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Starting Calculus for Biologists: Derivatives, Integration and Modeling By James Peterson
Hardcover: $48.95
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In this book, we learn how to use mathematics and computation to help us understand how to study biological sciences. The problem is the mathematics and computer science part seem to overwhelm all... More > of us and keep us from seeing how helpful it is to allow those extra points of view. We are going to try hard to avoid that trap, but make no mistake. We expect you to go on this journey eagerly and work hard to achieve the goals we set out.< Less
BioInformation Processing: A Primer On Cognitive Modeling Volume One By James Peterson
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This book is a primer on how information is processed in a typical mammalian brain. To talk about these ideas intelligently, the reader needs to use ideas from mathematics, computer science and many... More > areas of science. Intertwining these normally separate areas into a coherent whole provides an introduction to modern interdisciplinary work. In the book, we develop carefully how an excitable neuron collects information from many sources and then outputs a single voltage pulse which carries a variety of signaling information. Our modeling efforts are based on the use of MatLab (although octave is just fine) so it should be easy to do experiments yourself. We cover the usual basics of axonal pulse propagation including Hodgkin-Huxley models, dendritic cable models, first and second messenger signalling system abstractions and so forth. This book provides a good foundation towards building models of cognition which may be used for models of depression and other forms of dysfunction.< Less
Measure and Integration: First Steps By James Peterson
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This book introduces a beginning graduate student in Mathematics to the essentials of measure theory. This theory extends the notion of the length of an interval to more general notions of the size... More > of a set. These ideas are then used to build abstract versions of integration theory. We discuss how to build many such measures, Lebesgue and Lebesgue-Stieljes Integration and include a lengthy treatment of classical Riemann and Riemann-Stieljes integration tools as these are covered very incompletely these days.< Less
Calculus Two For Biologists: Higher Order Models and Their Analysis By James Peterson
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This book tries to show beginning biology majors how mathematics, computer science and biology can be usefully and pleasurably intertwined. After the necessary start up costs to develop... More > some essential calculus tools, we use a few select models to illustrate how these three fields influence each other in interesting and useful ways. Indeed, we believe that the three must be considered as part of a larger whole and that the use of these ideas is perhaps best described as an emergent phenomena! And we must always be careful to make sure our use of mathematics gives us insight. This fourth edition again adds a bit more biology and polishes the mathematical and numerical discussions. In addition,more exercises have been added and additional typographical errors have been found and corrected.< Less
More Calculus For Biologists: Partial Differential Equation Models By James Peterson
Hardcover: $50.95
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In this book, we continue to discuss how to blend mathematics, computational tools and science into a cohesive point of view. Hence, this text is a follow up to our book on mathematics for... More > biologists, Calculus for Biologists. We now add new mathematics such as the ideas of partial differentiation and approximation of functions of more than one variable and a more complete study of nonlinear differential equation models using these new tools. We also discuss more fully how to develop code with MatLab/ Octave to solve our problems numerically. We study a model of the excitable neuron which leads to the cable equation which is a standard equation in biological information processing. We use the cable equation to develop an input side model of an excitable neuron -- the dendrite -- and then build a model of the excitable neuron itself. This consists of a dendrite, a cell body or soma and the axon along which generates the action potential.< Less