Data Portal @ linkeddatafragments.org

Matches in Harvard for { <http://id.lib.harvard.edu/aleph/009018050/catalog> ?p ?o. }

• catalog abstract "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 Estimating the Error of Numerical Solutions of Systems of Nonlinear Reaction-Diffusion Equations with M. Larson and R. Williams (A.M.S. Memoirs, 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.".
• catalog contributor b12678552.
• catalog created "c2002.".
• catalog date "2002".
• catalog date "c2002.".
• catalog dateCopyrighted "c2002.".
• catalog description "Includes bibliographical references (p. [607]-608) and index.".
• catalog description "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.".
• catalog description "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 Estimating the Error of Numerical Solutions of Systems of Nonlinear Reaction-Diffusion Equations with M. Larson and R. Williams (A.M.S. Memoirs, 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.".
• catalog extent "xx, 621 p. :".
• catalog identifier "0387954848 (alk. paper)".
• catalog isPartOf "Undergraduate texts in mathematics".
• catalog issued "2002".
• catalog issued "c2002.".
• catalog language "eng".
• catalog publisher "New York : Springer,".
• catalog subject "515 21".
• catalog subject "Global analysis (Mathematics).".
• catalog subject "Mathematical analysis.".
• catalog subject "Mathematics.".
• catalog subject "QA300 .E785 2002".
• catalog tableOfContents "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.".
• catalog title "Practical analysis in one variable / Donald Estep.".
• catalog type "text".