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Political and Related Models
The purpose of this four volume series is to make available for college teachers and students samples of important and realistic applications of mathematics which can be covered in undergraduate programs. The goal is to provide illustrations of how modern mathematics is actually employed to solve relevant contemporary problems. Although these independent chapters were prepared primarily for teachers in the general mathematical sciences, they should prove valuable to students, teachers, and research scientists in many of the fields of application as well. Prerequisites for each chapter and suggestions for the teacher are provided. Several of these chapters have been tested in a variety of cla...
Discrete and System Models
The purpose of this four volume series is to make available for college teachers and students samples of important and realistic applications of mathematics which can be covered in undergraduate programs. The goal is to provide illustrations of how modem mathematics is actually employed to solve relevant contemporary problems. Although these independent chapters were prepared primarily for teachers in the general mathematical sciences, they should prove valuable to students, teachers, and research scientists in many of the fields of application as well. Prerequisites for each chapter and suggestions for the teacher are provided. Several of these chapters have been tested in a variety of clas...
Revolutions in Differential Equations
Discusses the direction in which the field of differential equations, and its teaching, is going.
Differential Equations
The Authors' goal is to communicate an exciting new approach to Differential Equations - through Modeling, Visualization and Dynamical Systems. This new way of looking at ODEs blends the tried and true analytical methods with mathematical modeling, applications to engineering and the sciences, and geometric visualization via numerical solvers. The resulting rich insight and highly motivated learning offers students a powerful, stimulating, yet accessible experience that brings them to a deep understanding of ODEs!
Differential Equations
This effective and practical new edition continues to focus on differential equations as a powerful tool in constructing mathematical models for the physical world. It emphasizes modeling and visualization of solutions throughout. Each chapter introduces a model and then goes on to look at solutions of the differential equations involved using an integrated analytical, numerical, and qualitative approach. The authors present the material in a way that's clear and understandable to students at all levels. Throughout the text the authors convey their enthusiasm and excitement for the study of ODEs.
The Center and Cyclicity Problems
Using a computational algebra approach, this comprehensive text addresses the center and cyclicity problems as behaviors of dynamical systems and families of polynomial systems. The book gives the main properties of ideals in polynomial rings and their affine varieties followed by a discussion on the theory of normal forms and stability of differential equations. It contains numerous examples, pseudocode displays of all the computational algorithms, historical notes, nearly two hundred exercises, and an extensive bibliography, making it a suitable graduate textbook as well as research reference.
Math and Bio 2010
"Math and bio 2010 grew out of 'Meeting the Challenges: Education across the Biological, Mathematical and Computer Sciences,' a joint project of the Mathematical Association of America (MAA), the National Science Foundation Division of Undergraduate Education (NSF DUE), the National Institute of General Medical Sciences (NIGMS), the American Association for the Advancement of Science (AAAS), and the American Society for Microbiology (ASM)."--Foreword, p. vi
Hesiod's Anvil
This book is about how poets, philosophers, storytellers, and scientists have described motion, beginning with Hesiod, who imagined that the expanse of heaven and the depth of hell was the distance that an anvil falls in nine days. The reader will learn that Dante's implicit model of the earth implies a black hole at its core, that Edmond Halley championed a hollow earth, and that Da Vinci knew that the acceleration due to Earth's gravity was a constant. There are chapters modeling Jules Verne's and H.G. Wells' imaginative flights to the moon and back, analyses of Edgar Alan Poe's descending pendulum, and the solution to an old problem perhaps inspired by one of the seven wonders of the ancient world. It blends with equal voice romantic whimsy and derived equations, and anyone interested in mathematics will find new and surprising ideas about motion and the people who thought about it.
Frontiers
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