Download or read book Fundamentals of Advanced Mathematics 1 written by Henri Bourles and published by Elsevier. This book was released on 2017-07-10 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This precis, comprised of three volumes, of which this book is the first, exposes the mathematical elements which make up the foundations of a number of contemporary scientific methods: modern theory on systems, physics and engineering. This first volume focuses primarily on algebraic questions: categories and functors, groups, rings, modules and algebra. Notions are introduced in a general framework and then studied in the context of commutative and homological algebra; their application in algebraic topology and geometry is therefore developed. These notions play an essential role in algebraic analysis (analytico-algebraic systems theory of ordinary or partial linear differential equations). The book concludes with a study of modules over the main types of rings, the rational canonical form of matrices, the (commutative) theory of elemental divisors and their application in systems of linear differential equations with constant coefficients. Part of the New Mathematical Methods, Systems, and Applications series Presents the notions, results, and proofs necessary to understand and master the various topics Provides a unified notation, making the task easier for the reader. Includes several summaries of mathematics for engineers

Download or read book Fundamentals of Advanced Mathematics V3 written by Henri Bourles and published by Elsevier. This book was released on 2019-10-11 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fundamentals of Advanced Mathematics, Volume Three, begins with the study of differential and analytic infinite-dimensional manifolds, then progresses into fibered bundles, in particular, tangent and cotangent bundles. In addition, subjects covered include the tensor calculus on manifolds, differential and integral calculus on manifolds (general Stokes formula, integral curves and manifolds), an analysis on Lie groups, the Haar measure, the convolution of functions and distributions, and the harmonic analysis over a Lie group. Finally, the theory of connections is (linear connections, principal connections, and Cartan connections) covered, as is the calculus of variations in Lagrangian and Hamiltonian formulations. This volume is the prerequisite to the analytic and geometric study of nonlinear systems. Includes sections on differential and analytic manifolds, vector bundles, tensors, Lie derivatives, applications to algebraic topology, and more Presents an ideal prerequisite resource on the analytic and geometric study of nonlinear systems Provides theory as well as practical information

Download or read book Fundamentals of Advanced Mathematics written by Zhien Ma and published by . This book was released on 2005 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Advanced Mathematics written by Stanley J. Farlow and published by John Wiley & Sons. This book was released on 2019-10-02 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a smooth and pleasant transition from first-year calculus to upper-level mathematics courses in real analysis, abstract algebra and number theory Most universities require students majoring in mathematics to take a “transition to higher math” course that introduces mathematical proofs and more rigorous thinking. Such courses help students be prepared for higher-level mathematics course from their onset. Advanced Mathematics: A Transitional Reference provides a “crash course” in beginning pure mathematics, offering instruction on a blendof inductive and deductive reasoning. By avoiding outdated methods and countless pages of theorems and proofs, this innovative textbook prompts students to think about the ideas presented in an enjoyable, constructive setting. Clear and concise chapters cover all the essential topics students need to transition from the "rote-orientated" courses of calculus to the more rigorous "proof-orientated” advanced mathematics courses. Topics include sentential and predicate calculus, mathematical induction, sets and counting, complex numbers, point-set topology, and symmetries, abstract groups, rings, and fields. Each section contains numerous problems for students of various interests and abilities. Ideally suited for a one-semester course, this book: Introduces students to mathematical proofs and rigorous thinking Provides thoroughly class-tested material from the authors own course in transitioning to higher math Strengthens the mathematical thought process of the reader Includes informative sidebars, historical notes, and plentiful graphics Offers a companion website to access a supplemental solutions manual for instructors Advanced Mathematics: A Transitional Reference is a valuable guide for undergraduate students who have taken courses in calculus, differential equations, or linear algebra, but may not be prepared for the more advanced courses of real analysis, abstract algebra, and number theory that await them. This text is also useful for scientists, engineers, and others seeking to refresh their skills in advanced math.

Download or read book Foundations for Advanced Mathematics written by Carol Avelsgaard and published by Scott Foresman & Company. This book was released on 1990 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Foundations of Advanced Mathematics written by William E. Kline and published by . This book was released on 1975 with total page 583 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Foundations of Advanced Mathematics written by William E. Kline and published by . This book was released on 1975 with total page 583 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Advanced Calculus Fundamentals of Mathematics written by Carlos Polanco and published by Bentham Science Publishers. This book was released on 2019-07-31 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vector calculus is an essential mathematical tool for performing mathematical analysis of physical and natural phenomena. It is employed in advanced applications in the field of engineering and computer simulations. This textbook covers the fundamental requirements of vector calculus in curricula for college students in mathematics and engineering programs. Chapters start from the basics of vector algebra, real valued functions, different forms of integrals, geometric algebra and the various theorems relevant to vector calculus and differential forms. Readers will find a concise and clear study of vector calculus, along with several examples, exercises, and a case study in each chapter. The solutions to the exercises are also included at the end of the book. This is an ideal book for students with a basic background in mathematics who wish to learn about advanced calculus as part of their college curriculum and equip themselves with the knowledge to apply theoretical concepts in practical situations.

Download or read book Advanced Calculus written by Lynn Harold Loomis and published by World Scientific Publishing Company. This book was released on 2014-02-26 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades. This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis. The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives. In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.

Download or read book Foundations of Higher Mathematics written by Peter Fletcher and published by . This book was released on 1992 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Proofs and Fundamentals written by Ethan D. Bloch and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to help students write mathematics better. Throughout it are large exercise sets well-integrated with the text and varying appropriately from easy to hard. Basic issues are treated, and attention is given to small issues like not placing a mathematical symbol directly after a punctuation mark. And it provides many examples of what students should think and what they should write and how these two are often not the same.

Download or read book Fundamentals of Advanced Mathematics 2 written by Henri Bourles and published by Elsevier. This book was released on 2018-02-03 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: The three volumes of this series of books, of which this is the second, put forward the mathematical elements that make up the foundations of a number of contemporary scientific methods: modern theory on systems, physics and engineering. Whereas the first volume focused on the formal conditions for systems of linear equations (in particular of linear differential equations) to have solutions, this book presents the approaches to finding solutions to polynomial equations and to systems of linear differential equations with varying coefficients. Fundamentals of Advanced Mathematics, Volume 2: Field Extensions, Topology and Topological Vector Spaces, Functional Spaces, and Sheaves begins with the classical Galois theory and the theory of transcendental field extensions. Next, the differential side of these theories is treated, including the differential Galois theory (Picard-Vessiot theory of systems of linear differential equations with time-varying coefficients) and differentially transcendental field extensions. The treatment of analysis includes topology (using both filters and nets), topological vector spaces (using the notion of disked space, which simplifies the theory of duality), and the radon measure (assuming that the usual theory of measure and integration is known). In addition, the theory of sheaves is developed with application to the theory of distributions and the theory of hyperfunctions (assuming that the usual theory of functions of the complex variable is known). This volume is the prerequisite to the study of linear systems with time-varying coefficients from the point-of-view of algebraic analysis and the algebraic theory of nonlinear systems. Present Galois Theory, transcendental field extensions, and Picard Includes sections on Vessiot theory, differentially transcendental field extensions, topology, topological vector spaces, Radon measure, differential calculus in Banach spaces, sheaves, distributions, hyperfunctions, algebraic analysis, and local analysis of systems of linear differential equations

Download or read book Advanced Mathematics for Engineering Students written by Brent J. Lewis and published by Butterworth-Heinemann. This book was released on 2021-05-20 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced Mathematics for Engineering Students: The Essential Toolbox provides a concise treatment for applied mathematics. Derived from two semester advanced mathematics courses at the author’s university, the book delivers the mathematical foundation needed in an engineering program of study. Other treatments typically provide a thorough but somewhat complicated presentation where students do not appreciate the application. This book focuses on the development of tools to solve most types of mathematical problems that arise in engineering – a “toolbox” for the engineer. It provides an important foundation but goes one step further and demonstrates the practical use of new technology for applied analysis with commercial software packages (e.g., algebraic, numerical and statistical). Delivers a focused and concise treatment on the underlying theory and direct application of mathematical methods so that the reader has a collection of important mathematical tools that are easily understood and ready for application as a practicing engineer The book material has been derived from class-tested courses presented over many years in applied mathematics for engineering students (all problem sets and exam questions given for the course(s) are included along with a solution manual) Provides fundamental theory for applied mathematics while also introducing the application of commercial software packages as modern tools for engineering application, including: EXCEL (statistical analysis); MAPLE (symbolic and numeric computing environment); and COMSOL (finite element solver for ordinary and partial differential equations)

Download or read book All the Mathematics You Missed written by Thomas A. Garrity and published by 清华大学出版社有限公司. This book was released on 2004 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Advanced Mathematics 1 written by Cuthbert W. Celia and published by Palgrave. This book was released on 1985-11-11 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Fundamentals of Mathematics written by Denny Burzynski and published by . This book was released on 2008 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fundamentals of Mathematics is a work text that covers the traditional study in a modern prealgebra course, as well as the topics of estimation, elementary analytic geometry, and introductory algebra. It is intended for students who: have had previous courses in prealgebra wish to meet the prerequisites of higher level courses such as elementary algebra need to review fundamental mathematical concenpts and techniques This text will help the student devlop the insight and intuition necessary to master arithmetic techniques and manipulative skills. It was written with the following main objectives: to provide the student with an understandable and usable source of information to provide the student with the maximum oppurtinity to see that arithmetic concepts and techniques are logically based to instill in the student the understanding and intuitive skills necessary to know how and when to use particular arithmetic concepts in subsequent material cources and nonclassroom situations to give the students the ability to correctly interpret arithmetically obtained results We have tried to meet these objects by presenting material dynamically much the way an instructure might present the material visually in a classroom. (See the development of the concept of addition and subtraction of fractions in section 5.3 for examples) Intuition and understanding are some of the keys to creative thinking, we belive that the material presented in this text will help students realize that mathematics is a creative subject.

Download or read book Fundamentals of Advanced Mathematics written by Alberto D. Yazon and published by Arcler Press. This book was released on 2019-11 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fundamentals of Advanced Mathematics explains the basic fundamentals of mathematics by introducing it to the readers. It further goes on to explain algebra and the basic math related to it and elaborate on the number theory and number system. Also discussed in the book are the relations and functions, the use of proportional logic, the graph theory and the mathematical induction and recursion and the various theorems and logics related to it. The book also delves upon the cardinal system. It gives some solved examples and the questions to be practiced in the later halves of the chapters.