Basic Analysis I: Functions of a Real Variable is designed for students who have completed the usual calculus and ordinary differential equation sequence and a basic course in linear algebra. This is a critical course in the use of abstraction, but is just first volume in a sequence of courses which prepare students to become practicing scientists. This book is written with the aim of balancing the theory and abstraction with clear explanations and arguments, so that students who are from a variety of different areas can follow this text and use it profitably for self-study. It can also be used as a supplementary text for anyone whose work requires that they begin to assimilate more abstract mathematical concepts as part of their professional growth. Features Can be used as a traditional textbook as well as for self-study Suitable for undergraduate mathematics students, or for those in other disciplines requiring a solid grounding in abstraction Emphasises learning how to understand the consequences of assumptions using a variety of tools to provide the proofs of propositions
Basic Analysis V: Functional Analysis and Topology introduces graduate students in science to concepts from topology and functional analysis, both linear and nonlinear. It is the fifth book in a series designed to train interested readers how to think properly using mathematical abstractions, and how to use the tools of mathematical analysis in applications. It is important to realize that the most difficult part of applying mathematical reasoning to a new problem domain is choosing the underlying mathematical framework to use on the problem. Once that choice is made, we have many tools we can use to solve the problem. However, a different choice would open up avenues of analysis from a different, perhaps more productive, perspective. In this volume, the nature of these critical choices is discussed using applications involving the immune system and cognition. Features Develops a proof of the Jordan Canonical form to show some basic ideas in algebraic topology Provides a thorough treatment of topological spaces, finishing with the Krein–Milman theorem Discusses topological degree theory (Brouwer, Leray–Schauder, and Coincidence) Carefully develops manifolds and functions on manifolds ending with Riemannian metrics Suitable for advanced students in mathematics and associated disciplines Can be used as a traditional textbook as well as for self-study Author James K. Peterson is an Emeritus Professor at the School of Mathematical and Statistical Sciences, Clemson University. He tries hard to build interesting models of complex phenomena using a blend of mathematics, computation, and science. To this end, he has written four books on how to teach such things to biologists and cognitive scientists. These books grew out of his Calculus for Biologists courses offered to the biology majors from 2007 to 2015. He has taught the analysis courses since he started teaching both at Clemson and at his previous post at Michigan Technological University. In between, he spent time as a senior engineer in various aerospace firms and even did a short stint in a software development company. The problems he was exposed to were very hard, and not amenable to solution using just one approach. Using tools from many branches of mathematics, from many types of computational languages, and from first-principles analysis of natural phenomena was absolutely essential to make progress. In both mathematical and applied areas, students often need to use advanced mathematics tools they have not learned properly. So, he has recently written a series of five books on mathematical analysis to help researchers with the problem of learning new things after they have earned their degrees and are practicing scientists. Along the way, he has also written papers in immunology, cognitive science, and neural network technology, in addition to having grants from the NSF, NASA, and the US Army. He also likes to paint, build furniture, and write stories.
Basic Analysis V: Functional Analysis and Topology introduces graduate students in science to concepts from topology and functional analysis, both linear and nonlinear. It is the fifth book in a series designed to train interested readers how to think properly using mathematical abstractions, and how to use the tools of mathematical analysis in applications. It is important to realize that the most difficult part of applying mathematical reasoning to a new problem domain is choosing the underlying mathematical framework to use on the problem. Once that choice is made, we have many tools we can use to solve the problem. However, a different choice would open up avenues of analysis from a different, perhaps more productive, perspective. In this volume, the nature of these critical choices is discussed using applications involving the immune system and cognition. Features Develops a proof of the Jordan Canonical form to show some basic ideas in algebraic topology Provides a thorough treatment of topological spaces, finishing with the Krein–Milman theorem Discusses topological degree theory (Brouwer, Leray–Schauder, and Coincidence) Carefully develops manifolds and functions on manifolds ending with Riemannian metrics Suitable for advanced students in mathematics and associated disciplines Can be used as a traditional textbook as well as for self-study Author James K. Peterson is an Emeritus Professor at the School of Mathematical and Statistical Sciences, Clemson University. He tries hard to build interesting models of complex phenomena using a blend of mathematics, computation, and science. To this end, he has written four books on how to teach such things to biologists and cognitive scientists. These books grew out of his Calculus for Biologists courses offered to the biology majors from 2007 to 2015. He has taught the analysis courses since he started teaching both at Clemson and at his previous post at Michigan Technological University. In between, he spent time as a senior engineer in various aerospace firms and even did a short stint in a software development company. The problems he was exposed to were very hard, and not amenable to solution using just one approach. Using tools from many branches of mathematics, from many types of computational languages, and from first-principles analysis of natural phenomena was absolutely essential to make progress. In both mathematical and applied areas, students often need to use advanced mathematics tools they have not learned properly. So, he has recently written a series of five books on mathematical analysis to help researchers with the problem of learning new things after they have earned their degrees and are practicing scientists. Along the way, he has also written papers in immunology, cognitive science, and neural network technology, in addition to having grants from the NSF, NASA, and the US Army. He also likes to paint, build furniture, and write stories.
Basic Analysis I: Functions of a Real Variable is designed for students who have completed the usual calculus and ordinary differential equation sequence and a basic course in linear algebra. This is a critical course in the use of abstraction, but is just first volume in a sequence of courses which prepare students to become practicing scientists. This book is written with the aim of balancing the theory and abstraction with clear explanations and arguments, so that students who are from a variety of different areas can follow this text and use it profitably for self-study. It can also be used as a supplementary text for anyone whose work requires that they begin to assimilate more abstract mathematical concepts as part of their professional growth. Features Can be used as a traditional textbook as well as for self-study Suitable for undergraduate mathematics students, or for those in other disciplines requiring a solid grounding in abstraction Emphasises learning how to understand the consequences of assumptions using a variety of tools to provide the proofs of propositions
This book shows how mathematics, computer science and science can be usefully and seamlessly intertwined. It begins with a general model of cognitive processes in a network of computational nodes, such as neurons, using a variety of tools from mathematics, computational science and neurobiology. It then moves on to solve the diffusion model from a low-level random walk point of view. It also demonstrates how this idea can be used in a new approach to solving the cable equation, in order to better understand the neural computation approximations. It introduces specialized data for emotional content, which allows a brain model to be built using MatLab tools, and also highlights a simple model of cognitive dysfunction.
Basic Analysis IV: Measure Theory and Integration introduces students to concepts from measure theory and continues their training in the abstract way of looking at the world. This is a most important skill to have when your life's work will involve quantitative modeling to gain insight into the real world. This text generalizes the notion of integration to a very abstract setting in a variety of ways. We generalize the notion of the length of an interval to the measure of a set and learn how to construct the usual ideas from integration using measures. We discuss carefully the many notions of convergence that measure theory provides. Features • Can be used as a traditional textbook as well as for self-study • Suitable for advanced students in mathematics and associated disciplines • Emphasises learning how to understand the consequences of assumptions using a variety of tools to provide the proofs of propositions
Basic Analysis II: A Modern Calculus in Many Variables focuses on differentiation in Rn and important concepts about mappings from Rn to Rm, such as the inverse and implicit function theorem and change of variable formulae for multidimensional integration. These topics converge nicely with many other important applied and theoretical areas which are no longer covered in mathematical science curricula. Although it follows on from the preceding volume, this is a self-contained book, accessible to undergraduates with a minimal grounding in analysis. Features Can be used as a traditional textbook as well as for self-study Suitable for undergraduates in mathematics and associated disciplines Emphasises learning how to understand the consequences of assumptions using a variety of tools to provide the proofs of propositions
Basic Analysis III: Mappings on Infinite Dimensional Spaces is intended as a first course in abstract linear analysis. This textbook cover metric spaces, normed linear spaces and inner product spaces, along with many other deeper abstract ideas such a completeness, operators and dual spaces. These topics act as an important tool in the development of a mathematically trained scientist. Feature: Can be used as a traditional textbook as well as for self-study Suitable for undergraduates in mathematics and associated disciplines Emphasizes learning how to understand the consequences of assumptions using a variety of tools to provide the proofs of propositions
This book offers a self-study program on how mathematics, computer science and science can be profitably and seamlessly intertwined. This book focuses on two variable ODE models, both linear and nonlinear, and highlights theoretical and computational tools using MATLAB to explain their solutions. It also shows how to solve cable models using separation of variables and the Fourier Series.
This is the first edition of a unique new plastics industry resource: Who's Who in Plastics & Polymers. It is the only biographical directory of its kind and includes contact, affiliation and background information on more than 3300 individuals who are active leaders in this industry and related organizations. The biographical directory is i
Addresses the biological effects of the large number of compounds that have been recognized as endocrine disrupters. This book presents the relevant fundamentals of the endocrine systems of animals and humans, the toxicology, developmental toxicology, ecology, and risk assessment methods, and lays out the state of understanding for the field.
A concise guide to the care of small mammals, Ferrets, Rabbits, and Rodents: Clinical Medicine and Surgery covers the conditions seen most often in veterinary practice. The book emphasizes preventive medicine along with topics including disease management, ophthalmology, dentistry, and zoonosis. More than 400 illustrations demonstrate key concepts related to radiographic interpretation, relevant anatomy, and diagnostic, surgical, and therapeutic techniques. Now in full color, this edition adds coverage of more surgical procedures and expands coverage of zoonotic disease. From editors Katherine Quesenberry and James W. Carpenter, along with a team of expert contributors, the "Pink Book" provides an authoritative, single source of information that is hard to find elsewhere. A logical organization makes it quick and easy to find important information, with each section devoted to a single animal and chapters within each section organized by body system. Over 400 photographs and illustrations highlight key concepts such as radiographic interpretation and the main points of diagnostic, surgical, and therapeutic techniques. A chapter on ophthalmology provides hard-to-find information on eye care for ferrets, rabbits, rodents, and other small mammals. Coverage of preventive medicine includes basic biology, husbandry, and routine care of the healthy animal. The drug formulary supplies dosage instructions for ferrets, rabbits, guinea pigs, chinchillas, hamsters, rats/mice, prairie dogs, hedgehogs, and sugar gliders. Chapter outlines offer at-a-glance overviews of the contents of each chapter. Handy tables and charts make it easy to find key information. Expanded Zoonotic Diseases chapter adds more depth along with the latest information on the rising potential for disease transmission to humans as exotic pets become more popular. Additional surgical procedures for each species are included, some with step-by-step instructions accompanied by color photographs and line drawings. Full-color images show the sometimes minute structures of these small animals and make accurate diagnoses easier, especially for lymphoproliferative diseases of rabbits, endoscopy, cytology, and hematology.
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