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Other titles in the Springer Undergraduate Mathematics series:
Fields, Flows, and Waves: An Introduction to Continuum Models (Springer Undergraduate Mathematics Series,)by D. F. Parker
Synopses & ReviewsPublisher Comments:This book, derived from an innovative course of lectures, is a first introduction to the mathematical description of fields, flows and waves. It shows students, early in their studies, how many of the topics they have encountered are useful in constructing, analysing and interpreting phenomena in the real world. Designed for secondyear undergraduate students in mathematics, mathematical physics, and engineering, it presumes only a limited familiarity with several variable calculus and vector fields. It develops the concepts of flux, conservation law and boundary value problem through simple examples of heat flow, electric potentials and gravitational fields. The ideas are developed through worked examples, and a range of exercises (with solutions) is provided to test understanding. Chapters 17 contain ample material for an introductory lecture course, while later chapters on waves in fluids, solids and electromagnetism, and on biomathematics, show how the extension of earlier ideas leads to the description and explanation of important topics in modern technology and science.
Synopsis:This book serves as an introduction to the use of mathematics in describing collective phenomena in physics and biology. Derived from a course of innovative lectures, the book shows students early in their studies how many of the topics they have encountered  partial differential equations, differential equations, Fourier series, and linear algebra  are useful in constructing, analysing and interpreting phenomena present in the real world. Throughout, ideas are developed using worked examples and exercises with solution. The text does not assume a strong background in physics.
Synopsis:Includes bibliographical references (p. 261262) and index.
Table of ContentsPreface. The Continuum Description. Unsteady Heat Flow. Fields and Potentials. Laplace's Equation and Poisson's Equation. Motion of an Elastic String. Fluid Flow. Elastic Deformations. Vibrations and Waves. Electromagnetic Waves and Light. Chemical and Biological Models. Solutions. Bibliography. Index
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