-level undergraduate students. It introduces the basic concepts in their simplest setting and illustrates its teachings with numerous examples, practical theorems, and coherent proofs.Starting with the structure of the system of real and complex numbers, the text deals at length with the convergence of sequences and series and explores the functions of a real variable and of several variables. Subsequent chapters offer a brief and self-contained introduction to vectors that covers important aspects, including gradients, divergence, and rotation. An entire chapter is devoted to the reversal of order in limiting processes, and the treatment concludes with an examination of Fourier series.
Advanced Calculus (Dover Books on Mathematics)
by Prof. Avner FriedmanThis rigorous two-part treatment advances from functions of one variable to those of several variables. Intended for students who have already completed a one-year course in elementary calculus, it defers the introduction of functions of several variables for as long as possible, and adds clarity and simplicity by avoiding a mixture of heuristic and rigorous arguments.The first part explores functions of one variable, including numbers and sequences, continuous functions, differentiable functions, integration, and sequences and series of functions. The second part examines functions of several variables: the space of several variables and continuous functions, differentiation, multiple integrals, and line and surface integrals, concluding with a selection of related topics. Complete solutions to the problems appear at the end of the text.
Advanced Calculus: Theory and Practice (Textbooks in Mathematics #12)
by John PetrovicAdvanced Calculus: Theory and Practice, Second Edition offers a text for a one- or two-semester course on advanced calculus or analysis. The text improves students’ problem-solving and proof-writing skills, familiarizes them with the historical development of calculus concepts, and helps them understand the connections among different topics. The book explains how various topics in calculus may seem unrelated but have common roots. Emphasizing historical perspectives, the text gives students a glimpse into the development of calculus and its ideas from the age of Newton and Leibniz to the twentieth century. Nearly 300 examples lead to important theorems.Features of the Second Edition: Improved Organization. Chapters are reorganized to address common preferences. Enhanced Coverage of Axiomatic Systems. A section is added to include Peano’s system of axioms for the set of natural numbers and their use in developing the well-known properties of the set N. Expanded and Organized Exercise Collection. There are close to 1,000 new exercises, many of them with solutions or hints. Exercises are classified based on the level of difficulty. Computation-oriented exercises are paired and solutions or hints provided for the odd-numbered questions. Enrichment Material. Historical facts and biographies of over 60 mathematicians. Illustrations. Thirty-five new illustrations are added in order to guide students through examples or proofs. About the Author:John Srdjan Petrovic is a professor at Western Michigan University.
Advanced Calculus
by D. C. Spencer H. K Nickerson N. E. SteenrodClassroom-tested in a Princeton University honors course, it offers students a unified introduction to advanced calculus. Starting with an abstract treatment of vector spaces and linear transforms, the authors introduce a single basic derivative in an invariant form. All other derivatives — gradient, divergent, curl, and exterior — are obtained from it by specialization. The corresponding theory of integration is likewise unified, and the various multiple integral theorems of advanced calculus appear as special cases of a general Stokes formula. The text concludes by applying these concepts to analytic functions of complex variables.
Advanced Calculus: An Introduction to Modern Analysis (Pure and Applied Mathematics #63)
by William L. VoxmanAdvanced Calculus: An Introduction to Modem Analysis, an advanced undergraduate textbook,provides mathematics majors, as well as students who need mathematics in their field of study,with an introduction to the theory and applications of elementary analysis. The text presents, in an accessible form, a carefully maintained balance between abstract concepts and applied results of significance that serves to bridge the gap between the two- or three-semester calculus sequence and senior/graduate level courses in the theory and applications of ordinary and partial differential equations, complex variables, numerical methods, and measure and integration theory.The book focuses on topological concepts, such as compactness, connectedness, and metric spaces,and topics from analysis including Fourier series, numerical analysis, complex integration, generalized functions, and Fourier and Laplace transforms. Applications from genetics, spring systems,enzyme transfer, and a thorough introduction to the classical vibrating string, heat transfer, and brachistochrone problems illustrate this book's usefulness to the non-mathematics major. Extensive problem sets found throughout the book test the student's understanding of the topics and help develop the student's ability to handle more abstract mathematical ideas.Advanced Calculus: An Introduction to Modem Analysis is intended for junior- and senior-level undergraduate students in mathematics, biology, engineering, physics, and other related disciplines.An excellent textbook for a one-year course in advanced calculus, the methods employed in this text will increase students' mathematical maturity and prepare them solidly for senior/graduate level topics. The wealth of materials in the text allows the instructor to select topics that are of special interest to the student.
Advanced Calculus: Second Edition
by David V. WidderThis classic text by a distinguished mathematician and former Professor of Mathematics at Harvard University, leads students familiar with elementary calculus into confronting and solving more theoretical problems of advanced calculus. In his preface to the first edition, Professor Widder also recommends various ways the book may be used as a text in both applied mathematics and engineering.Believing that clarity of exposition depends largely on precision of statement, the author has taken pains to state exactly what is to be proved in every case. Each section consists of definitions, theorems, proofs, examples and exercises. An effort has been made to make the statement of each theorem so concise that the student can see at a glance the essential hypotheses and conclusions.For this second edition, the author has improved the treatment of Stieltjes integrals to make it more useful to the reader less than familiar with the basic facts about theRiemann integral. In addition the material on series has been augmented by the inclusion of the method of partial summation of the Schwarz-Holder inequalities, and of additional results about power series. Carefully selected exercises, graded in difficulty, are found in abundance throughout the book; answers to many of them are contained in a final section.
Advanced Calculus and its Applications in Variational Quantum Mechanics and Relativity Theory
by Fabio Silva BotelhoThe first part of this book reviews some key topics on multi-variable advanced calculus. The approach presented includes detailed and rigorous studies on surfaces in Rn which comprises items such as differential forms and an abstract version of the Stokes Theorem in Rn. The conclusion section introduces readers to Riemannian geometry, which is used in the subsequent chapters. The second part reviews applications, specifically in variational quantum mechanics and relativity theory. Topics such as a variational formulation for the relativistic Klein-Gordon equation, the derivation of a variational formulation for relativistic mechanics firstly through (semi)-Riemannian geometry are covered. The second part has a more general context. It includes fundamentals of differential geometry. The later chapters describe a new interpretation for the Bohr atomic model through a semi-classical approach. The book concludes with a classical description of the radiating cavity model in quantum mechanics.
Advanced Calculus of a Single Variable
by Tunc GeveciThis advanced undergraduate textbook is based on a one-semester course on single variable calculus that the author has been teaching at San Diego State University for many years. The aim of this classroom-tested book is to deliver a rigorous discussion of the concepts and theorems that are dealt with informally in the first two semesters of a beginning calculus course. As such, students are expected to gain a deeper understanding of the fundamental concepts of calculus, such as limits (with an emphasis on ε-δ definitions), continuity (including an appreciation of the difference between mere pointwise and uniform continuity), the derivative (with rigorous proofs of various versions of L'Hôpital's rule) and the Riemann integral (discussing improper integrals in-depth, including the comparison and Dirichlet tests). Success in this course is expected to prepare students for more advanced courses in real and complex analysis and this book will help to accomplish this. The first semester of advanced calculus can be followed by a rigorous course in multivariable calculus and an introductory real analysis course that treats the Lebesgue integral and metric spaces, with special emphasis on Banach and Hilbert spaces.
Advanced Calculus of Several Variables (Dover Books on Mathematics)
by C. H. Edwards Jr.Modern conceptual treatment of multivariable calculus, emphasizing interplay of geometry and analysis via linear algebra and the approximation of nonlinear mappings by linear ones. Over 400 well-chosen problems. 1973 edition.
Advanced Calculus Problem Solver
by Editors of REAREA's Advanced Calculus Problem Solver Each Problem Solver is an insightful and essential study and solution guide chock-full of clear, concise problem-solving gems. Answers to all of your questions can be found in one convenient source from one of the most trusted names in reference solution guides. More useful, more practical, and more informative, these study aids are the best review books and textbook companions available. They're perfect for undergraduate and graduate studies. This highly useful reference is the finest overview of advanced calculus currently available, with hundreds of calculus problems that cover everything from point set theory and vector spaces to theories of differentiation and integrals. Each problem is clearly solved with step-by-step detailed solutions.
Advanced Chromatic Monitoring (Series in Sensors)
by Gordon R. Jones and Joseph W. SpencerAdvanced Chromatic Monitoring provides a major source of information about the novel approach of chromaticity with examples of how chromaticity may be deployed for various monitoring applications. It shows with examples what can be achieved with chromatic methods in producing relevant information with a variety of test techniques and in facilitating the interpretation of complex data about complicated situations. It will be of interest to postgraduates and researchers in a wide breadth of physical disciplines (engineering, medicine, environmental sciences) and those involved with data acquisition and analysis. Key Features: Applicable to a wide range of disciplines (engineering, medical, environmental, etc) and those interested in science, technology, data acquisition and analysis Provides an extrapolation of new knowledge well beyond that covered in existing literature with regard to dealing with complicated forms and sets of data Addresses inspiring and innovative areas of research including environmental, power delivery and medical monitoring About the Editors: Emeritus Professor Gordon R. Jones – founder and former Director of the Centre for Intelligent Monitoring Systems (CIMS), former Head of the Department of Electrical Engineering and Electronics, and former Director of Electric Arcs Research Group at the University of Liverpool. He was awarded the IEEE Education, Science and Technology Achievement Medal (1999). Professor Joe W. Spencer – the present Director of CIMS at the University of Liverpool, having been Head of the Department of Electrical Engineering and Electronics at Liverpool. He is involved in operating a multi-million pound technology transfer unit (Sensor City, Liverpool) with whose establishment he played a major role and with which CIMS has major interactions.
Advanced Classical and Quantum Probability Theory with Quantum Field Theory Applications
by Harish ParthasarathyThis book is based on three undergraduate and postgraduate courses taught by the author on Matrix theory, Probability theory and Antenna theory over the past several years. It discusses Matrix theory, Probability theory and Antenna theory with solved problems. It will be useful to undergraduate and postgraduate students of Electronics and Communications Engineering. Print edition not for sale in South Asia (India, Sri Lanka, Nepal, Bangladesh, Pakistan and Bhutan).
Advanced Classical Mechanics
by Bijan BagchiThis book is designed to serve as a textbook for postgraduates, researchers of applied mathematics, theoretical physics and students of engineering who need a good understanding of classical mechanics. In this book emphasis has been placed on the logical ordering of topics and appropriate formulation of the key mathematical equations with a view to imparting a clear idea of the basic tools of the subject and improving the problem solving skills of the students. The book provides a largely self-contained exposition to the topics with new ideas as a smooth continuation of the preceding ones. It is expected to give a systematic and comprehensive coverage of the methods of classical mechanics.
Advanced Color Image Processing and Analysis
by Christine Fernandez-MaloigneThis volume does much more than survey modern advanced color processing. Starting with a historical perspective on ways we have classified color, it sets out the latest numerical techniques for analyzing and processing colors, the leading edge in our search to accurately record and print what we see. The human eye perceives only a fraction of available light wavelengths, yet we live in a multicolor world of myriad shining hues. Colors rich in metaphorical associations make us "purple with rage" or "green with envy" and cause us to "see red." Defining colors has been the work of centuries, culminating in today's complex mathematical coding that nonetheless remains a work in progress: only recently have we possessed the computing capacity to process the algebraic matrices that reproduce color more accurately. With chapters on dihedral color and image spectrometers, this book provides technicians and researchers with the knowledge they need to grasp the intricacies of today's color imaging.
Advanced Common Core Math Explorations: Measurement & Polygons (Grades 5-8)
by Jerry BurkhartStudents become mathematical adventurers in these challenging and engaging activities designed to deepen and extend their understanding of concepts from the Common Core State Standards in Mathematics. The investigations in this book stretch students' mathematical imaginations to their limits as they create and manipulate geometric figures, draw and analyze complex designs, and develop and apply measurement strategies to solve challenging real-world and mathematical problems. Each activity comes with extensive support for classroom implementation including learning goals, discussion guides, detailed solutions, and suggestions for extending the investigation. There is also a free supplemental e-book offering strategies for motivation, assessment, parent communication, and suggestions for using the materials in different learning environments.Grades 5-8
Advanced Common Core Math Explorations: Fractions (Grades 5-8)
by Jerry BurkhartStudents become mathematical adventurers in these challenging and engaging activities designed to deepen and extend their understanding of concepts from the Common Core State Standards in Mathematics. The investigations in this book stretch students' mathematical imaginations to their limits as they solve puzzles, create stories, and explore fraction-related concepts that take them from the mathematics of ancient Greece to the outer reaches of infinity. Each activity comes with detailed support for classroom implementation including learning goals, discussion guides, detailed solutions, and suggestions for extending the investigation. There is also a free supplemental e-book offering strategies for motivation, assessment, parent communication, and suggestions for using the materials in different learning environments.Grades 5-8
Advanced Common Core Math Explorations: Probability and Statistics (Grades 5-8)
by Jerry BurkhartStretch your students' mathematical imaginations to their limits as they solve challenging real-world and mathematical problems that extend concepts from the Common Core State Standards for Mathematics in Advanced Common Core Math Explorations: Probability and Statistics. Students will learn powerful mathematical ideas about data and chance as they make sense of real-world situations from science, sports, and everyday life. Each activity comes with extensive teacher support, including student handouts, discussion guides, detailed solutions, and suggestions for extending the investigations.Grades 5-8
Advanced Common Core Math Explorations: Ratios, Proportions, and Similarity (Grades 5-8)
by Jerry BurkhartStretch your students' mathematical imaginations to their limits as they solve challenging real-world and mathematical problems that extend concepts from the Common Core State Standards for Mathematics in Advanced Common Core Math Explorations: Ratios, Proportions, and Similarity. Model the solar system, count the fish in a lake, choose the best gear for a bike ride, solve a middle school's overcrowding problem, and explore the mysteries of Fibonacci numbers and the golden ratio. Each activity comes with extensive teacher support including student handouts, discussion guides, detailed solutions, and suggestions for extending the investigations.Grades 5-8
Advanced Common Core Math Explorations: Factors and Multiples (Grades 5-8)
by Jerry BurkhartStudents become mathematical adventurers in these challenging and engaging activities designed to deepen and extend their understanding of concepts from the Common Core State Standards in Mathematics. The investigations in this book stretch students' mathematical imaginations to their limits as they explore mystifying patterns of colored blocks, analyze paths of pool balls, solve mathematical word puzzles, and unravel a baffling mathematical code. Each activity comes with detailed support for classroom implementation including learning goals, discussion guides, detailed solutions, and suggestions for extending the investigation. There is also a free supplemental e-book offering strategies for motivation, assessment, parent communication, and suggestions for using the materials in different learning environments.Grades 5-8
Advanced Common Core Math Explorations: Numbers and Operations (Grades 5-8)
by Jerry BurkhartStudents become mathematical adventurers in these challenging and engaging activities designed to deepen and extend their understanding of concepts from the Common Core State Standards in Mathematics. The investigations in this book stretch students' mathematical imaginations to their limits as they investigate the numeration systems of creatures from another planet, create and solve stories and problems with extreme numbers, use place value to design their own new divisibility strategies, and play with a strange kind of number line specially designed to multiply numbers without a calculator. Each activity comes with detailed support for classroom implementation including learning goals, discussion guides, detailed solutions, and suggestions for extending the investigation. There is also a free supplemental e-book offering strategies for motivation, assessment, parent communication, and suggestions for using the materials in different learning environments.Grades 5-8
Advanced Computational Applications of Geometric Algebra: ICACGA 2022, Denver, CO, USA, October 2–5 (Springer Proceedings in Mathematics & Statistics #445)
by Dietmar Hildenbrand Eckhard Hitzer David William Honorio Araujo Da SilvaHow Geometric Algebra can naturally serve for constructing solutions for pattern recognition, machine learning, data compression, games, robotics, quantum computing, data encoding, to cite a few. Moreover, there is ample evidence that further research on GA and related areas can significantly expand the number of real-world applications in a wide variety of areas. A mathematical system that is very easy to handle, highly robust and superior performance for engineering applications. Good thematic introduction for engineers and researchers new to the subject. Extensive illustrations and code examples. Thematically well structured with many hands on examples. Learning about GA and how to use it for daily tasks in engineering research and development.
Advanced Computational Applications of Geometric Algebra: First International Conference, ICACGA 2022, Denver, CO, USA, October 2-5, 2022, Proceedings (Lecture Notes in Computer Science #13771)
by David W. Silva Eckhard Hitzer Dietmar HildenbrandThis book constitutes the post-conference proceedings of the First International Conference on Advanced Computational Applications of Geometric Algebra, ICACGA 2022, held in Denver, CO, USA, during October 2-5, 2022. The 18 full papers presented in this book together with 12 abstracts of invited talks were carefully reviewed and selected from 24 submissions. The papers are grouped in the following topical sections: geometric applications; computer science applications; technological applications; and applications to physics and mathematics.
Advanced Computational Methods and Design for Greener Aviation (Computational Methods in Applied Sciences #59)
by Tero Tuovinen Jacques Periaux Jordi Pons-Prats Gabriel Bugeda Dietrich KnoerzerThis book presents a selection of scientific and technical results utilizing new computational methods, tools, and technologies in Aeronautical Design. Delve into the forefront of aerospace technology with this collection of articles featuring insights from the from the ECCOMAS CM3 2021 Thematic Conference in Barcelona and from the Special Technology Sessions of the ECCOMAS Congress 2022 in Oslo. Explore advancements in aeronautics design, numerical methods, and industrial technologies, including aerodynamic optimization and additive manufacturing, with contributions from leading experts and from research projects funded by the European Union. Whether you're a seasoned professional or a student, this volume offers invaluable insights into the future of aviation and transportation.
Advanced Computational Methods in Mechanical and Materials Engineering (Computational Intelligence Techniques)
by Kumar Ashwani Gori Yatika Dutt Nitesh Singla Kumar Maurya AmbrishThis book provides in-depth knowledge to solve engineering, geometrical, mathematical, and scientific problems with the help of advanced computational methods with a focus on mechanical and materials engineering. Divided into three subsections covering design and fluids, thermal engineering and materials engineering, each chapter includes exhaustive literature review along with thorough analysis and future research scope. Major topics covered pertains to computational fluid dynamics, mechanical performance, design, and fabrication including wide range of applications in industries as automotive, aviation, electronics, nuclear and so forth. Covers computational methods in design and fluid dynamics with a focus on computational fluid dynamics Explains advanced material applications and manufacturing in labs using novel alloys and introduces properties in material Discusses fabrication of graphene reinforced magnesium metal matrix for orthopedic applications Illustrates simulation and optimization gear transmission, heat sink and heat exchangers application Provides unique problem-solution approach including solutions, methodology, experimental setup, and results validation This book is aimed at researchers, graduate students in mechanical engineering, computer fluid dynamics,fluid mechanics, computer modeling, machine parts, and mechatronics.
Advanced Computer Architecture: 11th Conference, ACA 2016, Weihai, China, August 22-23, 2016, Proceedings (Communications in Computer and Information Science #626)
by Junjie Wu Lian LiThis book constitutes the refereed proceedings of the 11th Annual Conference on Advanced Computer Architecture, ACA 2016, held in Weihai, China, in August 2016. The 17 revised full papers presented were carefully reviewed and selected from 89 submissions. The papers address issues such as processors and circuits; high performance computing; GPUs and accelerators; cloud and data centers; energy and reliability; intelligence computing and mobile computing.