Normal 0 false false false Are you ready to ace calculus at the college level? With this book, you will be Professors often say "Students don't fail the calculus, they fail the algebra." In other words, even if you understand calculus, your algebra and trigonometry skills can hold you back. Here's a quick quiz--do you remember how to: Factor trinomials? Solve equations containing exponents and logs? Work with inverse trig functions? If not, that's where this book comes in handy "Just-in-Time" is designed to bolster the algebra and trigonometry skills you'll need while you study calculus. As you make your way through the course, "Just-in-Time" is with you every step of the way, showing you the exact algebra or trigonometry topics that you'll need and pointing out potential problem spots. The easy-to-use Table of Contents features the calculus subject listed directly across from the algebra/trigonometry skills needed to master that topic. Use this book as your study companion and put your anxiety to rest

This book is a new edition of "Tensors and Manifolds: With Applications to Mechanics and Relativity" which was published in 1992. It is based on courses taken by advanced undergraduate and beginning graduate students in mathematics and physics, giving an introduction to the expanse of modern mathematics and its application in modern physics. It aims to fill the gap between the basic courses and the highly technical and specialised courses which both mathematics and physics students require in their advanced training, while simultaneously trying to promote, at an early stage, a better appreciation and understanding of each other's discipline. The book sets forth the basic principles of tensors and manifolds, describing how the mathematics underlies elegant geometrical models of classical mechanics, relativity and elementary particle physics. The existing material from the first edition has been reworked and extended in some sections to provide extra clarity, as well as additional problems. Four new chapters on Lie groups and fibre bundles have been included, leading to an exposition of gauge theory and the standard model of elementary particle physics. Mathematical rigour combined with an informal style makes this a very accessible book and will provide the reader with an enjoyable panorama of interesting mathematics and physics.

Total Domination in Graphs gives a clear understanding of this topic to any interested reader who has a modest background in graph theory. This book provides and explores the fundamentals of total domination in graphs. Some of the topics featured include the interplay between total domination in graphs and transversals in hypergraphs, and the association with total domination in graphs and diameter-2-critical graphs. Several proofs are included in this text which enables readers to acquaint themselves with a toolbox of proof techniques and ideas with which to attack open problems in the field. This work is an excellent resource for students interested in beginning their research in this field. Additionally, established researchers will find the book valuable to have as it contains the latest developments and open problems.

SINGLE VARIABLE CALCULUS: EARLY TRANSCENDENTALS, Metric, 9th Edition, provides you with the strongest foundation for a STEM future. James Stewart's Calculus, Metric series is the top-seller in the world because of its problem-solving focus, mathematical precision and accuracy, and outstanding examples and problem sets. Selected and mentored by Stewart, Daniel Clegg and Saleem Watson continue his legacy and their careful refinements retain Stewart's clarity of exposition and make the 9th edition an even more usable learning tool. The accompanying WebAssign includes helpful learning support and new resources like Explore It interactive learning modules. Showing that Calculus is both practical and beautiful, the Stewart approach and WebAssign resources enhance understanding and build confidence for millions of students worldwide.

Piece-wise and Max-Type Difference Equations: Periodic and Eventually Periodic Solutions is intended for lower-level undergraduate students studying discrete mathematics. The book focuses on sequences as recursive relations and then transitions to periodic recursive patterns and eventually periodic recursive patterns. In addition to this, it will also focus on determining the patterns of periodic and eventually periodic solutions inductively. The aim of the author, throughout this book, is to get students to understand the significance of pattern recognition as a mathematical tool. Key Features Can provide possible topics for undergraduate research and for bachelor's thesis Provides supplementary practice problems and some open-ended research problems at the end of each chapter Focusses on determining the patterns of periodic and eventually periodic solutions inductively Enhances students' algebra skills before moving forward to upper level courses Familiarize students with the topics before they start undergraduate research by providing applications.

The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Ceara, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbanski, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Bostjan Gabrovsek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

This textbook provides a readable account of the examples and fundamental results of groups from a theoretical and geometrical point of view. This is the second book of the set of two books on groups theory. Topics on linear transformation and linear groups, group actions on sets, Sylow's theorem, simple groups, products of groups, normal series, free groups, platonic solids, Frieze and wallpaper symmetry groups and characters of groups have been discussed in depth. Covering all major topics, this book is targeted to advanced undergraduate students of mathematics with no prerequisite knowledge of the discussed topics. Each section ends with a set of worked-out problems and supplementary exercises to challenge the knowledge and ability of the reader.

A carefully prepared account of the basic ideas in Fourier analysis and its applications to the study of partial differential equations. The author succeeds to make his exposition accessible to readers with a limited background, for example, those not acquainted with the Lebesgue integral. Readers should be familiar with calculus, linear algebra, and complex numbers. At the same time, the author has managed to include discussions of more advanced topics such as the Gibbs phenomenon, distributions, Sturm-Liouville theory, Cesaro summability and multi-dimensional Fourier analysis, topics which one usually does not find in books at this level. A variety of worked examples and exercises will help the readers to apply their newly acquired knowledge.

This book is a detailed study of Gottfried Wilhelm Leibniz's creation of calculus from 1673 to the 1680s. We examine and analyze the mathematics in several of his early manuscripts as well as various articles published in the Acta Eruditorum. It studies some of the other lesser known "calculi" Leibniz created such as the Analysis Situs, delves into aspects of his logic, and gives an overview of his efforts to construct a Universal Characteristic, a goal that has its distant origin in the Ars Magna of the 13th century Catalan philosopher Raymond Llull, whose work enjoyed a renewed popularity in the century and a half prior to Leibniz.This book also touches upon a new look at the priority controversy with Newton and a Kuhnian interpretation of the nature of mathematical change. This book may be the only integrated treatment based on recent research and should be a thought-provoking contribution to the history of mathematics for scholars and students, interested in either Leibniz's mathematical achievement or general issues in the field.

This book introduces advanced numerical-functional analysis to beginning computer science researchers. The reader is assumed to have had basic courses in numerical analysis, computer programming, computational linear algebra, and an introduction to real, complex, and functional analysis. Although the book is of a theoretical nature, each chapter contains several new theoretical results and important applications in engineering, in dynamic economics systems, in input-output system, in the solution of nonlinear and linear differential equations, and optimization problem.

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This book begins with the basics of the geometry and topology of Euclidean space and continues with the main topics in the theory of functions of several real variables including limits, continuity, differentiation and integration. All topics and in particular, differentiation and integration, are treated in depth and with mathematical rigor. The classical theorems of differentiation and integration such as the Inverse and Implicit Function theorems, Lagrange's multiplier rule, Fubini's theorem, the change of variables formula, Green's, Stokes' and Gauss' theorems are proved in detail and many of them with novel proofs. The authors develop the theory in a logical sequence building one result upon the other, enriching the development with numerous explanatory remarks and historical footnotes. A number of well chosen illustrative examples and counter-examples clarify matters and teach the reader how to apply these results and solve problems in mathematics, the other sciences and economics. Each of the chapters concludes with groups of exercises and problems, many of them with detailed solutions while others with hints or final answers. More advanced topics, such as Morse's lemma, Sard's theorem, the Weierstrass approximation theorem, the Fourier transform, Vector fields on spheres, Brouwer's fixed point theorem, Whitney's embedding theorem, Picard's theorem, and Hermite polynomials are discussed in stared sections.

The aim of these lecture notes is to provide a self-contained exposition of several fascinating formulas discovered by Srinivasa Ramanujan. Two central results in these notes are: (1) the evaluation of the Rogers-Ramanujan continued fraction - a result that convinced G H Hardy that Ramanujan was a "mathematician of the highest class," and (2) what G. H. Hardy called Ramanujan's "Most Beautiful Identity." This book covers a range of related results, such as several proofs of the famous Rogers-Ramanujan identities and a detailed account of Ramanujan's congruences. It also covers a range of techniques in q-series.

This book begins with the basics of the geometry and topology of Euclidean space and continues with the main topics in the theory of functions of several real variables including limits, continuity, differentiation and integration. All topics and in particular, differentiation and integration, are treated in depth and with mathematical rigor. The classical theorems of differentiation and integration such as the Inverse and Implicit Function theorems, Lagrange's multiplier rule, Fubini's theorem, the change of variables formula, Green's, Stokes' and Gauss' theorems are proved in detail and many of them with novel proofs. The authors develop the theory in a logical sequence building one result upon the other, enriching the development with numerous explanatory remarks and historical footnotes. A number of well chosen illustrative examples and counter-examples clarify matters and teach the reader how to apply these results and solve problems in mathematics, the other sciences and economics. Each of the chapters concludes with groups of exercises and problems, many of them with detailed solutions while others with hints or final answers. More advanced topics, such as Morse's lemma, Sard's theorem, the Weierstrass approximation theorem, the Fourier transform, Vector fields on spheres, Brouwer's fixed point theorem, Whitney's embedding theorem, Picard's theorem, and Hermite polynomials are discussed in stared sections.

This book provides a general introduction to applied analysis; vector analysis with physical motivation, calculus of variation, Fourier analysis, eigenfunction expansion, distribution, and so forth, including a catalogue of mathematical theories, such as basic analysis, topological spaces, complex function theory, real analysis, and abstract analysis. This book also uses fundamental ideas of applied mathematics to discuss recent developments in nonlinear science, such as mathematical modeling of reinforced random motion of particles, semiconductor device equation in applied physics, and chemotaxis in biology. Several tools in linear PDE theory, such as fundamental solutions, Perron's method, layer potentials, and iteration scheme, are described, as well as systematic descriptions on the recent study of the blowup of the solution.

The volume presents extensive research devoted to a broad spectrum of mathematical analysis and probability theory. Subjects discussed in this Work are those treated in the so-called Strasbourg-Zurich Meetings. These meetings occur twice yearly in each of the cities, Strasbourg and Zurich, venues of vibrant mathematical communication and worldwide gatherings. The topical scope of the book includes the study of monochromatic random waves defined for general Riemannian manifolds, notions of entropy related to a compact manifold of negative curvature, interacting electrons in a random background, lp-cohomology (in degree one) of a graph and its connections with other topics, limit operators for circular ensembles, polyharmonic functions for finite graphs and Markov chains, the ETH-Approach to Quantum Mechanics, 2-dimensional quantum Yang-Mills theory, Gibbs measures of nonlinear Schroedinger equations, interfaces in spectral asymptotics and nodal sets. Contributions in this Work are composed by experts from the international community, who have presented the state-of-the-art research in the corresponding problems treated. This volume is expected to be a valuable resource to both graduate students and research mathematicians working in analysis, probability as well as their interconnections and applications.

This is a collection of surveys and research papers written by distinguished Chinese mathematicians from within the People's Republic of China and expatriates. The book covers topics in analytic function spaces of several complex variables, integral transforms, harmonic analysis on classical Lie groups and manifolds, LP- estimates of the Cauchy-Riemann equations and wavelet transforms. The reader will be able to trace the influence of the late Professor Loo-keng Hua's ideas and methods on research into harmonic analysis on classical domains and the theory of functions of several complex variables.

Scilab and its Scicos block diagram graphical editor, with a special emphasis on modeling and simulation tools. The first part is a detailed Scilab tutorial, and the second is dedicated to modeling and simulation of dynamical systems in Scicos. The concepts are illustrated through numerous examples, and all code used in the book is available to the reader.

The International Society for Analysis, its Applications and Computation (ISAAC) has held its international congresses biennially since 1997. This proceedings volume reports on the progress in analysis, applications and computation in recent years as covered and discussed at the 7th ISAAC Congress. This volume includes papers on partial differential equations, function spaces, operator theory, integral transforms and equations, potential theory, complex analysis and generalizations, stochastic analysis, inverse problems, homogenization, continuum mechanics, mathematical biology and medicine. With over 500 participants from almost 60 countries attending the congress, the book comprises a broad selection of contributions in different topics.

Addressed mainly to physicist and chemical physicist, this textbook is the result of a broad compilation of current knowledge on analytical properties of Airy functions. In particular, the calculus implying the Airy functions is developed with care. In the latter chapters, examples are given to succinctly illustrate the use of Airy functions in classical and quantum physics. The physicist, for instance in fluid mechanics, can find what he is looking for, in the references for works of molecular physics or in physics of surfaces, and vice versa.

The knowledge on Airy functions is frequently reviewed. The reason may be found in the need to express a physical phenomenon in terms of an effective and comprehensive analytical form for the whole scientific community.

This book deals with the existence and stability of solutions to initial and boundary value problems for functional differential and integral equations and inclusions involving the Riemann-Liouville, Caputo, and Hadamard fractional derivatives and integrals. A wide variety of topics is covered in a mathematically rigorous manner making this work a valuable source of information for graduate students and researchers working with problems in fractional calculus. Contents Preliminary Background Nonlinear Implicit Fractional Differential Equations Impulsive Nonlinear Implicit Fractional Differential Equations Boundary Value Problems for Nonlinear Implicit Fractional Differential Equations Boundary Value Problems for Impulsive NIFDE Integrable Solutions for Implicit Fractional Differential Equations Partial Hadamard Fractional Integral Equations and Inclusions Stability Results for Partial Hadamard Fractional Integral Equations and Inclusions Hadamard-Stieltjes Fractional Integral Equations Ulam Stabilities for Random Hadamard Fractional Integral Equations

One of the most important problems in the theory of entire functions is the distribution of the zeros of entire functions. Localization and Perturbation of Zeros of Entire Functions is the first book to provide a systematic exposition of the bounds for the zeros of entire functions and variations of zeros under perturbations. It also offers a new approach to the investigation of entire functions based on recent estimates for the resolvents of compact operators.

After presenting results about finite matrices and the spectral theory of compact operators in a Hilbert space, the book covers the basic concepts and classical theorems of the theory of entire functions. It discusses various inequalities for the zeros of polynomials, inequalities for the counting function of the zeros, and the variations of the zeros of finite-order entire functions under perturbations. The text then develops the perturbation results in the case of entire functions whose order is less than two, presents results on exponential-type entire functions, and obtains explicit bounds for the zeros of quasipolynomials. The author also offers additional results on the zeros of entire functions and explores polynomials with matrix coefficients, before concluding with entire matrix-valued functions.

This work is one of the first to systematically take the operator approach to the theory of analytic functions.

Basic Analysis: Volumes I-V is written with the aim of balancing theory and abstraction with clear explanations and arguments, so that students and researchers alike who are from a variety of different areas can follow this text and use it profitably for self-study. The first volume is designed for students who have completed the usual calculus and ordinary differential equation sequence and a basic course in linear algebra. This is a critical course in the use of abstraction, but is just first volume in a sequence of courses which prepare students to become practicing scientists. The second volume focuses on differentiation in n-dimensions and important concepts about mappings between finite dimensional Euclidean spaces, such as the inverse and implicit function theorem and change of variable formulae for multidimensional integration. These important topics provide background in important applied and theoretical areas which are no longer covered in mathematical science curricula. Although it follows on from the preceding volume, this is a self-contained book, accessible to undergraduates with a standard course in undergraduate analysis. The third volume is intended as a first course in abstract linear analysis. This textbook covers metric spaces, normed linear spaces and inner product spaces, along with many other deeper abstract ideas such a completeness, operators and dual spaces. These topics act as an important tool in the development of a mathematically trained scientist. The fourth volume introduces students to concepts from measure theory and continues their training in the abstract way of looking at the world. This is a most important skill to have when your life's work will involve quantitative modeling to gain insight into the real world. This text generalizes the notion of integration to a very abstract setting in a variety of ways. We generalize the notion of the length of an interval to the measure of a set and learn how to construct the usual ideas from integration using measures. We discuss carefully the many notions of convergence that measure theory provides. The final volume introduces graduate students in science with concepts from topology and functional analysis, both linear and nonlinear. It is the fifth book in a series designed to train interested readers how to think properly using mathematical abstractions, and how to use the tools of mathematical analysis in applications. It is important to realize that the most difficult part of applying mathematical reasoning to a new problem domain is choosing the underlying mathematical framework to use on the problem. Once that choice is made, we have many tools we can use to solve the problem. However, a different choice would open up avenues of analysis from a different, perhaps more productive perspective. In this volume, the nature of these critical choices is discussed using applications involving the immune system and cognition. Features: Can be used as a supplementary text for anyone whose work requires that they begin to assimilate more abstract mathematical concepts as part of their professional growth Function as a traditional textbook as well as a resource for self-study Suitable for mathematics students and for those in other disciplines such as biology, physics, and economics and others requiring a careful and solid grounding in the use of abstraction in problem solving Emphasizes learning how to understand the consequences of the underlying assumptions used in building a model Regularly uses computation tools to help understand abstract concepts.

In Mathematical Analysis and Optimization for Economists, the author aims to introduce students of economics to the power and versatility of traditional as well as contemporary methodologies in mathematics and optimization theory; and, illustrates how these techniques can be applied in solving microeconomic problems. This book combines the areas of intermediate to advanced mathematics, optimization, and microeconomic decision making, and is suitable for advanced undergraduates and first-year graduate students. This text is highly readable, with all concepts fully defined, and contains numerous detailed example problems in both mathematics and microeconomic applications. Each section contains some standard, as well as more thoughtful and challenging, exercises. Solutions can be downloaded from the CRC Press website. All solutions are detailed and complete. Features Contains a whole spectrum of modern applicable mathematical techniques, many of which are not found in other books of this type. Comprehensive and contains numerous and detailed example problems in both mathematics and economic analysis. Suitable for economists and economics students with only a minimal mathematical background. Classroom-tested over the years when the author was actively teaching at the University of Hartford. Serves as a beginner text in optimization for applied mathematics students. Accompanied by several electronic chapters on linear algebra and matrix theory, nonsmooth optimization, economic efficiency, and distance functions available for free on www.routledge.com/9780367759018.