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A Concise Introduction To Calculus
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Book Synopsis A Concise Introduction to Calculus by : Wu Yi Hsiang
Download or read book A Concise Introduction to Calculus written by Wu Yi Hsiang and published by World Scientific. This book was released on 1995 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: The student of calculus is entitled to ask what calculus is and what it can be used for. This short book provides an answer.The author starts by demonstrating that calculus provides a mathematical tool for the quantitative analysis of a wide range of dynamical phenomena and systems with variable quantities.He then looks at the origins and intuitive sources of calculus, its fundamental methodology, and its general framework and basic structure, before examining a few typical applications.The author's style is direct and pedagogical. The new student should find that the book provides a clear and strong grounding in this important technique.
Book Synopsis A Concise Introduction to Pure Mathematics by : Martin Liebeck
Download or read book A Concise Introduction to Pure Mathematics written by Martin Liebeck and published by CRC Press. This book was released on 2018-09-03 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accessible to all students with a sound background in high school mathematics, A Concise Introduction to Pure Mathematics, Fourth Edition presents some of the most fundamental and beautiful ideas in pure mathematics. It covers not only standard material but also many interesting topics not usually encountered at this level, such as the theory of solving cubic equations; Euler’s formula for the numbers of corners, edges, and faces of a solid object and the five Platonic solids; the use of prime numbers to encode and decode secret information; the theory of how to compare the sizes of two infinite sets; and the rigorous theory of limits and continuous functions. New to the Fourth Edition Two new chapters that serve as an introduction to abstract algebra via the theory of groups, covering abstract reasoning as well as many examples and applications New material on inequalities, counting methods, the inclusion-exclusion principle, and Euler’s phi function Numerous new exercises, with solutions to the odd-numbered ones Through careful explanations and examples, this popular textbook illustrates the power and beauty of basic mathematical concepts in number theory, discrete mathematics, analysis, and abstract algebra. Written in a rigorous yet accessible style, it continues to provide a robust bridge between high school and higher-level mathematics, enabling students to study more advanced courses in abstract algebra and analysis.
Book Synopsis A Concise Introduction to Analysis by : Daniel W. Stroock
Download or read book A Concise Introduction to Analysis written by Daniel W. Stroock and published by Springer. This book was released on 2015-10-31 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the basic ideas and tools used in mathematical analysis. It is a hybrid cross between an advanced calculus and a more advanced analysis text and covers topics in both real and complex variables. Considerable space is given to developing Riemann integration theory in higher dimensions, including a rigorous treatment of Fubini's theorem, polar coordinates and the divergence theorem. These are used in the final chapter to derive Cauchy's formula, which is then applied to prove some of the basic properties of analytic functions. Among the unusual features of this book is the treatment of analytic function theory as an application of ideas and results in real analysis. For instance, Cauchy's integral formula for analytic functions is derived as an application of the divergence theorem. The last section of each chapter is devoted to exercises that should be viewed as an integral part of the text. A Concise Introduction to Analysis should appeal to upper level undergraduate mathematics students, graduate students in fields where mathematics is used, as well as to those wishing to supplement their mathematical education on their own. Wherever possible, an attempt has been made to give interesting examples that demonstrate how the ideas are used and why it is important to have a rigorous grasp of them.
Book Synopsis Calculus of Variations and Optimal Control Theory by : Daniel Liberzon
Download or read book Calculus of Variations and Optimal Control Theory written by Daniel Liberzon and published by Princeton University Press. This book was released on 2012 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook offers a concise yet rigorous introduction to calculus of variations and optimal control theory, and is a self-contained resource for graduate students in engineering, applied mathematics, and related subjects. Designed specifically for a one-semester course, the book begins with calculus of variations, preparing the ground for optimal control. It then gives a complete proof of the maximum principle and covers key topics such as the Hamilton-Jacobi-Bellman theory of dynamic programming and linear-quadratic optimal control. Calculus of Variations and Optimal Control Theory also traces the historical development of the subject and features numerous exercises, notes and references at the end of each chapter, and suggestions for further study. Offers a concise yet rigorous introduction Requires limited background in control theory or advanced mathematics Provides a complete proof of the maximum principle Uses consistent notation in the exposition of classical and modern topics Traces the historical development of the subject Solutions manual (available only to teachers) Leading universities that have adopted this book include: University of Illinois at Urbana-Champaign ECE 553: Optimum Control Systems Georgia Institute of Technology ECE 6553: Optimal Control and Optimization University of Pennsylvania ESE 680: Optimal Control Theory University of Notre Dame EE 60565: Optimal Control
Book Synopsis General Relativity Without Calculus by : Jose Natario
Download or read book General Relativity Without Calculus written by Jose Natario and published by Springer Science & Business Media. This book was released on 2011-08-01 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: “General Relativity Without Calculus” offers a compact but mathematically correct introduction to the general theory of relativity, assuming only a basic knowledge of high school mathematics and physics. Targeted at first year undergraduates (and advanced high school students) who wish to learn Einstein’s theory beyond popular science accounts, it covers the basics of special relativity, Minkowski space-time, non-Euclidean geometry, Newtonian gravity, the Schwarzschild solution, black holes and cosmology. The quick-paced style is balanced by over 75 exercises (including full solutions), allowing readers to test and consolidate their understanding.
Book Synopsis Concise Introduction to Linear Algebra by : Qingwen Hu
Download or read book Concise Introduction to Linear Algebra written by Qingwen Hu and published by CRC Press. This book was released on 2017-09-22 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concise Introduction to Linear Algebra deals with the subject of linear algebra, covering vectors and linear systems, vector spaces, orthogonality, determinants, eigenvalues and eigenvectors, singular value decomposition. It adopts an efficient approach to lead students from vectors, matrices quickly into more advanced topics including, LU decomposition, orthogonal decomposition, Least squares solutions, Gram-Schmidt process, eigenvalues and eigenvectors, diagonalizability, spectral decomposition, positive definite matrix, quadratic forms, singular value decompositions and principal component analysis. This book is designed for onesemester teaching to undergraduate students.
Book Synopsis Mathematical Analysis by : Bernd S. W. Schröder
Download or read book Mathematical Analysis written by Bernd S. W. Schröder and published by John Wiley & Sons. This book was released on 2008-01-28 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained introduction to the fundamentals of mathematical analysis Mathematical Analysis: A Concise Introduction presents the foundations of analysis and illustrates its role in mathematics. By focusing on the essentials, reinforcing learning through exercises, and featuring a unique "learn by doing" approach, the book develops the reader's proof writing skills and establishes fundamental comprehension of analysis that is essential for further exploration of pure and applied mathematics. This book is directly applicable to areas such as differential equations, probability theory, numerical analysis, differential geometry, and functional analysis. Mathematical Analysis is composed of three parts: ?Part One presents the analysis of functions of one variable, including sequences, continuity, differentiation, Riemann integration, series, and the Lebesgue integral. A detailed explanation of proof writing is provided with specific attention devoted to standard proof techniques. To facilitate an efficient transition to more abstract settings, the results for single variable functions are proved using methods that translate to metric spaces. ?Part Two explores the more abstract counterparts of the concepts outlined earlier in the text. The reader is introduced to the fundamental spaces of analysis, including Lp spaces, and the book successfully details how appropriate definitions of integration, continuity, and differentiation lead to a powerful and widely applicable foundation for further study of applied mathematics. The interrelation between measure theory, topology, and differentiation is then examined in the proof of the Multidimensional Substitution Formula. Further areas of coverage in this section include manifolds, Stokes' Theorem, Hilbert spaces, the convergence of Fourier series, and Riesz' Representation Theorem. ?Part Three provides an overview of the motivations for analysis as well as its applications in various subjects. A special focus on ordinary and partial differential equations presents some theoretical and practical challenges that exist in these areas. Topical coverage includes Navier-Stokes equations and the finite element method. Mathematical Analysis: A Concise Introduction includes an extensive index and over 900 exercises ranging in level of difficulty, from conceptual questions and adaptations of proofs to proofs with and without hints. These opportunities for reinforcement, along with the overall concise and well-organized treatment of analysis, make this book essential for readers in upper-undergraduate or beginning graduate mathematics courses who would like to build a solid foundation in analysis for further work in all analysis-based branches of mathematics.
Book Synopsis The Calculus of Variations and Optimal Control by : George Leitmann
Download or read book The Calculus of Variations and Optimal Control written by George Leitmann and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: When the Tyrian princess Dido landed on the North African shore of the Mediterranean sea she was welcomed by a local chieftain. He offered her all the land that she could enclose between the shoreline and a rope of knotted cowhide. While the legend does not tell us, we may assume that Princess Dido arrived at the correct solution by stretching the rope into the shape of a circular arc and thereby maximized the area of the land upon which she was to found Carthage. This story of the founding of Carthage is apocryphal. Nonetheless it is probably the first account of a problem of the kind that inspired an entire mathematical discipline, the calculus of variations and its extensions such as the theory of optimal control. This book is intended to present an introductory treatment of the calculus of variations in Part I and of optimal control theory in Part II. The discussion in Part I is restricted to the simplest problem of the calculus of variations. The topic is entirely classical; all of the basic theory had been developed before the turn of the century. Consequently the material comes from many sources; however, those most useful to me have been the books of Oskar Bolza and of George M. Ewing. Part II is devoted to the elementary aspects of the modern extension of the calculus of variations, the theory of optimal control of dynamical systems.
Book Synopsis A Concise Introduction to the Theory of Integration by : Daniel W. Stroock
Download or read book A Concise Introduction to the Theory of Integration written by Daniel W. Stroock and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: This little book is the outgrowth of a one semester course which I have taught for each of the past four years at M. 1. T. Although this class used to be one of the standard courses taken by essentially every first year gradu ate student of mathematics, in recent years (at least in those when I was the instructor), the clientele has shifted from first year graduate students of mathematics to more advanced graduate students in other disciplines. In fact, the majority of my students have been from departments of engi neering (especially electrical engineering) and most of the rest have been economists. Whether this state of affairs is a reflection on my teaching, the increased importance of mathematical analysis in other disciplines, the superior undergraduate preparation of students coming to M. 1. T in mathematics, or simply the lack of enthusiasm that these students have for analysis, I have preferred not to examine too closely. On the other hand, the situation did force me to do a certain amount of thinking about what constitutes an appropriate course for a group of non-mathematicians who are courageous (foolish?) enough to sign up for an introduction to in tegration theory offered by the department of mathematics. In particular, I had to figure out what to do about that vast body of material which, in standard mathematics offerings, is "assumed to have been covered in your advanced calculus course".
Download or read book Calculus written by Gilbert Strang and published by . This book was released on 2016-03-07 with total page 824 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Published by OpenStax College, Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 2 covers integration, differential equations, sequences and series, and parametric equations and polar coordinates."--BC Campus website.
Book Synopsis The Calculus Primer by : William L. Schaaf
Download or read book The Calculus Primer written by William L. Schaaf and published by Courier Corporation. This book was released on 2014-03-05 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive but concise, this introduction to differential and integral calculus covers all the topics usually included in a first course. The straightforward development places less emphasis on mathematical rigor, and the informal manner of presentation sets students at ease. Many carefully worked-out examples illuminate the text, in addition to numerous diagrams, problems, and answers. Bearing the needs of beginners constantly in mind, the treatment covers all the basic concepts of calculus: functions, derivatives, differentiation of algebraic and transcendental functions, partial differentiation, indeterminate forms, general and special methods of integration, the definite integral, partial integration, and other fundamentals. Ample exercises permit students to test their grasp of subjects before moving forward, making this volume appropriate not only for classroom use but also for review and home study.
Book Synopsis Logic and Discrete Mathematics by : Willem Conradie
Download or read book Logic and Discrete Mathematics written by Willem Conradie and published by John Wiley & Sons. This book was released on 2015-05-08 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: Solutions manual to accompany Logic and Discrete Mathematics: A Concise Introduction This book features a unique combination of comprehensive coverage of logic with a solid exposition of the most important fields of discrete mathematics, presenting material that has been tested and refined by the authors in university courses taught over more than a decade. Written in a clear and reader-friendly style, each section ends with an extensive set of exercises, most of them provided with complete solutions which are available in this accompanying solutions manual.
Book Synopsis Introduction to Stochastic Calculus with Applications by : Fima C. Klebaner
Download or read book Introduction to Stochastic Calculus with Applications written by Fima C. Klebaner and published by Imperial College Press. This book was released on 2005 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a concise treatment of stochastic calculus and its applications. It gives a simple but rigorous treatment of the subject including a range of advanced topics, it is useful for practitioners who use advanced theoretical results. It covers advanced applications, such as models in mathematical finance, biology and engineering.Self-contained and unified in presentation, the book contains many solved examples and exercises. It may be used as a textbook by advanced undergraduates and graduate students in stochastic calculus and financial mathematics. It is also suitable for practitioners who wish to gain an understanding or working knowledge of the subject. For mathematicians, this book could be a first text on stochastic calculus; it is good companion to more advanced texts by a way of examples and exercises. For people from other fields, it provides a way to gain a working knowledge of stochastic calculus. It shows all readers the applications of stochastic calculus methods and takes readers to the technical level required in research and sophisticated modelling.This second edition contains a new chapter on bonds, interest rates and their options. New materials include more worked out examples in all chapters, best estimators, more results on change of time, change of measure, random measures, new results on exotic options, FX options, stochastic and implied volatility, models of the age-dependent branching process and the stochastic Lotka-Volterra model in biology, non-linear filtering in engineering and five new figures.Instructors can obtain slides of the text from the author.
Book Synopsis Calculus of Variations by : I. M. Gelfand
Download or read book Calculus of Variations written by I. M. Gelfand and published by Courier Corporation. This book was released on 2012-04-26 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fresh, lively text serves as a modern introduction to the subject, with applications to the mechanics of systems with a finite number of degrees of freedom. Ideal for math and physics students.
Book Synopsis Introduction to Tensor Analysis and the Calculus of Moving Surfaces by : Pavel Grinfeld
Download or read book Introduction to Tensor Analysis and the Calculus of Moving Surfaces written by Pavel Grinfeld and published by Springer Science & Business Media. This book was released on 2013-09-24 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is distinguished from other texts on the subject by the depth of the presentation and the discussion of the calculus of moving surfaces, which is an extension of tensor calculus to deforming manifolds. Designed for advanced undergraduate and graduate students, this text invites its audience to take a fresh look at previously learned material through the prism of tensor calculus. Once the framework is mastered, the student is introduced to new material which includes differential geometry on manifolds, shape optimization, boundary perturbation and dynamic fluid film equations. The language of tensors, originally championed by Einstein, is as fundamental as the languages of calculus and linear algebra and is one that every technical scientist ought to speak. The tensor technique, invented at the turn of the 20th century, is now considered classical. Yet, as the author shows, it remains remarkably vital and relevant. The author’s skilled lecturing capabilities are evident by the inclusion of insightful examples and a plethora of exercises. A great deal of material is devoted to the geometric fundamentals, the mechanics of change of variables, the proper use of the tensor notation and the discussion of the interplay between algebra and geometry. The early chapters have many words and few equations. The definition of a tensor comes only in Chapter 6 – when the reader is ready for it. While this text maintains a consistent level of rigor, it takes great care to avoid formalizing the subject. The last part of the textbook is devoted to the Calculus of Moving Surfaces. It is the first textbook exposition of this important technique and is one of the gems of this text. A number of exciting applications of the calculus are presented including shape optimization, boundary perturbation of boundary value problems and dynamic fluid film equations developed by the author in recent years. Furthermore, the moving surfaces framework is used to offer new derivations of classical results such as the geodesic equation and the celebrated Gauss-Bonnet theorem.
Author :Mangatiana A. Robdera Publisher :Springer Science & Business Media ISBN 13 :0857293478 Total Pages :370 pages Book Rating :4.8/5 (572 download)
Book Synopsis A Concise Approach to Mathematical Analysis by : Mangatiana A. Robdera
Download or read book A Concise Approach to Mathematical Analysis written by Mangatiana A. Robdera and published by Springer Science & Business Media. This book was released on 2011-06-27 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text introduces to undergraduates the more abstract concepts of advanced calculus, smoothing the transition from standard calculus to the more rigorous approach of proof writing and a deeper understanding of mathematical analysis. The first part deals with the basic foundation of analysis on the real line; the second part studies more abstract notions in mathematical analysis. Each topic contains a brief introduction and detailed examples.
Book Synopsis Learning Basic Calculus by : Alexander Hahn
Download or read book Learning Basic Calculus written by Alexander Hahn and published by Springer Science & Business Media. This book was released on 1998 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introductory calculus text was developed by the author through his teaching of an honors calculus course at Notre Dame. The book develops calculus, as well as the necessary trigonometry and analytic geometry, from witin the relevant historical context, and yet it is not a textbook in the history of mathematics as such. The notation is modern, and the material is selected to cover the basics of the subject. Special emphasis is placed on pedagogy throughout. Whhile emphasizing the broad applications of the subject, emphasis is placed on the mathematical content of the subject.
