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Exploring Calculus

Author: Crista Arangala
Publisher: CRC Press
ISBN: 1498771068
Size: 58.29 MB
Format: PDF, ePub
View: 1989
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This text is meant to be a hands-on lab manual that can be used in class every day to guide the exploration of the theory and applications of differential and integral calculus. For the most part, labs can be used individually or in a sequence. Each lab consists of an explanation of material with integrated exercises. Some labs are split into multiple subsections and thus exercises are separated by those subsections. The exercise sections integrate problems, technology, Mathematica R visualization, and Mathematica CDFs that allow students to discover the theory and applications of differential and integral calculus in a meaningful and memorable way.

Mathematical Modeling

Author: Crista Arangala
Publisher: CRC Press
ISBN: 1498771033
Size: 50.91 MB
Format: PDF, Kindle
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Mathematical Modeling: Branching Beyond Calculus reveals the versatility of mathematical modeling. The authors present the subject in an attractive manner and flexibley manner. Students will discover that the topic not only focuses on math, but biology, engineering, and both social and physical sciences. The book is written in a way to meet the needs of any modeling course. Each chapter includes examples, exercises, and projects offering opportunities for more in-depth investigations into the world of mathematical models. The authors encourage students to approach the models from various angles while creating a more complete understanding. The assortment of disciplines covered within the book and its flexible structure produce an intriguing and promising foundation for any mathematical modeling course or for self-study.

Exploring Linear Algebra

Author: Crista Arangala
Publisher: CRC Press
ISBN: 9781138063495
Size: 60.87 MB
Format: PDF, ePub
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This text is meant to be a hands-on lab manual that can be used in class everyday to guide the exploration of the theory and applications of linear algebra. For the most part, labs can be used individually or in a sequence. Each lab consists of and explanation of material with integrated exercises. Some labs are split into multiple subsections and thus exercises are separated by those subsections.The exercise sections integrate problems using Mathematica demonstrations (an online tool that can be used with an browser with java capabilities) and Matlab coding. This allows students to discover the theory and applications of linear algebra in a meaningful and memorable way

Exploring The Infinite

Author: Jennifer Brooks
Publisher: CRC Press
ISBN: 1498704506
Size: 78.11 MB
Format: PDF, ePub, Mobi
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Exploring the Infinite addresses the trend toward a combined transition course and introduction to analysis course. It guides the reader through the processes of abstraction and log- ical argumentation, to make the transition from student of mathematics to practitioner of mathematics. This requires more than knowledge of the definitions of mathematical structures, elementary logic, and standard proof techniques. The student focused on only these will develop little more than the ability to identify a number of proof templates and to apply them in predictable ways to standard problems. This book aims to do something more; it aims to help readers learn to explore mathematical situations, to make conjectures, and only then to apply methods of proof. Practitioners of mathematics must do all of these things. The chapters of this text are divided into two parts. Part I serves as an introduction to proof and abstract mathematics and aims to prepare the reader for advanced course work in all areas of mathematics. It thus includes all the standard material from a transition to proof" course. Part II constitutes an introduction to the basic concepts of analysis, including limits of sequences of real numbers and of functions, infinite series, the structure of the real line, and continuous functions. ? Features Two part text for the combined transition and analysis course New approach focuses on exploration and creative thought Emphasizes the limit and sequences Introduces programming skills to explore concepts in analysis Emphasis in on developing mathematical thought Exploration problems expand more traditional exercise sets

Exploring Geometry Second Edition

Author: Michael Hvidsten
Publisher: CRC Press
ISBN: 1498760821
Size: 29.71 MB
Format: PDF, ePub, Mobi
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This text promotes student engagement with the beautiful ideas of geometry. Every major concept is introduced in its historical context and connects the idea with real-life. A system of experimentation followed by rigorous explanation and proof is central. Exploratory projects play an integral role in this text. Students develop a better sense of how to prove a result and visualize connections between statements, making these connections real. They develop the intuition needed to conjecture a theorem and devise a proof of what they have observed.

A Bridge To Higher Mathematics

Author: Valentin Deaconu
Publisher: CRC Press
ISBN: 1498775268
Size: 76.91 MB
Format: PDF, Mobi
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A Bridge to Higher Mathematics is more than simply another book to aid the transition to advanced mathematics. The authors intend to assist students in developing a deeper understanding of mathematics and mathematical thought. The only way to understand mathematics is by doing mathematics. The reader will learn the language of axioms and theorems and will write convincing and cogent proofs using quantifiers. Students will solve many puzzles and encounter some mysteries and challenging problems. The emphasis is on proof. To progress towards mathematical maturity, it is necessary to be trained in two aspects: the ability to read and understand a proof and the ability to write a proof. The journey begins with elements of logic and techniques of proof, then with elementary set theory, relations and functions. Peano axioms for positive integers and for natural numbers follow, in particular mathematical and other forms of induction. Next is the construction of integers including some elementary number theory. The notions of finite and infinite sets, cardinality of counting techniques and combinatorics illustrate more techniques of proof. For more advanced readers, the text concludes with sets of rational numbers, the set of reals and the set of complex numbers. Topics, like Zorn’s lemma and the axiom of choice are included. More challenging problems are marked with a star. All these materials are optional, depending on the instructor and the goals of the course.

Mathematische Modellierung

Author: Christof Eck
Publisher: Springer-Verlag
ISBN: 3662543354
Size: 65.50 MB
Format: PDF
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Das Lehrbuch bietet eine lebendige und anschauliche Einführung in die mathematische Modellierung von Phänomenen aus den Natur- und Ingenieurwissenschaften. Leser lernen, mathematische Modelle zu verstehen und selbst herzuleiten und finden eine Fülle von Beispielen, u. a. aus den Bereichen chemische Reaktionskinetik, Populationsdynamik, Strömungsdynamik, Elastizitätstheorie und Kristallwachstum. Die Methoden der Linearen Algebra, der Analysis und der Theorie der gewöhnlichen und partiellen Differentialgleichungen werden sorgfältig eingeführt.

Algorithmen

Author: Jochen Ziegenbalg
Publisher: Springer
ISBN: 9783827401144
Size: 44.83 MB
Format: PDF
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Mit der Verbreitung des Computers hat u.a. der "Algorithmus" als ursAchlich mit diesem Werkzeug verbundener Begriff ins allgemeine VerstAndnis Einzug gehalten. TatsAchlich reichen aber Begriff und Begriffsinhalt weit zurA1/4ck, begleiten unsere Kulturgeschichte seit mehr als 2000 Jahren. Historisch (und schulisch) wesentliche Algorithmen sind beispielsweise das babylonische Verfahren des Wurzelziehens, das Verfahren des Archimedes zur Approximation der Kreiszahl Pi. Ziegenbalg stellt Algorithmik in den Kontext der Bildungsinformatik und schlieAt damit eine bestehende LA1/4cke in der Didaktik des Mathematikunterrichts.

Learning By Discovery

Author: Anita E. Solow
Publisher: Cambridge University Press
ISBN: 9780883850831
Size: 62.66 MB
Format: PDF, Mobi
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This book contains 26 laboratory modules for use in coursework or in independent projects.

Berraschende Mathematische Kurzgeschichten

Author: Matthias Müller
Publisher: Springer-Verlag
ISBN: 3658138955
Size: 51.92 MB
Format: PDF, Docs
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Dieses Buch beinhaltet etwa 20 spannende und überraschende mathematische Kurzgeschichten. Sie handeln von alltäglichen Phänomenen, amüsanten historischen Anekdoten, sportlichen Tatsachen und verblüffenden innermathematischen Problemstellungen. Kommen Sie mit auf einen mathematischen Spaziergang der abseits bekannter Pfade einlädt neue Entdeckungen zu machen. Das Buch regt auch zum vertiefenden Studium an oder gibt Ideen für Unterricht und Schule. Jeder Artikel greift eine alltägliche oder schulnahe Beobachtung auf und führt diese aus. Die Geschichten sind abwechslungsreich, informativ und unterhaltsam. Dabei runden die kleinen Comics die Geschichte auf amüsante Weise ab.