Robert P. Gilbert

Homogenization is a fairly new, yet deep field of mathematics which is used as a powerful tool for analysis of applied problems which involve multiple scales. Generally, homogenization is utilized as a modeling procedure to describe processes in complex structures. Applications of Homogenization Theory to the Study of Mineralized Tissue functions as an introduction to the theory of homogenization. At the same time, the book explains how to apply the theory to various application problems in biology, physics and engineering. The authors are experts in the field and collaborated to create this book which is a useful research monograph for applied mathematicians, engineers and geophysicists. As for students and instructors, this book is a well-rounded and comprehensive text on the topic of homogenization for graduate level courses or special mathematics classes.Features: Covers applications in both geophysics and biology. Includes recent results not found in classical books on the topic Focuses on evolutionary kinds of problems; there is little overlap with books dealing with variational methods and T-convergence Includes new results where the G-limits have different structures from the initial operators

Multivariable Calculus with Mathematica is a textbook addressing the calculus of several variables. Instead of just using Mathematica to directly solve problems, the students are encouraged to learn the syntax and to write their own code to solve problems. This not only encourages scientific computing skills but at the same time stresses the complete understanding of the mathematics. Questions are provided at the end of the chapters to test the student’s theoretical understanding of the mathematics, and there are also computer algebra questions which test the student’s ability to apply their knowledge in non-trivial ways.FeaturesEnsures that students are not just using the package to directly solve problems, but learning the syntax to write their own code to solve problemsSuitable as a main textbook for a Calculus III course, and as a supplementary text for topics scientific computing, engineering, and mathematical physicsWritten in a style that engages the students’ interest and encourages the understanding of the mathematical ideas

This book illustrates how MAPLE™ can be used to supplement a standard, elementary text in ordinary and partial differential equation. The authors are firm believers in the teaching of mathematics as an experimental science where the student does numerous calculations and then synthesizes these experiments into a general theory. The goal of the book is to teach the students enough about the computer algebra system MAPLE™ so that it can be used in an investigative way. This book was developed through ten years of instruction in the differential equations course.

This book illustrates how MAPLE™ can be used to supplement a standard, elementary text in ordinary and partial differential equation. The authors are firm believers in the teaching of mathematics as an experimental science where the student does numerous calculations and then synthesizes these experiments into a general theory. The goal of the book is to teach the students enough about the computer algebra system MAPLE™ so that it can be used in an investigative way. This book was developed through ten years of instruction in the differential equations course.

Homogenization is a fairly new, yet deep field of mathematics which is used as a powerful tool for analysis of applied problems which involve multiple scales. Generally, homogenization is utilized as a modeling procedure to describe processes in complex structures. Applications of Homogenization Theory to the Study of Mineralized Tissue functions as an introduction to the theory of homogenization. At the same time, the book explains how to apply the theory to various application problems in biology, physics and engineering. The authors are experts in the field and collaborated to create this book which is a useful research monograph for applied mathematicians, engineers and geophysicists. As for students and instructors, this book is a well-rounded and comprehensive text on the topic of homogenization for graduate level courses or special mathematics classes.Features: Covers applications in both geophysics and biology. Includes recent results not found in classical books on the topic Focuses on evolutionary kinds of problems; there is little overlap with books dealing with variational methods and T-convergence Includes new results where the G-limits have different structures from the initial operators

Multivariable Calculus with Mathematica is a textbook addressing the calculus of several variables. Instead of just using Mathematica to directly solve problems, the students are encouraged to learn the syntax and to write their own code to solve problems. This not only encourages scientific computing skills but at the same time stresses the complete understanding of the mathematics. Questions are provided at the end of the chapters to test the student’s theoretical understanding of the mathematics, and there are also computer algebra questions which test the student’s ability to apply their knowledge in non-trivial ways.FeaturesEnsures that students are not just using the package to directly solve problems, but learning the syntax to write their own code to solve problemsSuitable as a main textbook for a Calculus III course, and as a supplementary text for topics scientific computing, engineering, and mathematical physicsWritten in a style that engages the students’ interest and encourages the understanding of the mathematical ideas

Anläßlich eines Forschungsaufenthalts 1988/1989 von Bob Gilbert (University of De­ laware, USA) am Fachbereich Mathematik der Freien Universität Berlin wurde ich durch ihn auf die Verwendung symbolischer Mathematikprogramme, und zwar des Computeralgebrasystems MACSYMA, in der mathematischen Forschung aufmerk­ sam gemacht. Von diesem Zeitpunkt an kam ich von dem Gedanken der Benutzung solcher Programme in der mathematischen Lehre nicht mehr los. Die Miniaturisierung in der Computertechnologie hatte derartige Programme nun auf kleinsten Rechnern verfügbar gemacht, und ich war sicher, daß dies die Praxis von Mathematikerinnen und Mathematikern sowie Mathematikanwendern in der nahen Zukunft radikal verändern wird. Anstatt schwierige Integrale von Hand aus­ zurechnen - mit der Gefahr, sich in langwierigen Teilschritten zu verrechnen -, wird z. B. der zukünftige Bauingenieur versuchen, das betreffende Integral zunächst mit einem Mathematikprogramm zu lösen. Nur, wenn er hiermit scheitert, wird er zur bewährten Handberechnung übergehen. Wir wollen nicht verhehlen, daß auch dies eine nicht zu unterschätzende Gefahr birgt, nämlich die, Ergebnissen von Mathe­ matikprogrammen unbegrenzt Vertrauen zu schenken. Genauso, wie man ein von Hand berechnetes Resultat durch Kontrollrechnungen so lange überprüfen muß, bis man sich des Ergebnisses sicher ist, muß man die Ergebnisse, die ein Mathematik­ progamm erzeugt, einer sorgfältigen Überprüfung unterziehen. Wenn aber solche Programme sowohl in der Forschung als auch in der Praxis von Bedeutung sind, sollten sie in der mathematischen Lehre ebenfalls eine Rolle spie­ len. Weil die Praxis der Arbeit mit einem Mathematikprogramm einer entsprechen­ den Schulung bedarf, muß diese in die Mathematikausbildungintegriert werden.