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| calculus volume 2 tom m. apostol: Calculus, Volume Ii, 2nd Ed Multi-variable Calculus and Linear Algebra, with Applications to Differential Equations and Probabil Tom M. Apostol, 2007 · Linear Analysis · Linear Spaces · Linear Transformations and Matrices · Determinants · Eigenvalues and Eigenvectors · Eigenvalues of Operators Acting on Euclidean Spaces · Linear Differential Equations · Systems of Differential Equations · Nonlinear Analysis · Differential Calculus of Scalar and Vector Fields · Applications of the Differential Calculus · Line Integrals · Special Topics · Set Functions and Elementary Probability · Calculus of Probabilities · Introduction to Numerical Analysis |
| calculus volume 2 tom m. apostol: Calculus, Volume 2 Tom M. Apostol, 2019-04-26 Calculus, Volume 2, 2nd Edition An introduction to the calculus, with an excellent balance between theory and technique. Integration is treated before differentiation — this is a departure from most modern texts, but it is historically correct, and it is the best way to establish the true connection between the integral and the derivative. Proofs of all the important theorems are given, generally preceded by geometric or intuitive discussion. This Second Edition introduces the mean-value theorems and their applications earlier in the text, incorporates a treatment of linear algebra, and contains many new and easier exercises. As in the first edition, an interesting historical introduction precedes each important new concept. |
| calculus volume 2 tom m. apostol: New Horizons in Geometry Tom M. Apostol, Mamikon A. Mnatsakanian, 2017-10-24 Calculus problems solved by elementary geometrical methods --- page 4 of cover. |
| calculus volume 2 tom m. apostol: Calculus of Several Variables Serge Lang, 2012-12-06 This new, revised edition covers all of the basic topics in calculus of several variables, including vectors, curves, functions of several variables, gradient, tangent plane, maxima and minima, potential functions, curve integrals, Green’s theorem, multiple integrals, surface integrals, Stokes’ theorem, and the inverse mapping theorem and its consequences. It includes many completely worked-out problems. |
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| calculus volume 2 tom m. apostol: The Mechanical Universe Steven C. Frautschi, Richard P. Olenick, Tom M. Apostol, David L. Goodstein, 2008-01-14 This innovative physics textbook intended for science and engineering majors develops classical mechanics from a historical perspective. The presentation of the standard course material includes a discussion of the thought processes of the discoverers and a description of the methods by which they arrived at their theories. However the presentation proceeds logically rather than strictly chronologically, so new concepts are introduced at the natural moment. The book assumes a familiarity with calculus, includes a discussion of rigid body motion, and contains numerous thought-provoking problems. It is largely based in content on The Mechanical Universe: Introduction to Mechanics and Heat, a book designed in conjunction with a tele-course to be offered by PBS in the Fall of 1985. The advanced edition, however, does not coincide exactly with the video lessons, contains additional material, and develops the fundamental ideas introduced in the lower-level edition to a greater degree. |
| calculus volume 2 tom m. apostol: Real Mathematical Analysis Charles Chapman Pugh, 2013-03-19 Was plane geometry your favourite math course in high school? Did you like proving theorems? Are you sick of memorising integrals? If so, real analysis could be your cup of tea. In contrast to calculus and elementary algebra, it involves neither formula manipulation nor applications to other fields of science. None. It is Pure Mathematics, and it is sure to appeal to the budding pure mathematician. In this new introduction to undergraduate real analysis the author takes a different approach from past studies of the subject, by stressing the importance of pictures in mathematics and hard problems. The exposition is informal and relaxed, with many helpful asides, examples and occasional comments from mathematicians like Dieudonne, Littlewood and Osserman. The author has taught the subject many times over the last 35 years at Berkeley and this book is based on the honours version of this course. The book contains an excellent selection of more than 500 exercises. |
| calculus volume 2 tom m. apostol: Calculus, Volume I, 2nd Ed One-variable Calculus, with an Introduction to Linear Algebra Tom M. Apostol, 2007 · Some Basic Concepts Of The Theory Of Sets · A Set Of Axioms For The Real Number System · Mathematical Induction, Summation Notation, And Related Topics · The Concepts Of The Integral Calculus · Some Applications Of Differentiation · Continuous Functions · Differential Calculus · The Relation Between Integration And Differentiation · The Logarithm, The Exponential, And The Inverse Trigonometric Functions · Polynomial Approximations To Functions · Introduction To Differential Equations · Complex Numbers · Sequences, Infinite Series, Improper Integrals · Sequences And Series Of Functions · Vector Algebra · Applications Of Vector Algebra To Analytic Geometry · Calculus Of Vector-Valued Functions · Linear Spaces · Linear Transformations And Matrices |
| calculus volume 2 tom m. apostol: Linear Algebra Tom M. Apostol, 2014-08-22 Developed from the author's successful two-volume Calculus text this book presents Linear Algebra without emphasis on abstraction or formalization. To accommodate a variety of backgrounds, the text begins with a review of prerequisites divided into precalculus and calculus prerequisites. It continues to cover vector algebra, analytic geometry, linear spaces, determinants, linear differential equations and more. |
| calculus volume 2 tom m. apostol: Advanced Calculus (Revised Edition) Lynn Harold Loomis, Shlomo Zvi Sternberg, 2014-02-26 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. |
| calculus volume 2 tom m. apostol: Introduction to Analytic Number Theory Tom M. Apostol, 2013-06-29 This book is the first volume of a two-volume textbook for undergraduates and is indeed the crystallization of a course offered by the author at the California Institute of Technology to undergraduates without any previous knowledge of number theory. For this reason, the book starts with the most elementary properties of the natural integers. Nevertheless, the text succeeds in presenting an enormous amount of material in little more than 300 pages.-—MATHEMATICAL REVIEWS |
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| calculus volume 2 tom m. apostol: Calculus, Volume Ii, 2nd Ed Multi-variable Calculus and Linear Algebra, with Applications to Differential Equations and Probabil Tom M. Apostol, 2007 · Linear Analysis · Linear Spaces · Linear Transformations and Matrices · Determinants · Eigenvalues and Eigenvectors · Eigenvalues of Operators Acting on Euclidean Spaces · Linear Differential Equations · Systems of Differential Equations · Nonlinear Analysis · Differential Calculus of Scalar and Vector Fields · Applications of the Differential Calculus · Line Integrals · Special Topics · Set Functions and Elementary Probability · Calculus of Probabilities · Introduction to Numerical Analysis |
| calculus volume 2 tom m. apostol: Modular Functions and Dirichlet Series in Number Theory Tom M. Apostol, 2012-12-06 A new edition of a classical treatment of elliptic and modular functions with some of their number-theoretic applications, this text offers an updated bibliography and an alternative treatment of the transformation formula for the Dedekind eta function. It covers many topics, such as Hecke’s theory of entire forms with multiplicative Fourier coefficients, and the last chapter recounts Bohr’s theory of equivalence of general Dirichlet series. |
| calculus volume 2 tom m. apostol: Calculus Morris Kline, 2013-05-09 Application-oriented introduction relates the subject as closely as possible to science with explorations of the derivative; differentiation and integration of the powers of x; theorems on differentiation, antidifferentiation; the chain rule; trigonometric functions; more. Examples. 1967 edition. |
| calculus volume 2 tom m. apostol: Understanding Analysis Stephen Abbott, 2012-12-06 This elementary presentation exposes readers to both the process of rigor and the rewards inherent in taking an axiomatic approach to the study of functions of a real variable. The aim is to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on questions which give analysis its inherent fascination. Each chapter begins with the discussion of some motivating examples and concludes with a series of questions. |
| calculus volume 2 tom m. apostol: The Mechanical Universe Richard P. Olenick, Tom M. Apostol, David L. Goodstein, 2008-01-14 This book studies electricity and magnetism, light, the special theory of relativity, and modern physics. |
| calculus volume 2 tom m. apostol: Calculus Michael Spivak, 1980 |
| calculus volume 2 tom m. apostol: Ordinary Differential Equations Morris Tenenbaum, Harry Pollard, 1985-10-01 Skillfully organized introductory text examines origin of differential equations, then defines basic terms and outlines the general solution of a differential equation. Subsequent sections deal with integrating factors; dilution and accretion problems; linearization of first order systems; Laplace Transforms; Newton's Interpolation Formulas, more. |
| calculus volume 2 tom m. apostol: Advanced Calculus of Several Variables C. H. Edwards, 2014-05-10 Advanced Calculus of Several Variables provides a conceptual treatment of multivariable calculus. This book emphasizes the interplay of geometry, analysis through linear algebra, and approximation of nonlinear mappings by linear ones. The classical applications and computational methods that are responsible for much of the interest and importance of calculus are also considered. This text is organized into six chapters. Chapter I deals with linear algebra and geometry of Euclidean n-space Rn. The multivariable differential calculus is treated in Chapters II and III, while multivariable integral calculus is covered in Chapters IV and V. The last chapter is devoted to venerable problems of the calculus of variations. This publication is intended for students who have completed a standard introductory calculus sequence. |
| calculus volume 2 tom m. apostol: Waterlily Ella Cara Deloria, 2009-04-01 When Blue Bird and her grandmother leave their family?s camp to gather beans for the long, threatening winter, they inadvertently avoid the horrible fate that befalls the rest of the family. Luckily, the two women are adopted by a nearby Dakota community and are eventually integrated into their kinship circles. Ella Cara Deloria?s tale follows Blue Bird and her daughter, Waterlily, through the intricate kinship practices that created unity among her people. Waterlily, published after Deloria?s death and generally viewed as the masterpiece of her career, offers a captivating glimpse into the daily life of the nineteenth-century Sioux. This new Bison Books edition features an introduction by Susan Gardner and an index. |
| calculus volume 2 tom m. apostol: A Century of Calculus: 1894-1968 Tom M. Apostol, 1992 Selected papers reprinted from American mathematical monthly (Volumes 1 - 75) and Mathematics magazine (Volumes 1 - 40). |
| calculus volume 2 tom m. apostol: Calculus of One Variable Joseph W. Kitchen, 2020-01-15 Richly textured and versatile text characterizes real numbers as a complete, ordered field. Rigorous development of the calculus, plus thorough treatment of basic topics of limits and inequalities. 1968 edition. |
| calculus volume 2 tom m. apostol: Calculus With Applications Peter D. Lax, Maria Shea Terrell, 2013-09-21 Burstein, and Lax's Calculus with Applications and Computing offers meaningful explanations of the important theorems of single variable calculus. Written with students in mathematics, the physical sciences, and engineering in mind, and revised with their help, it shows that the themes of calculation, approximation, and modeling are central to mathematics and the main ideas of single variable calculus. This edition brings the innovation of the first edition to a new generation of students. New sections in this book use simple, elementary examples to show that when applying calculus concepts to approximations of functions, uniform convergence is more natural and easier to use than point-wise convergence. As in the original, this edition includes material that is essential for students in science and engineering, including an elementary introduction to complex numbers and complex-valued functions, applications of calculus to modeling vibrations and population dynamics, and an introduction to probability and information theory. |
| calculus volume 2 tom m. apostol: Calculus Michael Comenetz, 2002 This book provides a full and clear account of the essentials of calculus, presented in an engaging style that is both readable and mathematically precise. Concepts and central ideas are emphasized throughout. Physical examples and interpretations play a leading role, and alternative approaches to fundamental ways of thinking help the student develop the intuitive understanding so important in science and engineering. Many questions and problems, with detailed solutions, encourage active reading and independent thought. Usable either as a basic classroom text or as a supplement that will give the reader a grasp of calculus as a whole, the book is also ideally suited for self-study. |
| calculus volume 2 tom m. apostol: Modern Calculus and Analytic Geometry Richard A. Silverman, 2014-04-15 A self-contained text for an introductory course, this volume places strong emphasis on physical applications. Key elements of differential equations and linear algebra are introduced early and are consistently referenced, all theorems are proved using elementary methods, and numerous worked-out examples appear throughout. The highly readable text approaches calculus from the student's viewpoint and points out potential stumbling blocks before they develop. A collection of more than 1,600 problems ranges from exercise material to exploration of new points of theory — many of the answers are found at the end of the book; some of them worked out fully so that the entire process can be followed. This well-organized, unified text is copiously illustrated, amply cross-referenced, and fully indexed. |
| calculus volume 2 tom m. apostol: Maths for Chemists: Numbers, functions and calculus Martin Cockett, Graham Doggett, 2003 An excellent resource for students who need support and understanding in working with the diverse mathematical tools required in a typical chemistry degree course. |
| calculus volume 2 tom m. apostol: Combined Answer Book for Calculus, Third and Fourth Editions Michael Spivak, 2008 |
| calculus volume 2 tom m. apostol: Multivariable Calculus, Linear Algebra, and Differential Equations Stanley I. Grossman, 2014-05-10 Multivariable Calculus, Linear Algebra, and Differential Equations, Second Edition contains a comprehensive coverage of the study of advanced calculus, linear algebra, and differential equations for sophomore college students. The text includes a large number of examples, exercises, cases, and applications for students to learn calculus well. Also included is the history and development of calculus. The book is divided into five parts. The first part includes multivariable calculus material. The second part is an introduction to linear algebra. The third part of the book combines techniques from calculus and linear algebra and contains discussions of some of the most elegant results in calculus including Taylor's theorem in n variables, the multivariable mean value theorem, and the implicit function theorem. The fourth section contains detailed discussions of first-order and linear second-order equations. Also included are optional discussions of electric circuits and vibratory motion. The final section discusses Taylor's theorem, sequences, and series. The book is intended for sophomore college students of advanced calculus. |
| calculus volume 2 tom m. apostol: Calculus James Stewart, 2006-12 Stewart's CALCULUS: CONCEPTS AND CONTEXTS, 3rd Edition focuses on major concepts and supports them with precise definitions, patient explanations, and carefully graded problems. Margin notes clarify and expand on topics presented in the body of the text. The Tools for Enriching Calculus CD-ROM contains visualizations, interactive modules, and homework hints that enrich your learning experience. iLrn Homework helps you identify where you need additional help, and Personal Tutor with SMARTHINKING gives you live, one-on-one online help from an experienced calculus tutor. In addition, the Interactive Video Skillbuilder CD-ROM takes you step-by-step through examples from the book. The new Enhanced Review Edition includes new practice tests with solutions, to give you additional help with mastering the concepts needed to succeed in the course. |
| calculus volume 2 tom m. apostol: A First Course in Calculus Serge Lang, 2012-09-17 This fifth edition of Lang's book covers all the topics traditionally taught in the first-year calculus sequence. Divided into five parts, each section of A FIRST COURSE IN CALCULUS contains examples and applications relating to the topic covered. In addition, the rear of the book contains detailed solutions to a large number of the exercises, allowing them to be used as worked-out examples -- one of the main improvements over previous editions. |
| calculus volume 2 tom m. apostol: Calculus on Manifolds Michael Spivak, 1965 This book uses elementary versions of modern methods found in sophisticated mathematics to discuss portions of advanced calculus in which the subtlety of the concepts and methods makes rigor difficult to attain at an elementary level. |
| calculus volume 2 tom m. apostol: Linear Algebra Georgi? Evgen?evich Shilov, 1977-06-01 Covers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, Euclidean spaces, unitary spaces, quadratic forms in Euclidean and unitary spaces, finite-dimensional space. Problems with hints and answers. |
| calculus volume 2 tom m. apostol: Linear Ordinary Differential Equations Earl A. Coddington, Robert Carlson, 1997-01-01 Linear Ordinary Differential Equations, a text for advanced undergraduate or beginning graduate students, presents a thorough development of the main topics in linear differential equations. A rich collection of applications, examples, and exercises illustrates each topic. The authors reinforce students' understanding of calculus, linear algebra, and analysis while introducing the many applications of differential equations in science and engineering. Three recurrent themes run through the book. The methods of linear algebra are applied directly to the analysis of systems with constant or periodic coefficients and serve as a guide in the study of eigenvalues and eigenfunction expansions. The use of power series, beginning with the matrix exponential function leads to the special functions solving classical equations. Techniques from real analysis illuminate the development of series solutions, existence theorems for initial value problems, the asymptotic behavior solutions, and the convergence of eigenfunction expansions. |
| calculus volume 2 tom m. apostol: Differential and Integral Calculus, Volume 1 Richard Courant, 2011-08-15 The classic introduction to the fundamentals of calculus Richard Courant's classic text Differential and Integral Calculus is an essential text for those preparing for a career in physics or applied math. Volume 1 introduces the foundational concepts of function and limit, and offers detailed explanations that illustrate the why as well as the how. Comprehensive coverage of the basics of integrals and differentials includes their applications as well as clearly-defined techniques and essential theorems. Multiple appendices provide supplementary explanation and author notes, as well as solutions and hints for all in-text problems. |
| calculus volume 2 tom m. apostol: Analytic Geometry and Calculus Ansel Adams, Lovincy J. Adams, Paul A. White, 1968-12-31 |
| calculus volume 2 tom m. apostol: Single Variable Calculus Dennis Zill, Warren S. Wright, 2009-12-11 Dennis Zill's mathematics texts are renowned for their student-friendly presentation and robust examples and problem sets. The Fourth Edition of Single Variable Calculus: Early Transcendentals is no exception. This outstanding revision incorporates all of the exceptional learning tools that have made Zill's texts a resounding success. Appropriate for the first two terms in the college calculus sequence, students are provided with a solid foundation in important mathematical concepts and problem solving skills, while maintaining the level of rigor expected of a Calculus course. |
| calculus volume 2 tom m. apostol: Calculus Deborah Hughes-Hallett, Andrew M. Gleason, William G. McCallum, Daniel E. Flath, David O. Lomen, David Lovelock, Jeff Tecosky-Feldman, Thomas W. Tucker, Joseph Thrash, Karen R. Rhea, Andrew Pasquale, Sheldon P. Gordon, Douglas Quinney, Patti Frazer Lock, 1997-10-24 A revision of the best selling innovative Calculus text on the market. Functions are presented graphically, numerically, algebraically, and verbally to give readers the benefit of alternate interpretations. The text is problem driven with exceptional exercises based on real world applications from engineering, physics, life sciences, and economics. Revised edition features new sections on limits and continuity, limits, l'Hopital's Rule, and relative growth rates, and hyperbolic functions. |
| calculus volume 2 tom m. apostol: Linear Algebra Kenneth Hoffman, Ray Alden Kunze, 2015 |
| calculus volume 2 tom m. apostol: Single Variable Calculus James Stewart, Daniel K. Clegg, Saleem Watson, 2020-02-19 SINGLE VARIABLE CALCULUS provides you with the strongest foundation for a STEM future. James Stewart's Calculus 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. |
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Calculus, Volume 2 Tom M. Apostol,2019-04-26 Calculus, Volume 2, 2nd Edition An introduction to the calculus, with an excellent balance between theory and technique. Integration is treated …
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Calculus, Volume 2 Tom M. Apostol,2019-04-26 Calculus, Volume 2, 2nd Edition An introduction to the calculus, with an excellent balance between theory and technique. Integration is treated …
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Content Calculus, Volume 1 Tom M. Apostol,1991-01-16 An introduction to the Calculus, with an excellent balance between theory and technique. Integration is treated before differentiation- …
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Calculus, Volume 2 Tom M. Apostol,2019-04-26 Calculus, Volume 2, 2nd Edition An introduction to the calculus, with an excellent balance between theory and technique. Integration is treated …
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Calculus, Volume 2 Tom M. Apostol,2019-04-26 Calculus, Volume 2, 2nd Edition An introduction to the calculus, with an excellent balance between theory and technique. Integration is treated …
