Differential Equations and Linear Algebra: Pearson New International Edition


Author: C. Henry Edwards,David E. Penney
Publisher: Pearson Higher Ed
ISBN: 1292052805
Category: Mathematics
Page: 696
View: 1098

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For courses in Differential Equations and Linear Algebra. Acclaimed authors Edwards and Penney combine core topics in elementary differential equations with those concepts and methods of elementary linear algebra needed for a contemporary combined introduction to differential equations and linear algebra. Known for its real-world applications and its blend of algebraic and geometric approaches, this text discusses mathematical modeling of real-world phenomena, with a fresh new computational and qualitative flavor evident throughout in figures, examples, problems, and applications. In the Third Edition, new graphics and narrative have been added as needed—yet the proven chapter and section structure remains unchanged, so that class notes and syllabi will not require revision for the new edition.

Linear Algebra and Differential Equations

Pearson New International Edition
Author: Gary L. Peterson,James S. Sochacki
Publisher: N.A
ISBN: 9781292042732
Category: Algebras, Linear
Page: 480
View: 7933

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Linear Algebra and Differential Equations has been written for a one-semester combined linear algebra and differential equations course, yet it contains enough material for a two-term sequence in linear algebra and differential equations. By introducing matrices, determinants, and vector spaces early in the course, the authors are able to fully develop the connections between linear algebra and differential equations. The book is flexible enough to be easily adapted to fit most syllabi, including separate courses that that cover linear algebra in the first followed by differential equations in the second. Technology is fully integrated where appropriate, and the text offers fresh and relevant applications to motivate student interest.

Linear Algebra and Differential Equations: Pearson New International Edition


Author: Gary L. Peterson,James S. Sochacki
Publisher: Pearson Higher Ed
ISBN: 1292054883
Category: Mathematics
Page: 480
View: 4903

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Linear Algebra and Differential Equations has been written for a one-semester combined linear algebra and differential equations course, yet it contains enough material for a two-term sequence in linear algebra and differential equations. By introducing matrices, determinants, and vector spaces early in the course, the authors are able to fully develop the connections between linear algebra and differential equations. The book is flexible enough to be easily adapted to fit most syllabi, including separate courses that that cover linear algebra in the first followed by differential equations in the second. Technology is fully integrated where appropriate, and the text offers fresh and relevant applications to motivate student interest.

Differential Equations and Linear Algebra


Author: C. Henry Edwards,David E. Penney,David Calvis
Publisher: N.A
ISBN: 9780134497181
Category:
Page: 792
View: 3997

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For courses in Differential Equations and Linear Algebra . Concepts, methods, and core topics covering elementary differential equations and linear algebra through real-world applications In a contemporary introduction to differential equations and linear algebra, acclaimed authors Edwards and Penney combine core topics in elementary differential equations with concepts and methods of elementary linear algebra. Renowned for its real-world applications and blend of algebraic and geometric approaches, Differential Equations and Linear Algebra introduces you to mathematical modeling of real-world phenomena and offers the best problems sets in any differential equations and linear algebra textbook. The 4th Edition includes fresh new computational and qualitative flavor evident throughout in figures, examples, problems, and applications. Additionally, an Expanded Applications website containing expanded applications and programming tools is now available.

Algebra

Aus dem Englischen übersetzt von Annette A’Campo
Author: Michael Artin
Publisher: Birkhäuser
ISBN: 9783764359386
Category: Mathematics
Page: 705
View: 6708

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Ordinary Differential Equations and Linear Algebra: A Systems Approach


Author: Todd Kapitula
Publisher: SIAM
ISBN: 1611974097
Category: Mathematics
Page: 300
View: 8343

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Ordinary differential equations (ODEs) and linear algebra are foundational postcalculus mathematics courses in the sciences. The goal of this text is to help students master both subject areas in a one-semester course. Linear algebra is developed first, with an eye toward solving linear systems of ODEs. A computer algebra system is used for intermediate calculations (Gaussian elimination, complicated integrals, etc.); however, the text is not tailored toward a particular system.÷Ordinary Differential Equations and Linear Algebra: A Systems Approach÷systematically develops the linear algebra needed to solve systems of ODEs and includes over 15 distinct applications of the theory, many of which are not typically seen in a textbook at this level (e.g., lead poisoning, SIR models, digital filters). It emphasizes mathematical modeling and contains group projects at the end of each chapter that allow students to more fully explore the interaction between the modeling of a system, the solution of the model, and the resulting physical description.÷

Lineare Algebra


Author: Gilbert Strang
Publisher: Springer-Verlag
ISBN: 3642556310
Category: Mathematics
Page: 656
View: 6150

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Diese Einführung in die lineare Algebra bietet einen sehr anschaulichen Zugang zum Thema. Die englische Originalausgabe wurde rasch zum Standardwerk in den Anfängerkursen des Massachusetts Institute of Technology sowie in vielen anderen nordamerikanischen Universitäten. Auch hierzulande ist dieses Buch als Grundstudiumsvorlesung für alle Studenten hervorragend lesbar. Darüber hinaus gibt es neue Impulse in der Mathematikausbildung und folgt dem Trend hin zu Anwendungen und Interdisziplinarität. Inhaltlich umfasst das Werk die Grundkenntnisse und die wichtigsten Anwendungen der linearen Algebra und eignet sich hervorragend für Studierende der Ingenieurwissenschaften, Naturwissenschaften, Mathematik und Informatik, die einen modernen Zugang zum Einsatz der linearen Algebra suchen. Ganz klar liegt hierbei der Schwerpunkt auf den Anwendungen, ohne dabei die mathematische Strenge zu vernachlässigen. Im Buch wird die jeweils zugrundeliegende Theorie mit zahlreichen Beispielen aus der Elektrotechnik, der Informatik, der Physik, Biologie und den Wirtschaftswissenschaften direkt verknüpft. Zahlreiche Aufgaben mit Lösungen runden das Werk ab.

Differential Equations

Computing and Modeling
Author: Charles Henry Edwards,David E. Penney,David Calvis
Publisher: Prentice Hall
ISBN: 9780136004387
Category: Computers
Page: 575
View: 5403

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For introductory courses in Differential Equations. This text provides the conceptual development and geometric visualization of a modern differential equations course that is still essential to science and engineering students. It reflects the new emphases that permeate the learning of elementary differential equations, including the wide availability of scientific computing environments like Maple, Mathematica, and MATLAB; its focus has shifted from the traditional manual methods to new computer-based methods that illuminate qualitative phenomena and make accessible a wider range of more realistic applications. Seldom-used topics have been trimmed and new topics added: it starts and ends with discussions of mathematical modeling of real-world phenomena, evident in figures, examples, problems, and applications throughout the text.

Lineare Algebra

Einführung, Grundlagen, Übungen
Author: Howard Anton
Publisher: Springer Verlag
ISBN: 9783827403247
Category: Mathematics
Page: 680
View: 406

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In Ihrer Hand liegt ein Lehrbuch - in sieben englischsprachigen Ausgaben praktisch erprobt - das Sie mit groem didaktischen Geschick, zudem angereichert mit zahlreichen Ubungsaufgaben, in die Grundlagen der linearen Algebra einfuhrt. Kenntnisse der Analysis werden fur das Verstandnis nicht generell vorausgesetzt, sind jedoch fur einige besonders gekennzeichnete Beispiele notig. Padagogisch erfahren, behandelt der Autor grundlegende Beweise im laufenden Text; fur den interessierten Leser jedoch unverzichtbare Beweise finden sich am Ende der entsprechenden Kapitel. Ein weiterer Vorzug des Buches: Die Darstellung der Zusammenhange zwischen den einzelnen Stoffgebieten - linearen Gleichungssystemen, Matrizen, Determinanten, Vektoren, linearen Transformationen und Eigenwerten.

Differentialgeometrie von Kurven und Flächen


Author: Manfredo P. do Carmo
Publisher: Springer-Verlag
ISBN: 3322850722
Category: Technology & Engineering
Page: 263
View: 5252

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Inhalt: Kurven - Reguläre Flächen - Die Geometrie der Gauß-Abbildung - Die innere Geometrie von Flächen - Anhang

Differentialgleichungen und ihre Anwendungen


Author: Martin Braun
Publisher: Springer-Verlag
ISBN: 3642975151
Category: Mathematics
Page: 598
View: 5867

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Dieses richtungsweisende Lehrbuch für die Anwendung der Mathematik in anderen Wissenschaftszweigen gibt eine Einführung in die Theorie der gewöhnlichen Differentialgleichungen. Fortran und APL-Programme geben den Studenten die Möglichkeit, verschiedene numerische Näherungsverfahren an ihrem PC selbst durchzurechnen. Aus den Besprechungen: "Die Darstellung ist überall mathematisch streng und zudem ungemein anregend. Abgesehen von manchen historischen Bemerkungen ... tragen dazu die vielen mit ausführlichem Hintergrund sehr eingehend entwickelten praktischen Anwendungen bei. ... Besondere Aufmerksamkeit wird der physikalisch und technisch so wichtigen Frage nach Stabilität von Lösungen eines Systems von Differentialgleichungen gewidmet. Das Buch ist wegen seiner geringen Voraussetzungen und vorzüglichen Didaktik schon für alle Studenten des 3. Semesters geeignet; seine eminent praktische Haltung empfiehlt es aber auch für alle Physiker, die mit Differentialgleichungen und ihren Anwendungen umzugehen haben." #Physikalische Blätter#

Applied Linear Algebra


Author: Peter J. Olver,Chehrzad Shakiban
Publisher: Springer
ISBN: 3319910418
Category: Mathematics
Page: 679
View: 3419

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This textbook develops the essential tools of linear algebra, with the goal of imparting technique alongside contextual understanding. Applications go hand-in-hand with theory, each reinforcing and explaining the other. This approach encourages students to develop not only the technical proficiency needed to go on to further study, but an appreciation for when, why, and how the tools of linear algebra can be used across modern applied mathematics. Providing an extensive treatment of essential topics such as Gaussian elimination, inner products and norms, and eigenvalues and singular values, this text can be used for an in-depth first course, or an application-driven second course in linear algebra. In this second edition, applications have been updated and expanded to include numerical methods, dynamical systems, data analysis, and signal processing, while the pedagogical flow of the core material has been improved. Throughout, the text emphasizes the conceptual connections between each application and the underlying linear algebraic techniques, thereby enabling students not only to learn how to apply the mathematical tools in routine contexts, but also to understand what is required to adapt to unusual or emerging problems. No previous knowledge of linear algebra is needed to approach this text, with single-variable calculus as the only formal prerequisite. However, the reader will need to draw upon some mathematical maturity to engage in the increasing abstraction inherent to the subject. Once equipped with the main tools and concepts from this book, students will be prepared for further study in differential equations, numerical analysis, data science and statistics, and a broad range of applications. The first author’s text, Introduction to Partial Differential Equations, is an ideal companion volume, forming a natural extension of the linear mathematical methods developed here.

Differential Dynamical Systems, Revised Edition


Author: James D. Meiss
Publisher: SIAM
ISBN: 161197464X
Category: Mathematics
Page: 392
View: 9004

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Differential equations are the basis for models of any physical systems that exhibit smooth change. This book combines much of the material found in a traditional course on ordinary differential equations with an introduction to the more modern theory of dynamical systems. Applications of this theory to physics, biology, chemistry, and engineering are shown through examples in such areas as population modeling, fluid dynamics, electronics, and mechanics.÷ Differential Dynamical Systems begins with coverage of linear systems, including matrix algebra; the focus then shifts to foundational material on nonlinear differential equations, making heavy use of the contraction-mapping theorem. Subsequent chapters deal specifically with dynamical systems concepts?flow, stability, invariant manifolds, the phase plane, bifurcation, chaos, and Hamiltonian dynamics. This new edition contains several important updates and revisions throughout the book. Throughout the book, the author includes exercises to help students develop an analytical and geometrical understanding of dynamics. Many of the exercises and examples are based on applications and some involve computation; an appendix offers simple codes written in Maple?, Mathematica?, and MATLAB? software to give students practice with computation applied to dynamical systems problems.

Advanced Engineering Mathematics


Author: H. C. Taneja
Publisher: I. K. International Pvt Ltd
ISBN: 9380026846
Category: Engineering mathematics
Page: 908
View: 1886

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The complete text has been divided into two volumes: Volume I (Ch. 1-13) & Volume II (Ch. 14-25). In addition To The review material and some basic topics as discussed in the opening chapter, The main text in Volume I covers topics on infinite series, differential and integral calculus, matrices, vector calculus, ordinary differential equations, special functions and Laplace transforms. The Volume II, which is in sequel to Volume I, covers topics on complex analysis, Fourier analysis, partial differential equations, statistics, numerical methods and linear programming. The self-contained text has numerous distinguishing features over the already existing books on the same topic. The chapters have been planned to create interest among the readers to study and apply the mathematical tools. The subject has been presented in a very lucid and precise manner with a wide variety of examples and exercises, which would eventually help the reader for hassle-free study. The book can be used as a text for Engineering Mathematics Course at various levels. New in this Edition * Numerical Methods in General * Numerical Methods for Differential Equations * Linear Programming

Linear Algebra and Its Applications


Author: David C. Lay,Steven R. Lay,Judith McDonald
Publisher: Pearson
ISBN: 9780321982384
Category: Mathematics
Page: 576
View: 1054

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NOTE: Before purchasing, check with your instructor to ensure you select the correct ISBN. Several versions of Pearson's MyLab & Mastering products exist for each title, and registrations are not transferable. To register for and use Pearson's MyLab & Mastering products, you may also need a Course ID, which your instructor will provide. Used books, rentals, and purchases made outside of Pearson If purchasing or renting from companies other than Pearson, the access codes for Pearson's MyLab & Mastering products may not be included, may be incorrect, or may be previously redeemed. Check with the seller before completing your purchase. Note: You are purchasing a standalone product; MyMathLab does not come packaged with this content. MyMathLab is not a self-paced technology and should only be purchased when required by an instructor. If you would like to purchase both the physical text and MyMathLab, search for: 9780134022697 / 0134022696 Linear Algebra and Its Applications plus New MyMathLab with Pearson eText -- Access Card Package, 5/e With traditional linear algebra texts, the course is relatively easy for students during the early stages as material is presented in a familiar, concrete setting. However, when abstract concepts are introduced, students often hit a wall. Instructors seem to agree that certain concepts (such as linear independence, spanning, subspace, vector space, and linear transformations) are not easily understood and require time to assimilate. These concepts are fundamental to the study of linear algebra, so students' understanding of them is vital to mastering the subject. This text makes these concepts more accessible by introducing them early in a familiar, concrete Rn setting, developing them gradually, and returning to them throughout the text so that when they are discussed in the abstract, students are readily able to understand.

Gewöhnliche Differentialgleichungen


Author: Vladimir I. Arnold
Publisher: Springer-Verlag
ISBN: 3642564801
Category: Mathematics
Page: 344
View: 6056

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nen (die fast unverändert in moderne Lehrbücher der Analysis übernommen wurde) ermöglichten ihm nach seinen eigenen Worten, "in einer halben Vier telstunde" die Flächen beliebiger Figuren zu vergleichen. Newton zeigte, daß die Koeffizienten seiner Reihen proportional zu den sukzessiven Ableitungen der Funktion sind, doch ging er darauf nicht weiter ein, da er zu Recht meinte, daß die Rechnungen in der Analysis bequemer auszuführen sind, wenn man nicht mit höheren Ableitungen arbeitet, sondern die ersten Glieder der Reihenentwicklung ausrechnet. Für Newton diente der Zusammenhang zwischen den Koeffizienten der Reihe und den Ableitungen eher dazu, die Ableitungen zu berechnen als die Reihe aufzustellen. Eine von Newtons wichtigsten Leistungen war seine Theorie des Sonnensy stems, die in den "Mathematischen Prinzipien der Naturlehre" ("Principia") ohne Verwendung der mathematischen Analysis dargestellt ist. Allgemein wird angenommen, daß Newton das allgemeine Gravitationsgesetz mit Hilfe seiner Analysis entdeckt habe. Tatsächlich hat Newton (1680) lediglich be wiesen, daß die Bahnkurven in einem Anziehungsfeld Ellipsen sind, wenn die Anziehungskraft invers proportional zum Abstandsquadrat ist: Auf das Ge setz selbst wurde Newton von Hooke (1635-1703) hingewiesen (vgl. § 8) und es scheint, daß es noch von weiteren Forschern vermutet wurde.

Vorlesungen über partielle Differentialgleichungen


Author: Vladimir I. Arnold
Publisher: Springer-Verlag
ISBN: 3540350314
Category: Mathematics
Page: 174
View: 5712

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Nach seinem bekannten und viel verwendeten Buch über gewöhnliche Differentialgleichungen widmet sich der berühmte Mathematiker Vladimir Arnold nun den partiellen Differentialgleichungen in einem neuen Lehrbuch. In seiner unnachahmlich eleganten Art führt er über einen geometrischen, anschaulichen Weg in das Thema ein, und ermöglicht den Lesern so ein vertieftes Verständnis der Natur der partiellen Differentialgleichungen. Für Studierende der Mathematik und Physik ist dieses Buch ein Muss. Wie alle Bücher Vladimir Arnolds ist dieses Buch voller geometrischer Erkenntnisse. Arnold illustriert jeden Grundsatz mit einer Abbildung. Das Buch behandelt die elementarsten Teile des Fachgebiets and beschränkt sich hauptsächlich auf das Cauchy-Problem und das Neumann-Problems für die klassischen Lineargleichungen der mathematischen Physik, insbesondere auf die Laplace-Gleichung und die Wellengleichung, wobei die Wärmeleitungsgleichung und die Korteweg-de-Vries-Gleichung aber ebenfalls diskutiert werden. Die physikalische Intuition wird besonders hervorgehoben. Eine große Anzahl von Problemen ist übers ganze Buch verteilt, und ein ganzer Satz von Aufgaben findet sich am Ende. Was dieses Buch so einzigartig macht, ist das besondere Talent Arnolds, ein Thema aus einer neuen, frischen Perspektive zu beleuchten. Er lüftet gerne den Schleier der Verallgemeinerung, der so viele mathematische Texte umgibt, und enthüllt die im wesentlichen einfachen, intuitiven Ideen, die dem Thema zugrunde liegen. Das kann er besser als jeder andere mathematische Autor.