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    Broschiertes Buch

This book attempts to place the basic ideas of real analysis and numerical analysis together in an applied setting that is both accessible and motivational to young students. The essentials of real analysis are presented in the context of a fundamental problem of applied mathematics, which is to approximate the solution of a physical model. The framework of existence, uniqueness, and methods to approximate solutions of model equations is sufficiently broad to introduce and motivate all the basic ideas of real analysis. The book includes background and review material, numerous examples,…mehr

Produktbeschreibung
This book attempts to place the basic ideas of real analysis and numerical analysis together in an applied setting that is both accessible and motivational to young students. The essentials of real analysis are presented in the context of a fundamental problem of applied mathematics, which is to approximate the solution of a physical model. The framework of existence, uniqueness, and methods to approximate solutions of model equations is sufficiently broad to introduce and motivate all the basic ideas of real analysis. The book includes background and review material, numerous examples, visualizations and alternate explanations of some key ideas, and a variety of exercises ranging from simple computations to analysis and estimates to computations on a computer. The book can be used in an honor calculus sequence typically taken by freshmen planning to major in engineering, mathematics, and science, or in an introductory course in rigorous real analysis offered to mathematics majors. Donald Estep is Professor of Mathematics at Colorado State University. He is the author of Computational Differential Equations, with K. Eriksson, P. Hansbo and C. Johnson (Cambridge University Press 1996) and Error of Numerical Solutions of Systems of Nonlinear Reaction-Diffusion Equations with M. Larson and R. Williams (A.M.S. 2000), and recently co-edited Collected Lectures on the Preservation of Stability under Discretization, with Simon Tavener (S.I.A.M., 2002), as well as numerous research articles. His research interests include computational error estimation and adaptive finite element methods, numerical solution of evolutionary problems, and computational investigation of physical models. This text places the basic ideas of real analysis and numerical analysis together in an applied setting that is both accessible and motivational to young students. The essentials of real analysis are presented in the context of a fundamental problem of applied mathematics, which is to approximate the solution of a physical model. The framework of existence, uniqueness, and methods to approximate solutions of model equations is sufficiently broad to introduce and motivate all the basic ideas of real analysis. The book includes background and review material, numerous examples, visualizations and alternate explanations of some key ideas, and a variety of exercises ranging from simple computations to analysis and estimates to computations on a computer.
  • Produktdetails
  • Undergraduate Texts in Mathematics
  • Verlag: Springer, Berlin
  • Softcover reprint of the original 1st ed. 2002
  • Seitenzahl: 648
  • Erscheinungstermin: 1. Dezember 2010
  • Englisch
  • Abmessung: 235mm x 155mm x 34mm
  • Gewicht: 966g
  • ISBN-13: 9781441930217
  • ISBN-10: 1441930213
  • Artikelnr.: 32168957
Inhaltsangabe
Preface Introduction I. Numbers and Functions, Sequences and Limits Mathematical Modeling Natural Numbers Just Aren't Enough Infinity and Mathematical Induction Rational Numbers Functions Polynomials Functions, Functions, and More Functions Lipschitz Continuity Sequences and Limits Solving the Muddy Yard Model Real Numbers Functions of Real Numbers The Bisection Algorithm Inverse Functions Fixed Points and Contraction Maps II. Differential and Integral Calculus The Linearization of a Function at a Point Analyzing the Behavior of a Population Model Interpretations of the Derivative Differentiability on Intervals Useful Properties of the Derivative The Mean Value Theorem Derivatives of Inverse Functions Modeling with Differential Equations Antidifferentiation Integration Properties of the Integral Applications of the Integral Rocket Propulsion and the Logarithm Constant Relative Rate of Change and the Exponential A Mass-Spring System and the Trigonometric Functions Fixed Point Iteration and Newton's Method Calculus Quagmires III. You Want Analysis? We've Got Your Analysis Right Here Notions of Continuity and Differentiability Sequences of Functions Relaxing Integration Delicate Limits and Gross Behavior The Weierstrass Approximation Theorem The Taylor Polynomial Polynomial Interpolation Nonlinear Differential Equations The Picard Iteration The Forward Euler Method A Conclusion or an Introduction? References Index
Rezensionen
From the reviews: MAA ONLINE "I confess that when I first started reading this book I was intrigued by the new approach of real analysis but did not quite see what it might be good for. In the end, however, I was convinced that it could be a very good textbook, especially in courses taken mostly by engineering majors: I am sure these students would find the approach to the book attractive and motivating."