The book first ponders on the properties of determinants and solution of systems of equations. The text then gives emphasis to linear transformations and quadratic forms. Topics include coordinate transformations in three-dimensional space; covariant and contravariant affine vectors; unitary and orthogonal transformations; and basic matrix calculus.
The selection also focuses on basic theory of groups and linear representations of groups. Representation of a group by linear transformations; linear representations of the unitary group in two variables; linear representations of the rotation group; and Abelian groups and representations of the first degree are discussed. Other considerations include integration over groups, Lorentz transformations, permutations, and classes and normal subgroups.
The text is a vital source of information for students, mathematicians, and physicists.
This volume discusses linear algebra, quadratic forms theory, and the theory of groups. The properties of determinants are discussed for determinants offer the solution of systems of equations. Cramer's theorem is used to find the solution of a system of linear equations that has as many equations as unknowns. Linear transformations and quadratic forms, for example, coordinate transformation in three-dimensional space and general linear transformation of real three-dimensional space, are considered. The formula for n-dimensional complex space and the transformation of a quadratic form to a sum of squares are analyzed. The latter is explained by using Jacobi's formula to arrive at a significant form of the reduction of a quadratic form to a sum of squares. The basic theory of groups, linear representations of groups, and the theory of partial differential equations that is the basis of the formation of groups with given structural constants are explained.
This book is recommended for mathematicians, students, and professors in higher mathematics and theoretical physics.
This book is organized into five chapters. Chapter I discusses the theory of the classical Stieltjes integral and space C of continuous functions, while Chapter II deals with the foundations of the metric theory of functions of a real variable and Lebesgue-Stieltjes integral. The theory of completely additive set functions and case of the one-dimensional Hellinger integral are analyzed in Chapter III. Chapter IV contains an exposition of the foundations of the general theory of metric and normed spaces. The general theory of Hilbert space is covered in Chapter V.
This volume is suitable for engineers, physicists, and students of pure mathematics.
This volume is divided into seven chapters and begins with a full discussion of the solution of ordinary differential equations with many applications to the treatment of physical problems. This topic is followed by an account of the properties of multiple integrals and of line integrals, with a valuable section on the theory of measurable sets and of multiple integrals. The subsequent chapters deal with the mathematics necessary to the examination of problems in classical field theories in vector algebra and vector analysis and the elements of differential geometry in three-dimensional space. The final chapters explore the Fourier series and the solution of the partial differential equations of classical mathematical physics.
This book will prove useful to advanced mathematics students, engineers, and physicists.
This volume deals with calculus and principles of mathematical analysis including topics on functions of single and multiple variables. The functional relationships, theory of limits, and the concept of differentiation, whether as theories and applications, are discussed. This book also examines the applications of differential calculus to geometry. For example, the equations to determine the differential of arc or the parameters of a curve are shown. This text then notes the basic problems involving integral calculus, particularly regarding indefinite integrals and their properties. The application of definite integrals in the calculation of area of a sector, the length of arc, and the calculation of the volumes of solids of a given cross-section are explained. This book further discusses the basic theory of infinite series, applications to approximate evaluations, Taylor's formula, and its extension. Finally, the geometrical approach to the concept of a number is reviewed.
This text is suitable for physicists, engineers, mathematicians, and students in higher mathematics.
The book first discusses the Stieltjes integral. Concerns include sets and their powers, Darboux sums, improper Stieltjes integral, jump functions, Helly’s theorem, and selection principles. The text then takes a look at set functions and the Lebesgue integral. Operations on sets, measurable sets, properties of closed and open sets, criteria for measurability, and exterior measure and its properties are discussed.
The text also examines set functions, absolute continuity, and generalization of the integral. Absolutely continuous set functions; absolutely continuous functions of several variables; supplementary propositions; and the properties of the Hellinger integral are presented. The text also focuses on metric and normed spaces. Separability, compactness, linear functionals, conjugate spaces, and operators in normed spaces are underscored.
The book also discusses Hilbert space. Linear functionals, projections, axioms of the space, sequences of operators, and weak convergence are described.
The text is a valuable source of information for students and mathematicians interested in studying the theory of functions.
Understanding precalculus often opens the door to learning more advanced and practical math subjects, and can also help satisfy college requisites. Precalculus Demystified, Second Edition, is your key to mastering this sometimes tricky subject.
This self-teaching guide presents general precalculus concepts first, so you'll ease into the basics. You'll gradually master functions, graphs of functions, logarithms, exponents, and more. As you progress, you'll also conquer topics such as absolute value, nonlinear inequalities, inverses, trigonometric functions, and conic sections. Clear, detailed examples make it easy to understand the material, and end-of-chapter quizzes and a final exam help reinforce key ideas.
It's a no-brainer! You'll learn about:Linear questions Functions Polynomial division The rational zero theorem Logarithms Matrix arithmetic Basic trigonometry
Simple enough for a beginner but challenging enough for an advanced student, Precalculus Demystified, Second Edition, Second Edition, helps you master this essential subject.
Whether you're new to functions, analytic geometry, and matrices or just brushing up on those topics, CliffsQuickReview Precalculus can help. This guide introduces each topic, defines key terms, and walks you through each sample problem step-by-step. In no time, you'll be ready to tackle other concepts in this book such asArithmetic and algebraic skillsFunctions and their graphsPolynomials, including binomial expansionRight and oblique angle trigonometryEquations and graphs of conic sectionsMatrices and their application to systems of equations
CliffsQuickReview Precalculus acts as a supplement to your textbook and to classroom lectures. Use this reference in any way that fits your personal style for study and review — you decide what works best with your needs. You can either read the book from cover to cover or just look for the information you want and put it back on the shelf for later. What's more, you canUse the free Pocket Guide full of essential informationGet a glimpse of what you’ll gain from a chapter by reading through the Chapter Check-In at the beginning of each chapterUse the Chapter Checkout at the end of each chapter to gauge your grasp of the important information you need to knowTest your knowledge more completely in the CQR Review and look for additional sources of information in the CQR Resource CenterUse the glossary to find key terms fast.
With titles available for all the most popular high school and college courses, CliffsQuickReview guides are a comprehensive resource that can help you get the best possible grades.
Get hooked on math as Alex delves deep into humankind’s turbulent relationship with numbers, and reveals how they have shaped the world we live in.
Get the question-and-answer practice you need with McGraw-Hill's 500 College Precalculus Questions. Organized for easy reference and intensive practice, the questions cover all essential precalculus topics and include detailed answer explanations.
The 500 practice questions are similar to course exam questions so you will know what to expect on test day. Each question includes a fully detailed answer that puts the subject in context. This additional practice helps you build your knowledge, strengthen test-taking skills, and build confidence. From ethical theory to epistemology, this book covers the key topics in precalculus.
Prepare for exam day with:500 essential precalculus questions and answers organized by subject Detailed answers that provide important context for studying Content that follows the current college 101 course curriculum
"... To sum up, this book helps to learn algebraic geometry in a short time, its concrete style is enjoyable for students and reveals the beauty of mathematics." Acta Scientiarum Mathematicarum
An Elementary Approach to Homological Algebra fills that void. Designed to meet the needs of beginning graduate students, it presents the material in a clear, easy-to-understand manner. Complete, detailed proofs make the material easy to follow, numerous worked examples help readers understand the concepts, and an abundance of exercises test and solidify their understanding.
Often perceived as dry and abstract, homological algebra nonetheless has important applications in many important areas. The author highlights some of these, particularly several related to group theoretic problems, in the concluding chapter. Beyond making classical homological algebra accessible to students, the author's level of detail, while not exhaustive, also makes the book useful for self-study and as a reference for researchers.
Bellos has traveled all around the globe and has plunged into history to uncover fascinating stories of mathematical achievement, from the breakthroughs of Euclid, the greatest mathematician of all time, to the creations of the Zen master of origami, one of the hottest areas of mathematical work today. Taking us into the wilds of the Amazon, he tells the story of a tribe there who can count only to five and reports on the latest findings about the math instinct—including the revelation that ants can actually count how many steps they’ve taken. Journeying to the Bay of Bengal, he interviews a Hindu sage about the brilliant mathematical insights of the Buddha, while in Japan he visits the godfather of Sudoku and introduces the brainteasing delights of mathematical games.
Exploring the mysteries of randomness, he explains why it is impossible for our iPods to truly randomly select songs. In probing the many intrigues of that most beloved of numbers, pi, he visits with two brothers so obsessed with the elusive number that they built a supercomputer in their Manhattan apartment to study it. Throughout, the journey is enhanced with a wealth of intriguing illustrations, such as of the clever puzzles known as tangrams and the crochet creation of an American math professor who suddenly realized one day that she could knit a representation of higher dimensional space that no one had been able to visualize.
Whether writing about how algebra solved Swedish traffic problems, visiting the Mental Calculation World Cup to disclose the secrets of lightning calculation, or exploring the links between pineapples and beautiful teeth, Bellos is a wonderfully engaging guide who never fails to delight even as he edifies. Here’s Looking at Euclid is a rare gem that brings the beauty of math to life.
The authors, a pair of noted mathematicians, start with a discussion of divisibility and proceed to examine Gaussian primes (their determination and role in Fermat's theorem); polynomials over a field (including the Eisenstein irreducibility criterion); algebraic number fields; bases (finite extensions, conjugates and discriminants, and the cyclotomic field); and algebraic integers and integral bases. After establishing a firm introductory foundation, the text explores the uses of arithmetic in algebraic number fields; the fundamental theorem of ideal theory and its consequences; ideal classes and class numbers; and the Fermat conjecture (concluding with discussions of Pythagorean triples, units in cyclotomic fields, and Kummer's theorem).
In addition to a helpful list of symbols and an index, a set of carefully chosen problems appears at the end of each chapter to reinforce mathematics covered. Students and teachers of undergraduate mathematics courses will find this volume a first-rate introduction to algebraic number theory.
A secondary, and more important aim of this book, is to acquaint the reader with two very important branches of modern mathematics: group theory and theory of functions of a complex variable.
This book also has the added bonus of an extensive appendix devoted to the differential Galois theory, written by Professor A.G. Khovanskii.
As this text has been written assuming no specialist prior knowledge and is composed of definitions, examples, problems and solutions, it is suitable for self-study or teaching students of mathematics, from high school to graduate.
In addition to the primary information given in the Handbook, there are references to relevant articles, books or lecture notes to help the reader. An excellent index has been included which is extensive and not limited to definitions, theorems etc.
The Handbook of Algebra will publish articles as they are received and thus the reader will find in this third volume articles from twelve different sections. The advantages of this scheme are two-fold: accepted articles will be published quickly and the outline of the Handbook can be allowed to evolve as the various volumes are published.
A particularly important function of the Handbook is to provide professional mathematicians working in an area other than their own with sufficient information on the topic in question if and when it is needed.
- Thorough and practical source of information
- Provides in-depth coverage of new topics in algebra
- Includes references to relevant articles, books and lecture notes
After an introduction to the geometry of polynomials and a discussion of refinements of the Fundamental Theorem of Algebra, the book turns to a consideration of various special polynomials. Chebyshev and Descartes systems are then introduced, and Müntz systems and rational systems are examined in detail. Subsequent chapters discuss denseness questions and the inequalities satisfied by polynomials and rational functions. Appendices on algorithms and computational concerns, on the interpolation theorem, and on orthogonality and irrationality conclude the book.
Algorithms for Computer Algebra is suitable for use as a textbook for a course on algebraic algorithms at the third-year, fourth-year, or graduate level. Although the mathematical development uses concepts from modern algebra, the book is self-contained in the sense that a one-term undergraduate course introducing students to rings and fields is the only prerequisite assumed. The book also serves well as a supplementary textbook for a traditional modern algebra course, by presenting concrete applications to motivate the understanding of the theory of rings and fields.
Trying to tackle algebra but nothing's adding up? No problem! Factor in Algebra Demystified, Second Edition and multiply your chances of learning this important branch of mathematics.
Written in a step-by-step format, this practical guide covers fractions, variables, decimals, negative numbers, exponents, roots, and factoring. Techniques for solving linear and quadratic equations and applications are discussed in detail. Clear examples, concise explanations, and worked problems with complete solutions make it easy to understand the material, and end-of-chapter quizzes and a final exam help reinforce learning.
It's a no-brainer! You'll learn how to:Translate English sentences into mathematical symbols Write the negative of numbers and variables Factor expressions Use the distributive property to expand expressions Solve applied problems
Simple enough for a beginner, but challenging enough for an advanced student, Algebra Demystified, Second Edition helps you master this essential math subject. It's also the perfect resource for preparing you for higher level math classes and college placement tests.
For courses in Finite Element Analysis, offered in departments of Mechanical or Civil and Environmental Engineering.
While many good textbooks cover the theory of finite element modeling, Finite Element Analysis: Theory and Application with ANSYS is the only text available that incorporates ANSYS as an integral part of its content. Moaveni presents the theory of finite element analysis, explores its application as a design/modeling tool, and explains in detail how to use ANSYS intelligently and effectively.
Teaching and Learning Experience
This program will provide a better teaching and learning experience—for you and your students. It will help:Present the Theory of Finite Element Analysis: The presentation of theoretical aspects of finite element analysis is carefully designed not to overwhelm students. Explain How to Use ANSYS Effectively: ANSYS is incorporated as an integral part of the content throughout the book. Explore How to Use FEA as a Design/Modeling Tool: Open-ended design problems help students apply concepts.
Published nearly forty years after the first edition, this long-awaited Second Edition also:Studies the Fourier transform of functions in the spaces L1, L2, and Lp, 1 p Shows the Hilbert transform to be a bounded operator on L2, as an application of the L2 theory of the Fourier transform in the one-dimensional case Covers fractional integration and some topics related to mean oscillation properties of functions, such as the classes of Hölder continuous functions and the space of functions of bounded mean oscillation Derives a subrepresentation formula, which in higher dimensions plays a role roughly similar to the one played by the fundamental theorem of calculus in one dimension Extends the subrepresentation formula derived for smooth functions to functions with a weak gradient Applies the norm estimates derived for fractional integral operators to obtain local and global first-order Poincaré–Sobolev inequalities, including endpoint cases Proves the existence of a tangent plane to the graph of a Lipschitz function of several variables Includes many new exercises not present in the first edition
This widely used and highly respected text for upper-division undergraduate and first-year graduate students of mathematics, statistics, probability, or engineering is revised for a new generation of students and instructors. The book also serves as a handy reference for professional mathematicians.
Major changes in the new edition relate to Bose--Einstein condensation, the dynamics of the X-Y model and questions on phase transitions. Notes and remarks have been considerably augmented.
The first four chapters present basic concepts and introductory principles in set theory, metric spaces, topological spaces, and linear spaces. The next two chapters consider linear functionals and linear operators, with detailed discussions of continuous linear functionals, the conjugate space, the weak topology and weak convergence, generalized functions, basic concepts of linear operators, inverse and adjoint operators, and completely continuous operators. The final four chapters cover measure, integration, differentiation, and more on integration. Special attention is here given to the Lebesque integral, Fubini's theorem, and the Stieltjes integral. Each individual section — there are 37 in all — is equipped with a problem set, making a total of some 350 problems, all carefully selected and matched.
With these problems and the clear exposition, this book is useful for self-study or for the classroom — it is basic one-year course in real analysis. Dr. Silverman is a former member of the Institute of Mathematical Sciences of New York University and the Lincoln Library of M.I.T. Along with his translation, he has revised the text with numerous pedagogical and mathematical improvements and restyled the language so that it is even more readable.
Chapters 1 through 4 employ infinitesimals to quickly develop the basic concepts of derivatives, continuity, and integrals. Chapter 5 introduces the traditional limit concept, using approximation problems as the motivation. Later chapters develop transcendental functions, series, vectors, partial derivatives, and multiple integrals. The theory differs from traditional courses, but the notation and methods for solving practical problems are the same. The text suggests a variety of applications to both natural and social sciences.