[PDF] Real Analysis With Economic Applications eBook

Author : Efe A. Ok
Publisher : Princeton University Press
Page : 833 pages
File Size : 14,79 MB
Release : 2011-09-05
Category : Business & Economics
ISBN : 1400840899

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There are many mathematics textbooks on real analysis, but they focus on topics not readily helpful for studying economic theory or they are inaccessible to most graduate students of economics. Real Analysis with Economic Applications aims to fill this gap by providing an ideal textbook and reference on real analysis tailored specifically to the concerns of such students. The emphasis throughout is on topics directly relevant to economic theory. In addition to addressing the usual topics of real analysis, this book discusses the elements of order theory, convex analysis, optimization, correspondences, linear and nonlinear functional analysis, fixed-point theory, dynamic programming, and calculus of variations. Efe Ok complements the mathematical development with applications that provide concise introductions to various topics from economic theory, including individual decision theory and games, welfare economics, information theory, general equilibrium and finance, and intertemporal economics. Moreover, apart from direct applications to economic theory, his book includes numerous fixed point theorems and applications to functional equations and optimization theory. The book is rigorous, but accessible to those who are relatively new to the ways of real analysis. The formal exposition is accompanied by discussions that describe the basic ideas in relatively heuristic terms, and by more than 1,000 exercises of varying difficulty. This book will be an indispensable resource in courses on mathematics for economists and as a reference for graduate students working on economic theory.

Author : Dean Corbae
Publisher : Princeton University Press
Page : 696 pages
File Size : 24,89 MB
Release : 2009-02-17
Category : Business & Economics
ISBN : 1400833086

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Providing an introduction to mathematical analysis as it applies to economic theory and econometrics, this book bridges the gap that has separated the teaching of basic mathematics for economics and the increasingly advanced mathematics demanded in economics research today. Dean Corbae, Maxwell B. Stinchcombe, and Juraj Zeman equip students with the knowledge of real and functional analysis and measure theory they need to read and do research in economic and econometric theory. Unlike other mathematics textbooks for economics, An Introduction to Mathematical Analysis for Economic Theory and Econometrics takes a unified approach to understanding basic and advanced spaces through the application of the Metric Completion Theorem. This is the concept by which, for example, the real numbers complete the rational numbers and measure spaces complete fields of measurable sets. Another of the book's unique features is its concentration on the mathematical foundations of econometrics. To illustrate difficult concepts, the authors use simple examples drawn from economic theory and econometrics. Accessible and rigorous, the book is self-contained, providing proofs of theorems and assuming only an undergraduate background in calculus and linear algebra. Begins with mathematical analysis and economic examples accessible to advanced undergraduates in order to build intuition for more complex analysis used by graduate students and researchers Takes a unified approach to understanding basic and advanced spaces of numbers through application of the Metric Completion Theorem Focuses on examples from econometrics to explain topics in measure theory

Author : N. L. Carothers
Publisher : Cambridge University Press
Page : 420 pages
File Size : 27,75 MB
Release : 2000-08-15
Category : Mathematics
ISBN : 9780521497565

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A text for a first graduate course in real analysis for students in pure and applied mathematics, statistics, education, engineering, and economics.

Author : Angel de la Fuente
Publisher : Cambridge University Press
Page : 630 pages
File Size : 31,4 MB
Release : 2000-01-28
Category : Business & Economics
ISBN : 9780521585293

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A textbook for a first-year PhD course in mathematics for economists and a reference for graduate students in economics.

Author : Frank Morgan
Publisher : American Mathematical Soc.
Page : 170 pages
File Size : 20,71 MB
Release : 2005
Category : Mathematics
ISBN : 0821836706

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Real Analysis builds the theory behind calculus directly from the basic concepts of real numbers, limits, and open and closed sets in $\mathbb{R}^n$. It gives the three characterizations of continuity: via epsilon-delta, sequences, and open sets. It gives the three characterizations of compactness: as ``closed and bounded,'' via sequences, and via open covers. Topics include Fourier series, the Gamma function, metric spaces, and Ascoli's Theorem. The text not only provides efficient proofs, but also shows the student how to come up with them. The excellent exercises come with select solutions in the back. Here is a real analysis text that is short enough for the student to read and understand and complete enough to be the primary text for a serious undergraduate course. Frank Morgan is the author of five books and over one hundred articles on mathematics. He is an inaugural recipient of the Mathematical Association of America's national Haimo award for excellence in teaching. With this book, Morgan has finally brought his famous direct style to an undergraduate real analysis text.

Author : Michael R. Caputo
Publisher : Cambridge University Press
Page : 632 pages
File Size : 27,37 MB
Release : 2005-01-10
Category : Business & Economics
ISBN : 1107717639

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Foundations of Dynamic Economic Analysis presents a modern and thorough exposition of the fundamental mathematical formalism used to study optimal control theory, i.e., continuous time dynamic economic processes, and to interpret dynamic economic behavior. The style of presentation, with its continual emphasis on the economic interpretation of mathematics and models, distinguishes it from several other excellent texts on the subject. This approach is aided dramatically by introducing the dynamic envelope theorem and the method of comparative dynamics early in the exposition. Accordingly, motivated and economically revealing proofs of the transversality conditions come about by use of the dynamic envelope theorem. Furthermore, such sequencing of the material naturally leads to the development of the primal-dual method of comparative dynamics and dynamic duality theory, two modern approaches used to tease out the empirical content of optimal control models. The stylistic approach ultimately draws attention to the empirical richness of optimal control theory, a feature missing in virtually all other textbooks of this type.

Author : Christopher Heil
Publisher : Springer
Page : 386 pages
File Size : 40,58 MB
Release : 2019-07-20
Category : Mathematics
ISBN : 3030269035

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Developed over years of classroom use, this textbook provides a clear and accessible approach to real analysis. This modern interpretation is based on the author’s lecture notes and has been meticulously tailored to motivate students and inspire readers to explore the material, and to continue exploring even after they have finished the book. The definitions, theorems, and proofs contained within are presented with mathematical rigor, but conveyed in an accessible manner and with language and motivation meant for students who have not taken a previous course on this subject. The text covers all of the topics essential for an introductory course, including Lebesgue measure, measurable functions, Lebesgue integrals, differentiation, absolute continuity, Banach and Hilbert spaces, and more. Throughout each chapter, challenging exercises are presented, and the end of each section includes additional problems. Such an inclusive approach creates an abundance of opportunities for readers to develop their understanding, and aids instructors as they plan their coursework. Additional resources are available online, including expanded chapters, enrichment exercises, a detailed course outline, and much more. Introduction to Real Analysis is intended for first-year graduate students taking a first course in real analysis, as well as for instructors seeking detailed lecture material with structure and accessibility in mind. Additionally, its content is appropriate for Ph.D. students in any scientific or engineering discipline who have taken a standard upper-level undergraduate real analysis course.

Author : William P. Ziemer
Publisher : Springer
Page : 389 pages
File Size : 12,94 MB
Release : 2017-11-30
Category : Mathematics
ISBN : 331964629X

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This first year graduate text is a comprehensive resource in real analysis based on a modern treatment of measure and integration. Presented in a definitive and self-contained manner, it features a natural progression of concepts from simple to difficult. Several innovative topics are featured, including differentiation of measures, elements of Functional Analysis, the Riesz Representation Theorem, Schwartz distributions, the area formula, Sobolev functions and applications to harmonic functions. Together, the selection of topics forms a sound foundation in real analysis that is particularly suited to students going on to further study in partial differential equations. This second edition of Modern Real Analysis contains many substantial improvements, including the addition of problems for practicing techniques, and an entirely new section devoted to the relationship between Lebesgue and improper integrals. Aimed at graduate students with an understanding of advanced calculus, the text will also appeal to more experienced mathematicians as a useful reference.

Author : Gábor Békés
Publisher : Cambridge University Press
Page : 741 pages
File Size : 15,21 MB
Release : 2021-05-06
Category : Business & Economics
ISBN : 1108483011

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A comprehensive textbook on data analysis for business, applied economics and public policy that uses case studies with real-world data.

Author : Richard S. Conway Jr.
Publisher : Springer Nature
Page : 276 pages
File Size : 36,35 MB
Release : 2022-04-23
Category : Business & Economics
ISBN : 3030766462

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This textbook offers an introduction to empirical regional economics, including a comprehensive and systematic overview of the fundamentals, history, development, and applications of economic base models. It not only provides a sound basis for regional economics and regional economic analysis, but it also includes numerous applications of the underlying theory. The book has an empirical orientation, highlighting the value of observation and testing in order to explain regional economic behavior. Theory plays an important role in this study, but it is only a starting point. The book is divided into three parts: the first discusses the economic base theory of regional growth and the empirical evidence supporting it, while the second part covers the specification and application of four increasingly complex regional economic models: the economic base model, the input-output model, the interindustry econometric model, and the structural time-series model. Lastly, the third part presents forty-eight regional economic case studies organized under seven headings, including economic cycles, economic policy, and regional forecasting. Given its scope, the book appeals to upper-undergraduate and graduate students majoring in economics, economic geography, and business, as well as to anyone in the private or public sector interested in gaining a better understanding of practical methods of regional economic forecasting and analysis. For additional course material, please check the author's website: https://www.empiricalregionaleconomics.com/