Fundamentals of Scientific Mathematics

Author: George E. Owen
Publisher: Courier Corporation
ISBN: 0486164586
Format: PDF, Mobi
Download Now
Offering undergraduates a solid mathematical background (and functioning equally well for independent study), this rewarding, beautifully illustrated text covers geometry and matrices, vector algebra, analytic geometry, functions, and differential and integral calculus. 1961 edition.

Fundamentals of Scientific Computing

Author: Bertil Gustafsson
Publisher: Springer Science & Business Media
ISBN: 9783642194955
Format: PDF, ePub
Download Now
The book of nature is written in the language of mathematics -- Galileo Galilei How is it possible to predict weather patterns for tomorrow, with access solely to today’s weather data? And how is it possible to predict the aerodynamic behavior of an aircraft that has yet to be built? The answer is computer simulations based on mathematical models – sets of equations – that describe the underlying physical properties. However, these equations are usually much too complicated to solve, either by the smartest mathematician or the largest supercomputer. This problem is overcome by constructing an approximation: a numerical model with a simpler structure can be translated into a program that tells the computer how to carry out the simulation. This book conveys the fundamentals of mathematical models, numerical methods and algorithms. Opening with a tutorial on mathematical models and analysis, it proceeds to introduce the most important classes of numerical methods, with finite element, finite difference and spectral methods as central tools. The concluding section describes applications in physics and engineering, including wave propagation, heat conduction and fluid dynamics. Also covered are the principles of computers and programming, including MATLAB®.

Mathematical Foundations of Scientific Visualization Computer Graphics and Massive Data Exploration

Author: Torsten Möller
Publisher: Springer Science & Business Media
ISBN: 3540499261
Format: PDF, Kindle
Download Now
The goal of visualization is the accurate, interactive, and intuitive presentation of data. Complex numerical simulations, high-resolution imaging devices and incre- ingly common environment-embedded sensors are the primary generators of m- sive data sets. Being able to derive scienti?c insight from data increasingly depends on having mathematical and perceptual models to provide the necessary foundation for effective data analysis and comprehension. The peer-reviewed state-of-the-art research papers included in this book focus on continuous data models, such as is common in medical imaging or computational modeling. From the viewpoint of a visualization scientist, we typically collaborate with an application scientist or engineer who needs to visually explore or study an object which is given by a set of sample points, which originally may or may not have been connected by a mesh. At some point, one generally employs low-order piecewise polynomial approximationsof an object, using one or several dependent functions. In order to have an understanding of a higher-dimensional geometrical “object” or function, ef?cient algorithms supporting real-time analysis and manipulation (- tation, zooming) are needed. Often, the data represents 3D or even time-varying 3D phenomena (such as medical data), and the access to different layers (slices) and structures (the underlying topology) comprising such data is needed.

Fundamentals of Advanced Mathematics 1

Author: Henri Bourles
Publisher: Elsevier
ISBN: 0081021127
Format: PDF, Kindle
Download Now
This precis, comprised of three volumes, of which this book is the first, exposes the mathematical elements which make up the foundations of a number of contemporary scientific methods: modern theory on systems, physics and engineering. This first volume focuses primarily on algebraic questions: categories and functors, groups, rings, modules and algebra. Notions are introduced in a general framework and then studied in the context of commutative and homological algebra; their application in algebraic topology and geometry is therefore developed. These notions play an essential role in algebraic analysis (analytico-algebraic systems theory of ordinary or partial linear differential equations). The book concludes with a study of modules over the main types of rings, the rational canonical form of matrices, the (commutative) theory of elemental divisors and their application in systems of linear differential equations with constant coefficients. Part of the New Mathematical Methods, Systems, and Applications series Presents the notions, results, and proofs necessary to understand and master the various topics Provides a unified notation, making the task easier for the reader. Includes several summaries of mathematics for engineers

Fundamentals of Mathematics

Author: James Van Dyke
Publisher: Cengage Learning
ISBN: 0538497971
Format: PDF, ePub, Mobi
Download Now
The FUNDAMENTALS OF MATHEMATICS, Tenth Edition, offers a comprehensive and objectives-based review of all basic mathematics concepts. The authors prepare students for further coursework by addressing three important student needs: 1) establishing good study habits and overcoming math anxiety, 2) making the connections between mathematics and their modern, day-to-day activities, and 3) being paced and challenged according to their individual level of understanding whether right out of high school or returning to school later in life. The clear exposition and the consistency of presentation make learning arithmetic accessible for all. Key concepts presented in section objectives and further defined within the context of How and Why provide a strong foundation for learning and lasting comprehension. With a predominant emphasis on problem-solving skills, concepts, and applications based on real world data (with some introductory algebra integrated throughout), this book is suitable for individual study or for a variety of course formats: lab, self-paced, lecture, group, or combined formats. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

Wissenschaftliches Rechnen mit MATLAB

Author: Alfio Quarteroni
Publisher: Springer-Verlag
ISBN: 3540293078
Format: PDF, ePub, Docs
Download Now
Aus den Rezensionen der englischen Auflage: Dieses Lehrbuch ist eine Einführung in das Wissenschaftliche Rechnen und diskutiert Algorithmen und deren mathematischen Hintergrund. Angesprochen werden im Detail nichtlineare Gleichungen, Approximationsverfahren, numerische Integration und Differentiation, numerische Lineare Algebra, gewöhnliche Differentialgleichungen und Randwertprobleme. Zu den einzelnen Themen werden viele Beispiele und Übungsaufgaben sowie deren Lösung präsentiert, die durchweg in MATLAB formuliert sind. Der Leser findet daher nicht nur die graue Theorie sondern auch deren Umsetzung in numerischen, in MATLAB formulierten Code. MATLAB select 2003, Issue 2, p. 50. [Die Autoren] haben ein ausgezeichnetes Werk vorgelegt, das MATLAB vorstellt und eine sehr nützliche Sammlung von MATLAB Funktionen für die Lösung fortgeschrittener mathematischer und naturwissenschaftlicher Probleme bietet. [...] Die Präsentation des Stoffs ist durchgängig gut und leicht verständlich und beinhaltet Lösungen für die Übungen am Ende jedes Kapitels. Als exzellenter Neuzugang für Universitätsbibliotheken- und Buchhandlungen wird dieses Buch sowohl beim Selbststudium als auch als Ergänzung zu anderen MATLAB-basierten Büchern von großem Nutzen sein. Alles in allem: Sehr empfehlenswert. Für Studenten im Erstsemester wie für Experten gleichermassen. S.T. Karris, University of California, Berkeley, Choice 2003.

Reality Rules The Fundamentals

Author: John Casti
Publisher: John Wiley & Sons
ISBN: 9780471184355
Format: PDF, Docs
Download Now
"Casti Tours offers the most spectacular vistas of modern appliedmathematics" â??Nature Mathematical modeling is about rulesâ??the rules of reality.Reality Rules explores the syntax and semantics of the language inwhich these rules are written, the language of mathematics.Characterized by the clarity and vision typical of the author'sprevious books, Reality Rules is a window onto the competingdialects of this languageâ??in the form of mathematical modelsof real-world phenomenaâ??that researchers use today to frametheir views of reality. Moving from the irreducible basics of modeling to the upper reachesof scientific and philosophical speculation, Volumes 1 and 2, TheFundamentals and The Frontier, are ideal complements, equallymatched in difficulty, yet unique in their coverage of issuescentral to the contemporary modeling of complex systems. Engagingly written and handsomely illustrated, Reality Rules is afascinating journey into the conceptual underpinnings of realityitself, one that examines the major themes in dynamical systemtheory and modeling and the issues related to mathematical modelsin the broader contexts of science and philosophy. Far-reaching andfar-sighted, Reality Rules is destined to shape the insight andwork of students, researchers, and scholars in mathematics,science, and the social sciences for generations to come. Of related interest . . . ALTERNATE REALITIES Mathematical Models of Nature and Man John L. Casti A thoroughly modern account of the theory and practice ofmathematical modeling with a treatment focusing on system-theoreticconcepts such as complexity, self-organization, adaptation,bifurcation, resilience, surprise and uncertainty, and themathematical structures needed to employ these in a formalsystem. An Instructor's Manual presenting detailed solutions to all theproblems in the book is available from the Wiley editorialdepartment.

Fundamentals of Teaching Mathematics at University Level

Author: B Baumslag
Publisher: World Scientific
ISBN: 1783261773
Format: PDF
Download Now
This unique book presents a personal and global approach to teaching mathematics at university level. It is impressively broad in its scope, and thought-provoking in its advice. The author writes with a love of his subject and the benefit of a long and varied career. He compares and contrasts various educational systems and philosophies. Furthermore, by constantly drawing on his own experiences and those of his colleagues, he offers useful suggestions on how teachers can respond to the problems they face. This book will interest educationalists, policy advisers, administrators, lecturers, and instructors of lecturers. Contents:Education Systems in BriefThe Expansion of EducationAimsUniversities and GovernmentTeachingStudy SkillsRules of TeachingOrganisation and ExaminationsPlanningMethods of Teaching and EquipmentLecturer's ApproachSome Practical PointsAssessment of Teaching Readership: Academics and lecturers involved in mathematics teaching at higher education level. Keywords:Mathematics Education;University Mathematics;EducationReviews:“The book contains many sensible ideas on how teaching and learning should be organised. In particular the author emphasizes that to improve the quality of teaching the whole department should work together and that programmes should be carefully planned … this book is an excellent overview of mathematics teaching at university level and I would recommend it to anyone interested in pedagogical issues.”

Fundamentals of Calculus and Probability

Author: Timothy C. Kearns
Publisher: Author House
ISBN: 1496904826
Format: PDF, Kindle
Download Now
This book is a good supplementary reading of important subjects in mathematical and statistical analysis for undergraduates, or for returning students that need to have a good background in math and statistics for their studies at the graduate level. It is not a textbook, but it is an organized and easy to follow exposition of finite and infinite sets, functions, the real number system, single­variable calculus, probability, introductory statistics, and more. It has no exercises, but it has many examples throughout to reinforce the reader's understanding of important concepts. It is assumed that the reader has had some exposure to college­level math, which usually includes one or two courses in calculus and statistics. This book can help give the student a good mathematical foundation for graduate study in the mathematical sciences, especially statistics . As for my background, I have a B.S. degree in Statistics, as well as a strong minor in mathematics from Virginia Tech, and I have completed some graduate level work in mathematics at George Mason University in Northern Virginia. For many years I have been an avid reader of math and science outside of my formal education, and I have been a college­level math tutor for the past 11 years. Many of my students have told me, during my tutoring career, that I am a very good teacher of math. I sincerely feel that reading this book would teach the student about most of the fundamental concepts of mathematical and statistical analysis, and boost the student's confidence with math and statistics for their graduate studies.