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The study of electrophysiology has progressed rapidly because of the precise, delicate, and in- nious experimental studies of many investigators. The ?eld has also made great strides by uni- ingtheseexperimentalobservationsthroughmathematicaldescriptionsbasedonelectromagnetic ?eld theory, electrochemistry, etc. , which underlie these experiments. In turn, these quantitative materialsprovideanunderstandingofmanyelectrophysiologicalapplicationsthrougharelatively small number of fundamental ideas. This text is an introduction to electrophysiology, following a quantitative approach. The ?rst chapter summarizes much of the mathematics required in the following chapters. The second chapter presents a very concise overview of the principles of electrical ?elds and the concomitant current ?ow in conducting media. It utilizes basic principles from the physical sciences and engineering but takes into account the biological applications. The following six chapters are the core material of this text. Chapter 3 includes a description of how voltages/currents exist across membranes and how these are evaluated using the Nernst-Planck equation. The membrane channels, which are the basis for cell excitability, are described in Chapter 4. An examination of the time course of changes in membrane voltages that produce action potentials are considered in Chapter 5. Propagation of action potentials down ?bers is the subject of Chapter 6, and the response of ?bers to arti?cial stimuli, such as those used in cardiac pacemakers, is treated in Chapter 7. The voltages and currents produced by these active processes in the surrounding extracellular space is described in Chapter 8.