How to Integrate It

A Practical Guide to Finding Elementary Integrals

Author: Seán M. Stewart

Publisher: Cambridge University Press

ISBN: 1108314147

Category: Mathematics

Page: N.A

View: 9232

While differentiating elementary functions is merely a skill, finding their integrals is an art. This practical introduction to the art of integration gives readers the tools and confidence to tackle common and uncommon integrals. After a review of the basic properties of the Riemann integral, each chapter is devoted to a particular technique of elementary integration. Thorough explanations and plentiful worked examples prepare the reader for the extensive exercises at the end of each chapter. These exercises increase in difficulty from warm-up problems, through drill examples, to challenging extensions which illustrate such advanced topics as the irrationality of π and e, the solution of the Basel problem, Leibniz's series and Wallis's product. The author's accessible and engaging manner will appeal to a wide audience, including students, teachers and self-learners. The book can serve as a complete introduction to finding elementary integrals, or as a supplementary text for any beginning course in calculus.

Introduction to Integration

Author: Hilary A. Priestley

Publisher: Oxford University Press

ISBN: 0198501242

Category: Mathematics

Page: 306

View: 5091

Introduction to integration provides a unified account of integration theory, giving a practical guide to the Lebesgue integral and its uses, with a wealth of illustrative examples and exercises. The book begins with a simplified Lebesgue-style integral (in lieu of the more traditional Riemann integral), intended for a first course in integration. This suffices for elementary applications, and serves as an introduction to the core of the book. The final chapters present selected applications, mostly drawn from Fourier analysis. The emphasis throughout is on integrable functions rather than on measure. The book is designed primarily as an undergraduate or introductory graduate textbook. It is similar in style and level to Priestley's Introduction to complex analysis, for which it provides a companion volume, and is aimed at both pure and applied mathematicians. Prerequisites are the rudiments of integral calculus and a first course in real analysis.


European Conference on Computer Algebra, Leipzig, GDR, June 2-5, 1987. Proceedings

Author: James H. Davenport

Publisher: Springer Science & Business Media

ISBN: 9783540515173

Category: Computers

Page: 499

View: 1429

This is the sixth in a series of conference proceedings of international conferences on computer algebra held in Europe. All the preceding ones have also been published as Lecture Notes in Computer Science. They contain original research material not published elsewhere, and a few invited lectures summarising the state of the art. Computer algebra is the science of using computers to do algebraic calculations, rather than the purely arithmetic calculations which we all know computers can do. These calculations may be polynomial-like calculations - one thread of the conference was devoted to polynomial algorithms - or may relate to other areas of mathematics such as integration, the solution of differential equations, or geometry - a second thread was devoted to those topics. The calculations can be applied in a wide range of scientific and engineering subjects, and in branches of mathematics. Physics has benefitted especially from these calculations, and the proceedings contain many papers on this, and also papers on applications in computer aided design and robotics, to name but a few other applications. The third thread of the proceedings was devoted to these applications and to the computer algebra systems which perform these calculations.

Fundamentals of Modern Mathematics

A Practical Review

Author: David B. MacNeil

Publisher: Courier Corporation

ISBN: 0486316149

Category: Mathematics

Page: 320

View: 6763

Students and others wishing to know more about the practical side of mathematics will find this volume a highly informative resource. Accessible explanations of important concepts feature worked examples and diagrams. 1963 edition.

A Guided Inquiry Approach to High School Research

Author: Randell K. Schmidt

Publisher: ABC-CLIO

ISBN: 1610692888

Category: Education

Page: 179

View: 9332

This book helps educators foster academic success and college readiness: it demonstrates how to instruct high school students to find, process, and think about new information, and then synthesize that knowledge. • Introduces the Information Search Process to students • Supplies step-by-step lesson plans that educators can utilize to guide students with their chosen inquiry • Examines the task of the teaching team in guiding students in their inquiry and to provide them with the skills to find, process, and synthesize new information on their own

The Idealist Illusion and Other Essays

Translation and Introduction by Fiachra Long, Annotations by Fiachra Long and Claude Troisfontaines

Author: Maurice Blondel

Publisher: Springer Science & Business Media

ISBN: 9401593639

Category: Philosophy

Page: 156

View: 2335

I was very happy when in 1997 Fiachra Long came to spend part of his sabbatical leave at the Archives Maurice Blondel at Louvain-Ia-Neuve. This allowed him to bring together and complete his translation of three important articles from Maurice Blondel, known as the philosopher of Aix-en-Province. These three articles fonn a unity: they make explicit certain aspects of the method used in the great thesis of 1893, Action. This thesis, it is well known, aroused many polemic debates after its appearance. Thomist theologians accused Blondel of turning back towards Kantian idealism whereas the philosophers of the Revue de metaphysique et de morale accused him on the contrary of falling back on a pre-critical realism. The three articles translated here, each in its own way, attempt to pass beyond these two opposite charges. The Idealist Illusion (1898) underlines the fact that the content of consciousness should be unfurled as it appears, by withdrawing from any idealist or realist prejudice, before judging the consistency of its content as a whole. In this way Blondel supports the "phenomenological" method used in his thesis. The Elementary Principle of a Logic of the Moral Life (1903) is a very well-worked text which shows that "the logic of possession and privation" is broader than "the logic of amnnation and negation. " Using these words, Blondel develops certain striking laws of action such as that of the "parallelogram of contrary forces.

From Rigorous Standards to Student Achievement

A Practical Process

Author: Michael D. Rettig

Publisher: Eye On Education

ISBN: 1930556624

Category: Academic achievement

Page: 146

View: 2534

This book showcases strategies which support teachers and principals as they implement high standards for students. At the same time, it demonstrates how to meet the needs of diverse learners.

Introduction to Fluorescence Sensing

Author: Alexander P. Demchenko

Publisher: Springer Science & Business Media

ISBN: 140209003X

Category: Medical

Page: 590

View: 4285

Fluorescence sensing is a rapidly developing field of research and technology. Its target is nearly the whole world of natural and synthetic compounds being detected in different media including living bodies. The application area range from control of industrial processes to environment monitoring and clinical diagnostics. Among different detection methods fluorescence techniques are distinguished by ultimate sensitivity, high temporal and spatial resolution and versatility that allows not only remote detection of different targets but their imaging within the living cells. The basic mechanism of sensing is the transmission of the signal produced by molecular interaction with the target to fluorescent molecules, nanoparticles and nanocomposites with the detection by devices based on modern electronics and optics. In this interdisciplinary field of research and development the book is primarily intended to be a guide for students and young researchers. It is also addressed to professionals involved in active research and product development serving as a reference for the recent achievements. The users of these products will find description of principles that could allow proper selection of sensors for particular needs. Making a strong link between education, research and product development, this book discusses future directions.

Annals of Language and Learning: Proceedings of the 2009 International Online Language Conference (IOLC 2009)

Author: Azadeh Shafaei,Mehran Nejati

Publisher: Universal-Publishers

ISBN: 1599428733


Page: N.A

View: 6924

Annals of Language and Learning is the conference proceedings of the Second International Online Language Conference which was successfully held in July 2009. This event allowed professors, Master's students, Ph.D. students, and academics from around the world to submit papers pertaining to the areas of the conference theme. The conference was organized by International Online Knowledge Service Provider (IOKSP).

Applied Mathematics

Author: J. David Logan

Publisher: John Wiley & Sons

ISBN: 1118501705

Category: Mathematics

Page: 680

View: 310

Praise for the Third Edition “Future mathematicians, scientists, and engineers shouldfind the book to be an excellent introductory text for courseworkor self-study as well as worth its shelf space forreference.” —MAA Reviews Applied Mathematics, Fourth Edition is a thoroughly updated andrevised edition on the applications of modeling and analyzingnatural, social, and technological processes. The book covers awide range of key topics in mathematical methods and modeling andhighlights the connections between mathematics and the applied andnatural sciences. The Fourth Edition covers both standard and moderntopics, including scaling and dimensional analysis; regular andsingular perturbation; calculus of variations; Green’sfunctions and integral equations; nonlinear wave propagation; andstability and bifurcation. The book provides extended coverage ofmathematical biology, including biochemical kinetics, epidemiology,viral dynamics, and parasitic disease. In addition, the new editionfeatures: Expanded coverage on orthogonality, boundary value problems,and distributions, all of which are motivated by solvability andeigenvalue problems in elementary linear algebra Additional MATLAB® applications for computer algebrasystem calculations Over 300 exercises and 100 illustrations that demonstrateimportant concepts New examples of dimensional analysis and scaling along with newtables of dimensions and units for easy reference Review material, theory, and examples of ordinary differentialequations New material on applications to quantum mechanics, chemicalkinetics, and modeling diseases and viruses Written at an accessible level for readers in a wide range ofscientific fields, Applied Mathematics, Fourth Edition is anideal text for introducing modern and advanced techniques ofapplied mathematics to upper-undergraduate and graduate-levelstudents in mathematics, science, and engineering. The book is alsoa valuable reference for engineers and scientists in government andindustry.

The Historical Development of Quantum Theory

Author: Jagdish Mehra,Helmut Rechenberg

Publisher: Springer Science & Business Media

ISBN: 9780387951799

Category: Science

Page: 366

View: 5934

Quantum Theory, together with the principles of special and general relativity, constitute a scientific revolution that has profoundly influenced the way in which we think about the universe and the fundamental forces that govern it. The Historical Development of Quantum Theory is a definitive historical study of that scientific work and the human struggles that accompanied it from the beginning. Drawing upon such materials as the resources of the Archives for the History of Quantum Physics, the Niels Bohr Archives, and the archives and scientific correspondence of the principal quantum physicists, as well as Jagdish Mehra's personal discussions over many years with most of the architects of quantum theory, the authors have written a rigorous scientific history of quantum theory in a deeply human context. This multivolume work presents a rich account of an intellectual triumph: a unique analysis of the creative scientific process. The Historical Development of Quantum Theory is science, history, and biography, all wrapped in the story of a great human enterprise. Its lessons will be an aid to those working in the sciences and humanities alike.

Teaching and Learning of Knot Theory in School Mathematics

Author: Akio Kawauchi,Tomoko Yanagimoto

Publisher: Springer Science & Business Media

ISBN: 4431541381

Category: Mathematics

Page: 188

View: 6452

​This book is the result of a joint venture between Professor Akio Kawauchi, Osaka City University, well-known for his research in knot theory, and the Osaka study group of mathematics education, founded by Professor Hirokazu Okamori and now chaired by his successor Professor Tomoko Yanagimoto, Osaka Kyoiku University. The seven chapters address the teaching and learning of knot theory from several perspectives. Readers will find an extremely clear and concise introduction to the fundamentals of knot theory, an overview of curricular developments in Japan, and in particular a series of teaching experiments at all levels which not only demonstrate the creativity and the professional expertise of the members of the study group, but also give a lively impression of students’ learning processes. In addition the reports show that elementary knot theory is not just a preparation for advanced knot theory but also an excellent means to develop spatial thinking. The book can be highly recommended for several reasons: First of all, and that is the main intention of the book, it serves as a comprehensive text for teaching and learning knot theory. Moreover it provides a model for cooperation between mathematicians and mathematics educators based on substantial mathematics. And finally it is a thorough introduction to the Japanese art of lesson studies–again in the context of substantial mathematics.

Engineering Mathematics : Volume Iii

Author: A.C. Srivastava, P.K. Srivastava,Srivastava P. K.,Srivastava A. C.

Publisher: PHI Learning Pvt. Ltd.

ISBN: 9788120342934


Page: N.A

View: 6331


Introduction to the Numerical Modeling of Groundwater and Geothermal Systems

Fundamentals of Mass, Energy and Solute Transport in Poroelastic Rocks

Author: Jochen Bundschuh,Mario César Suárez A.

Publisher: CRC Press

ISBN: 0203848101

Category: Technology & Engineering

Page: 522

View: 5117

This book provides an introduction to the scientific fundamentals of groundwater and geothermal systems. In a simple and didactic manner the different water and energy problems existing in deformable porous rocks are explained as well as the corresponding theories and the mathematical and numerical tools that lead to modeling and solving them. This approach provides the reader with a thorough understanding of the basic physical laws of thermoporoelastic rocks, the partial differential equations representing these laws and the principal numerical methods, which allow finding approximate solutions of the corresponding mathematical models. The book also presents the form in which specific useful models can be generated and solved. The text is introductory in the sense that it explains basic themes of the systems mentioned in three areas: engineering, physics and mathematics. All the laws and equations introduced in this book are formulated carefully based on fundamental physical principles. This way, the reader will understand the key importance of mathematics applied to all the subjects. Simple models are emphasized and solved with numerous examples. For more sophisticated and advanced models the numerical techniques are described and developed carefully. This book will serve as a synoptic compendium of the fundamentals of fluid, solute and heat transport, applicable to all types of subsurface systems, ranging from shallow aquifers down to deep geothermal reservoirs. The book will prove to be a useful textbook to senior undergraduate and graduate students, postgraduates, professional geologists and geophysicists, engineers, mathematicians and others working in the vital areas of groundwater and geothermal resources.

Organic Structures from Spectra

Author: L. D. Field,S. Sternhell,John R. Kalman

Publisher: John Wiley & Sons

ISBN: 111996461X

Category: Science

Page: 468

View: 2876

Organic Structures from Spectra, Fourth Edition consists of a carefully selected set of over 300 structural problems involving the use of all the major spectroscopic techniques. The problems are graded to develop and consolidate the student’s understanding of Organic Spectroscopy, with the accompanying text outlining the basic theoretical aspects of major spectroscopic techniques at a level sufficient to tackle the problems. Specific changes for the new edition will include A significantly expanded section on 2D NMR spectroscopy focusing on COSY, NOESY and CH-Correlation Incorporating new material into some tables to provide extra characteristic data for various classes of compounds Additional basic information on how to solve spectroscopic problems Providing new problems within the area of 10 2D NMR spectroscopy More problems at the ‘simpler’ end of the range As with previous editions, this book combines basic theory, practical advice and sensible approaches to solving spectra problems. It will therefore continue to prove invaluable to students studying organic spectroscopy across a range of disciplines.

Stress Analysis by Boundary Element Methods

Author: J. Balaš,J. Sládek,V. Sládek

Publisher: Elsevier

ISBN: 148329174X

Category: Computers

Page: 699

View: 8054

The boundary element method is an extremely versatile and powerful tool of computational mechanics which has already become a popular alternative to the well established finite element method. This book presents a comprehensive and up-to-date treatise on the boundary element method (BEM) in its applications to various fields of continuum mechanics such as: elastostatics, elastodynamics, thermoelasticity, micropolar elasticity, elastoplasticity, viscoelasticity, theory of plates and stress analysis by hybrid methods. The fundamental solution of governing differential equations, integral representations of the displacement and temperature fields, regularized integral representations of the stress field and heat flux, boundary integral equations and boundary integro-differential equations are derived. Besides the mathematical foundations of the boundary integral method, the book deals with practical applications of this method. Most of the applications concentrate mainly on the computational problems of fracture mechanics. The method has been found to be very efficient in stress-intensity factor computations. Also included are developments made by the authors in the boundary integral formulation of thermoelasticity, micropolar elasticity, viscoelasticity, plate theory, hybrid method in elasticity and solution of crack problems. The solution of boundary-value problems of thermoelasticity and micropolar thermoelasticity is formulated for the first time as the solution of pure boundary problems. A new unified formulation of general crack problems is presented by integro-differential equations.

Theoretical Numerical Analysis

An Introduction to Advanced Techniques

Author: Peter Linz

Publisher: Courier Corporation

ISBN: 9780486417080

Category: Mathematics

Page: 228

View: 1486

Concise text introduces numerical analysis as a practical, problem-solving discipline, focusing on fundamentals of functional analysis and approximation theory, the major results of theoretical numerical analysis; and specific topics that illustrate the power and usefulness of theoretical analysis. Ideal for use in a one-year graduate course, the text also offers engineers and scientists a simple introduction to major ideas of modern numerical analysis. A knowledge of advanced calculus is assumed.

Science for English Language Learners

Developing Academic Language Through Inquiry-Based Instruction

Author: Eugenia Mora-Flores,Dolores Beltran,Lilia Sarmiento

Publisher: Teacher Created Materials

ISBN: 1425894879

Category: Education

Page: 0

View: 2458

Perfect for K-12 English language learners classrooms, this professional resource demonstrates how academic language can and should be developed during science instruction. It provides rich strategies and ideas for academic language development in science for English language learners while demonstrating the 5E model of instruction-Engage, Explore, Explain, Extend, and Evaluate. Filled with great stories and vignettes, teachers will enjoy reading this book while learning how to develop students' language abilities in science and improve English language learners' content knowledge. This resource helps teachers understand further how to model, activate prior knowledge, question, and explicitly develop students' language abilities.

Differential and Integral Calculus

Author: Richard Courant

Publisher: John Wiley & Sons

ISBN: 1118031490

Category: Mathematics

Page: 640

View: 8017

The classic introduction to the fundamentals of calculus Richard Courant's classic text Differential and Integral Calculus is an essential text for those preparing for a career in physics or applied math. Volume 1 introduces the foundational concepts of "function" and "limit", and offers detailed explanations that illustrate the "why" as well as the "how". Comprehensive coverage of the basics of integrals and differentials includes their applications as well as clearly-defined techniques and essential theorems. Multiple appendices provide supplementary explanation and author notes, as well as solutions and hints for all in-text problems.

A Concise Handbook of Mathematics, Physics, and Engineering Sciences

Author: Andrei D. Polyanin,Alexei I. Chernoutsan

Publisher: CRC Press

ISBN: 9781439806401

Category: Mathematics

Page: 1125

View: 3369

A Concise Handbook of Mathematics, Physics, and Engineering Sciences takes a practical approach to the basic notions, formulas, equations, problems, theorems, methods, and laws that most frequently occur in scientific and engineering applications and university education. The authors pay special attention to issues that many engineers and students find difficult to understand. The first part of the book contains chapters on arithmetic, elementary and analytic geometry, algebra, differential and integral calculus, functions of complex variables, integral transforms, ordinary and partial differential equations, special functions, and probability theory. The second part discusses molecular physics and thermodynamics, electricity and magnetism, oscillations and waves, optics, special relativity, quantum mechanics, atomic and nuclear physics, and elementary particles. The third part covers dimensional analysis and similarity, mechanics of point masses and rigid bodies, strength of materials, hydrodynamics, mass and heat transfer, electrical engineering, and methods for constructing empirical and engineering formulas. The main text offers a concise, coherent survey of the most important definitions, formulas, equations, methods, theorems, and laws. Numerous examples throughout and references at the end of each chapter provide readers with a better understanding of the topics and methods. Additional issues of interest can be found in the remarks. For ease of reading, the supplement at the back of the book provides several long mathematical tables, including indefinite and definite integrals, direct and inverse integral transforms, and exact solutions of differential equations.