The author can awaken for you a faculty which is surprisingly dormant in accountants, engineers, scientists, businesspeople, and others who work with figures. This is "number sense" — or the ability to recognize relations between numbers considered as whole quantities. Lack of this number sense makes it entirely possible for a scientist to be proficient in higher mathematics, but to bog down in the arithmetic of everyday life.
This book teaches the necessary mathematical techniques that schools neglect to teach: Horizontal addition, left to right multiplication and division, etc. You will learn a method of multiplication so rapid that you'll be able to do products in not much more time than it would take to write the problem down on paper.
This is not a collection of tricks that work in only a very few special cases, but a serious, capably planned course of basic mathematics for self-instruction. It contains over 9,000 short problems and their solutions for you to work during spare moments. Five or ten minutes spent daily on this book will, within ten weeks, give you a number sense that will double or triple your calculation speed.
In this charming volume, a noted English mathematician uses humor and anecdote to illuminate the concepts underlying "new math": groups, sets, subsets, topology, Boolean algebra, and more. According to Professor Stewart, an understanding of these concepts offers the best route to grasping the true nature of mathematics, in particular the power, beauty, and utility of pure mathematics. No advanced mathematical background is needed (a smattering of algebra, geometry, and trigonometry is helpful) to follow the author's lucid and thought-provoking discussions of such topics as functions, symmetry, axiomatics, counting, topology, hyperspace, linear algebra, real analysis, probability, computers, applications of modern mathematics, and much more.
By the time readers have finished this book, they'll have a much clearer grasp of how modern mathematicians look at figures, functions, and formulas and how a firm grasp of the ideas underlying "new math" leads toward a genuine comprehension of the nature of mathematics itself.
The book begins with a short review of calculus and ordinary differential equations, then moves on to explore integral curves and surfaces of vector fields, quasi-linear and linear equations of first order, series solutions and the Cauchy Kovalevsky theorem. It then delves into linear partial differential equations, examines the Laplace, wave and heat equations, and concludes with a brief treatment of hyperbolic systems of equations.
Among the most important features of the text are the challenging problems at the end of each section which require a wide variety of responses from students, from providing details of the derivation of an item presented to solving specific problems associated with partial differential equations. Requiring only a modest mathematical background, the text will be indispensable to those who need to use partial differential equations in solving physical problems. It will provide as well the mathematical fundamentals for those who intend to pursue the study of more advanced topics, including modern theory.
An Introduction to Numerical Methods and Analysis, SecondEdition reflects the latest trends in the field, includesnew material and revised exercises, and offers a unique emphasis onapplications. The author clearly explains how to both construct andevaluate approximations for accuracy and performance, which are keyskills in a variety of fields. A wide range of higher-level methodsand solutions, including new topics such as the roots ofpolynomials, spectral collocation, finite element ideas, andClenshaw-Curtis quadrature, are presented from an introductoryperspective, and theSecond Edition also features:ulstyle="line-height: 25px; margin-left: 15px; margin-top: 0px; font-family: Arial; font-size: 13px;"Chapters and sections that begin with basic, elementarymaterial followed by gradual coverage of more advancedmaterialExercises ranging from simple hand computations to challengingderivations and minor proofs to programming exercisesWidespread exposure and utilization of MATLAB®An appendix that contains proofs of various theorems and othermaterial
In addition to expanded explanations, the 11th edition includes new problems, updated figures and examples to help motivate students. The program is primarily intended for undergraduate students of mathematics, science, or engineering, who typically take a course on differential equations during their first or second year of study. The main prerequisite for engaging with the program is a working knowledge of calculus, gained from a normal two?] or three?] semester course sequence or its equivalent. Some familiarity with matrices will also be helpful in the chapters on systems of differential equations.
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Elementary Differential Equations and Boundary Value Problems 11e, like its predecessors, is written from the viewpoint of the applied mathematician, whose interest in differential equations may sometimes be quite theoretical, sometimes intensely practical, and often somewhere in between. The authors have sought to combine a sound and accurate (but not abstract) exposition of the elementary theory of differential equations with considerable material on methods of solution, analysis, and approximation that have proved useful in a wide variety of applications. While the general structure of the book remains unchanged, some notable changes have been made to improve the clarity and readability of basic material about differential equations and their applications. In addition to expanded explanations, the 11th edition includes new problems, updated figures and examples to help motivate students.
The program is primarily intended for undergraduate students of mathematics, science, or engineering, who typically take a course on differential equations during their first or second year of study. The main prerequisite for engaging with the program is a working knowledge of calculus, gained from a normal twoï¿1?2 or threeï¿1?2 semester course sequence or its equivalent. Some familiarity with matrices will also be helpful in the chapters on systems of differential equations.
This highly useful text shows the reader how to formulate a partial differential equation from the physical problem (constructing the mathematical model) and how to solve the equation (along with initial and boundary conditions). Written for advanced undergraduate and graduate students, as well as professionals working in the applied sciences, this clearly written book offers realistic, practical coverage of diffusion-type problems, hyperbolic-type problems, elliptic-type problems, and numerical and approximate methods. Each chapter contains a selection of relevant problems (answers are provided) and suggestions for further reading.
The book contains the existing approximation theory for elliptic problems including partial differential operators with nonsmooth coefficients. Furthermore, it presents in full detail the adaptive cross approximation method for the efficient treatment of integral operators with non-local kernel functions. The theory is supported by many numerical experiments from real applications.
This edition is organized into nine well-defined chapters: Trigonometric Fourier Series, Orthogonal Systems, Convergence of Trigonometric Fourier Series, Trigonometric Series with Decreasing Coefficients, Operations on Fourier Series, Summation of Trigonometric Fourier Series, Double Fourier Series and the Fourier Integral, Bessel Functions and Fourier-Bessel Series, and the Eigenfunction Method and its Applications to Mathematical Physics. Every chapter moves clearly from topic to topic and theorem to theorem, with many theorem proofs given. A total of 107 problems will be found at the ends of the chapters, including many specially added to this English-language edition, and answers are given at the end of the text. Richard Silverman's excellent translation makes this book readily accessible to mathematicians and math students, as well as workers and students in the fields of physics and engineering. He has also added a bibliography, containing suggestions for collateral and supplementary reading. 1962 edition.
Many of the fundamental laws of physics, chemistry, biology, andeconomics can be formulated as differential equations. Thisplain-English guide explores the many applications of thismathematical tool and shows how differential equations can help usunderstand the world around us. Differential Equations ForDummies is the perfect companion for a college differentialequations course and is an ideal supplemental resource for othercalculus classes as well as science and engineering courses. Itoffers step-by-step techniques, practical tips, numerous exercises,and clear, concise examples to help readers improve theirdifferential equation-solving skills and boost their testscores.