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| differential equations in economics: Partial Differential Equations in Economics and Finance Suren Basov, 2007 This book reviews the basic theory of partial differential equations of the first and second order and discusses their applications in economics and finance. It starts with well-known applications to consumer and producer theory, and to the theory of option pricing and then introduces new applications that emerge from current research (some of which is the author's own) in bounded rationality, game theory, and multi-dimensional screening. |
| differential equations in economics: Differential Equations, Bifurcations, and Chaos in Economics Wei-Bin Zhang, 2005 Although the application of differential equations to economics is a vast and vibrant area, the subject has not been systematically studied; it is often treated as a subsidiary part of mathematical economics textbooks. This book aims to fill that void by providing a unique blend of the theory of differential equations and their exciting applications to dynamic economics. Containing not just a comprehensive introduction to the applications of the theory of linear (and linearized) differential equations to economic analysis, the book also studies nonlinear dynamical systems, which have only been widely applied to economic analysis in recent years. It provides comprehensive coverage of the most important concepts and theorems in the theory of differential equations in a way that can be understood by any reader who has a basic knowledge of calculus and linear algebra. In addition to traditional applications of the theory to economic dynamics, the book includes many recent developments in different fields of economics. |
| differential equations in economics: Economic Dynamics Amnon Levy, 1992 A textbook for graduate or undergraduate economics students, in such courses as mathematical economics, macrodynamics, and resource economics; also suitable as an introduction to dynamic modelization for research economists. Assumes an elementary knowledge of calculus, linear algebra, and economic theory. Acidic paper. Annotation copyright by Book News, Inc., Portland, OR |
| differential equations in economics: Differential Equations, Stability, and Chaos in Dynamic Economics William A. Brock, A. G. Malliaris, 1989 This is the first economics work of its kind offering the economist the opportunity to acquire new and important analytical tools. It introduces the reader to three advanced mathematical methods by presenting both their theoretical bases and their applications to a wide range of economic models. The mathematical methods presented are ordinary differential equations, stability techniques and chaotic dynamics. Topics such as existence, continuation of solutions, uniqueness, dependence on initial data and parameters, linear systems, stability of linear systems, two dimensional phase analysis, local and global stability, the stability manifold, stability of optimal control and empirical tests for chaotic dynamics are covered and their use in economic theory is illustrated in numerous applications. These applications include microeconomic dynamics, investment theory, macroeconomic policies, capital theory, business cycles, financial economics and many others. All chapters conclude with two sections on miscellaneous applications and exercises and further remarks and references. In total the reader will find a valuable guide to over 500 selected references that use differential equations, stability analysis and chaotic dynamics. Graduate students in economics with a special interest in economic theory, economic researchers and applied mathematicians will all benefit from this volume. |
| differential equations in economics: Differential Equations, Bifurcations And Chaos In Economics Wei-bin Zhang, 2005-07-18 Although the application of differential equations to economics is a vast and vibrant area, the subject has not been systematically studied; it is often treated as a subsidiary part of mathematical economics textbooks. This book aims to fill that void by providing a unique blend of the theory of differential equations and their exciting applications to dynamic economics. Containing not just a comprehensive introduction to the applications of the theory of linear (and linearized) differential equations to economic analysis, the book also studies nonlinear dynamical systems, which have only been widely applied to economic analysis in recent years. It provides comprehensive coverage of the most important concepts and theorems in the theory of differential equations in a way that can be understood by any reader who has a basic knowledge of calculus and linear algebra. In addition to traditional applications of the theory to economic dynamics, the book includes many recent developments in different fields of economics. |
| differential equations in economics: Mathematical Modeling in Economics and Finance: Probability, Stochastic Processes, and Differential Equations Steven R. Dunbar, 2019-04-03 Mathematical Modeling in Economics and Finance is designed as a textbook for an upper-division course on modeling in the economic sciences. The emphasis throughout is on the modeling process including post-modeling analysis and criticism. It is a textbook on modeling that happens to focus on financial instruments for the management of economic risk. The book combines a study of mathematical modeling with exposure to the tools of probability theory, difference and differential equations, numerical simulation, data analysis, and mathematical analysis. Students taking a course from Mathematical Modeling in Economics and Finance will come to understand some basic stochastic processes and the solutions to stochastic differential equations. They will understand how to use those tools to model the management of financial risk. They will gain a deep appreciation for the modeling process and learn methods of testing and evaluation driven by data. The reader of this book will be successfully positioned for an entry-level position in the financial services industry or for beginning graduate study in finance, economics, or actuarial science. The exposition in Mathematical Modeling in Economics and Finance is crystal clear and very student-friendly. The many exercises are extremely well designed. Steven Dunbar is Professor Emeritus of Mathematics at the University of Nebraska and he has won both university-wide and MAA prizes for extraordinary teaching. Dunbar served as Director of the MAA's American Mathematics Competitions from 2004 until 2015. His ability to communicate mathematics is on full display in this approachable, innovative text. |
| differential equations in economics: Advances in Cross-Section Data Methods in Applied Economic Research Nicholas Tsounis, Aspasia Vlachvei, 2020-02-24 This proceedings volume presents new methods and applications in applied economics with special interest in advanced cross-section data estimation methodology. Featuring select contributions from the 2019 International Conference on Applied Economics (ICOAE 2019) held in Milan, Italy, this book explores areas such as applied macroeconomics, applied microeconomics, applied financial economics, applied international economics, applied agricultural economics, applied marketing and applied managerial economics. International Conference on Applied Economics (ICOAE) is an annual conference that started in 2008, designed to bring together economists from different fields of applied economic research, in order to share methods and ideas. Applied economics is a rapidly growing field of economics that combines economic theory with econometrics, to analyze economic problems of the real world, usually with economic policy interest. In addition, there is growing interest in the field of applied economics for cross-section data estimation methods, tests and techniques. This volume makes a contribution in the field of applied economic research by presenting the most current research. Featuring country specific studies, this book is of interest to academics, students, researchers, practitioners, and policy makers in applied economics, econometrics and economic policy. |
| differential equations in economics: Theory of Stochastic Differential Equations with Jumps and Applications Rong SITU, 2006-05-06 Stochastic differential equations (SDEs) are a powerful tool in science, mathematics, economics and finance. This book will help the reader to master the basic theory and learn some applications of SDEs. In particular, the reader will be provided with the backward SDE technique for use in research when considering financial problems in the market, and with the reflecting SDE technique to enable study of optimal stochastic population control problems. These two techniques are powerful and efficient, and can also be applied to research in many other problems in nature, science and elsewhere. |
| differential equations in economics: Differential Games in Economics and Management Science Engelbert Dockner, 2000-11-16 A comprehensive, self-contained survey of the theory and applications of differential games, one of the most commonly used tools for modelling and analysing economics and management problems which are characterised by both multiperiod and strategic decision making. Although no prior knowledge of game theory is required, a basic knowledge of linear algebra, ordinary differential equations, mathematical programming and probability theory is necessary. Part One presents the theory of differential games, starting with the basic concepts of game theory and going on to cover control theoretic models, Markovian equilibria with simultaneous play, differential games with hierarchical play, trigger strategy equilibria, differential games with special structures, and stochastic differential games. Part Two offers applications to capital accumulation games, industrial organization and oligopoly games, marketing, resources and environmental economics. |
| differential equations in economics: Economic Dynamics: Methods and Models G Gandolfo, 1971-01-01 Economic Dynamics: Methods and Models aims to give a simple but comprehensive treatment of mathematical methods used in economic dynamics and show how they are utilized to build and to analyze dynamic models. The text also focuses on methods, and every mathematical technique introduced is followed by its application to selected models. The book is divided into three different parts. Part I: Different Equations discusses general principles; first-order, second-order, higher-order equations; simultaneous systems; and their economic applications. Part II: Differential Equations also discusses the same areas as those in Part I, but instead features differential equations, as what the section name suggests. Part III: More Advanced Material covers comparative statistics and the comparative principle; stability of equilibrium and Liapunov's second method; and linear mixed differential and difference equations, as well as its other related topics. The text is recommended for mathematicians and economists who have an idea on advanced mathematics and would like to know more about its applications in economics. |
| differential equations in economics: Mathematical Methods in Dynamic Economics A. Simonovits, 2000-06-05 This book contains a concise description of important mathematical methods of dynamics and suitable economic models. It covers discrete as well as continuous-time systems, linear and nonlinear models. Mixing traditional and modern materials, the study covers dynamics with and without optimization, naive and rational expectations, respectively. In addition to standard models of growth and cycles, the book also contains original studies on control of a multisector economy and expectations-driven multicohort economy. Numerous examples, problems (with solutions) and figures complete the book. |
| differential equations in economics: Mathematics and Methodology for Economics Wolfgang Eichhorn, Winfried Gleißner, 2016-02-11 This book about mathematics and methodology for economics is the result of the lifelong experience of the authors. It is written for university students as well as for students of applied sciences. This self-contained book does not assume any previous knowledge of high school mathematics and helps understanding the basics of economic theory-building. Starting from set theory it thoroughly discusses linear and non-linear functions, differential equations, difference equations, and all necessary theoretical constructs for building sound economic models. The authors also present a solid introduction to linear optimisation and game theory using production systems. A detailed discussion on market equilibrium, in particular on Nash Equilibrium, and on non-linear optimisation is also provided. Throughout the book the student is well supplied with numerous examples, some 2000 problems and their solutions to apply the knowledge to economic theories and models. |
| differential equations in economics: An Introduction to Mathematics for Economics Akihito Asano, 2012-11-08 A concise, accessible introduction to maths for economics with lots of practical applications to help students learn in context. |
| differential equations in economics: Mathematics for Economics Michael Hoy, 2001 This text offers a presentation of the mathematics required to tackle problems in economic analysis. After a review of the fundamentals of sets, numbers, and functions, it covers limits and continuity, the calculus of functions of one variable, linear algebra, multivariate calculus, and dynamics. |
| differential equations in economics: Attractors, Bifurcations, & Chaos Tönu Puu, 2003-07-10 Attractors, Bifurcations, & Chaos - now in its second edition - begins with an introduction to mathematical methods in modern nonlinear dynamics and deals with differential equations. Phenomena such as bifurcations and deterministic chaos are given considerable emphasis, both in the methodological part, and in the second part, containing various applications in economics and in regional science. Coexistence of attractors and the multiplicity of development paths in nonlinear systems are central topics. The applications focus on issues such as business cycles, oligopoly, interregional trade dynamics, and economic development theory. |
| differential equations in economics: Uncertain Differential Equations Kai Yao, 2016-08-29 This book introduces readers to the basic concepts of and latest findings in the area of differential equations with uncertain factors. It covers the analytic method and numerical method for solving uncertain differential equations, as well as their applications in the field of finance. Furthermore, the book provides a number of new potential research directions for uncertain differential equation. It will be of interest to researchers, engineers and students in the fields of mathematics, information science, operations research, industrial engineering, computer science, artificial intelligence, automation, economics, and management science. |
| differential equations in economics: Mathematics for Economics and Finance Martin Anthony, Norman Biggs, 1996-07-13 Mathematics has become indispensable in the modelling of economics, finance, business and management. Without expecting any particular background of the reader, this book covers the following mathematical topics, with frequent reference to applications in economics and finance: functions, graphs and equations, recurrences (difference equations), differentiation, exponentials and logarithms, optimisation, partial differentiation, optimisation in several variables, vectors and matrices, linear equations, Lagrange multipliers, integration, first-order and second-order differential equations. The stress is on the relation of maths to economics, and this is illustrated with copious examples and exercises to foster depth of understanding. Each chapter has three parts: the main text, a section of further worked examples and a summary of the chapter together with a selection of problems for the reader to attempt. For students of economics, mathematics, or both, this book provides an introduction to mathematical methods in economics and finance that will be welcomed for its clarity and breadth. |
| differential equations in economics: Economic Dynamics with Memory Vasily E. Tarasov, Valentina V. Tarasova, 2021-01-18 This book presents the applications of fractional calculus, fractional operators of non-integer orders and fractional differential equations in describing economic dynamics with long memory. Generalizations of basic economic concepts, notions and methods for the economic processes with memory are suggested. New micro and macroeconomic models with continuous time are proposed to describe the fractional economic dynamics with long memory as well. |
| differential equations in economics: Dynamical Systems Pierre N.V. Tu, 2013-11-11 Dynamic tools of analysis and modelling are increasingly used in Economics and Biology and have become more and more sophisticated in recent years, to the point where the general students without training in Dynamic Systems (DS) would be at a loss. No doubt they are referred to the original sources of mathematical theorems used in the various proofs, but the level of mathematics is generally beyond them. Students are thus left with the burden of somehow understanding advanced mathematics by themselves, with· very little help. It is to these general students, equipped only with a modest background of Calculus and Matrix Algebra that this book is dedicated. It aims at providing them with a fairly comprehensive box of dynamical tools they are expected to have at their disposal. The first three Chapters start with the most elementary notions of first and second order Differential and Difference Equations. For these, no matrix theory and hardly any calculus are needed. Then, before embarking on linear and nonlinear DS, a review of some Linear Algebra in Chapter 4 provides the bulk of matrix theory required for the study of later Chapters. Systems of Linear Differ ential Equations (Ch. 5) and Difference Equations (Ch. 6) then follow to provide students with a good background in linear DS, necessary for the subsequent study of nonlinear systems. Linear Algebra, reviewed in Ch. 4, is used freely in these and subsequent chapters to save space and time. |
| differential equations in economics: Numerical Methods in Economics Kenneth L. Judd, 1998-09-28 To harness the full power of computer technology, economists need to use a broad range of mathematical techniques. In this book, Kenneth Judd presents techniques from the numerical analysis and applied mathematics literatures and shows how to use them in economic analyses. The book is divided into five parts. Part I provides a general introduction. Part II presents basics from numerical analysis on R^n, including linear equations, iterative methods, optimization, nonlinear equations, approximation methods, numerical integration and differentiation, and Monte Carlo methods. Part III covers methods for dynamic problems, including finite difference methods, projection methods, and numerical dynamic programming. Part IV covers perturbation and asymptotic solution methods. Finally, Part V covers applications to dynamic equilibrium analysis, including solution methods for perfect foresight models and rational expectation models. A website contains supplementary material including programs and answers to exercises. |
| differential equations in economics: Optimal Control Theory with Applications in Economics Thomas A. Weber, 2011-09-30 A rigorous introduction to optimal control theory, with an emphasis on applications in economics. This book bridges optimal control theory and economics, discussing ordinary differential equations, optimal control, game theory, and mechanism design in one volume. Technically rigorous and largely self-contained, it provides an introduction to the use of optimal control theory for deterministic continuous-time systems in economics. The theory of ordinary differential equations (ODEs) is the backbone of the theory developed in the book, and chapter 2 offers a detailed review of basic concepts in the theory of ODEs, including the solution of systems of linear ODEs, state-space analysis, potential functions, and stability analysis. Following this, the book covers the main results of optimal control theory, in particular necessary and sufficient optimality conditions; game theory, with an emphasis on differential games; and the application of control-theoretic concepts to the design of economic mechanisms. Appendixes provide a mathematical review and full solutions to all end-of-chapter problems. The material is presented at three levels: single-person decision making; games, in which a group of decision makers interact strategically; and mechanism design, which is concerned with a designer's creation of an environment in which players interact to maximize the designer's objective. The book focuses on applications; the problems are an integral part of the text. It is intended for use as a textbook or reference for graduate students, teachers, and researchers interested in applications of control theory beyond its classical use in economic growth. The book will also appeal to readers interested in a modeling approach to certain practical problems involving dynamic continuous-time models. |
| differential equations in economics: Mathematical Methods and Models in Economic Dynamics Giancarlo Gandolfo, 1972 Textbook on mathematics methodology and economic models commonly used in economic dynamics (economic analysis) - comprises two sections on the techniques of difference and differential equations. Bibliography pp. 489 to 498. |
| differential equations in economics: Fuzzy Mathematics in Economics and Engineering James J. Buckley, Esfandiar Eslami, Thomas Feuring, 2013-06-05 The book aims at surveying results in the application of fuzzy sets and fuzzy logic to economics and engineering. New results include fuzzy non-linear regression, fully fuzzified linear programming, fuzzy multi-period control, fuzzy network analysis, each using an evolutionary algorithm; fuzzy queuing decision analysis using possibility theory; fuzzy differential equations; fuzzy difference equations; fuzzy partial differential equations; fuzzy eigenvalues based on an evolutionary algorithm; fuzzy hierarchical analysis using an evolutionary algorithm; fuzzy integral equations. Other important topics covered are fuzzy input-output analysis; fuzzy mathematics of finance; fuzzy PERT (project evaluation and review technique). No previous knowledge of fuzzy sets is needed. The mathematical background is assumed to be elementary calculus. |
| differential equations in economics: The Economics of Continuous-Time Finance Bernard Dumas, Elisa Luciano, 2017-10-27 An introduction to economic applications of the theory of continuous-time finance that strikes a balance between mathematical rigor and economic interpretation of financial market regularities. This book introduces the economic applications of the theory of continuous-time finance, with the goal of enabling the construction of realistic models, particularly those involving incomplete markets. Indeed, most recent applications of continuous-time finance aim to capture the imperfections and dysfunctions of financial markets—characteristics that became especially apparent during the market turmoil that started in 2008. The book begins by using discrete time to illustrate the basic mechanisms and introduce such notions as completeness, redundant pricing, and no arbitrage. It develops the continuous-time analog of those mechanisms and introduces the powerful tools of stochastic calculus. Going beyond other textbooks, the book then focuses on the study of markets in which some form of incompleteness, volatility, heterogeneity, friction, or behavioral subtlety arises. After presenting solutions methods for control problems and related partial differential equations, the text examines portfolio optimization and equilibrium in incomplete markets, interest rate and fixed-income modeling, and stochastic volatility. Finally, it presents models where investors form different beliefs or suffer frictions, form habits, or have recursive utilities, studying the effects not only on optimal portfolio choices but also on equilibrium, or the price of primitive securities. The book strikes a balance between mathematical rigor and the need for economic interpretation of financial market regularities, although with an emphasis on the latter. |
| differential equations in economics: Differential Equations, Discrete Systems and Control A. Halanay, J. Samuel, 2013-03-13 This volume presents some of the most important mathematical tools for studying economic models. It contains basic topics concerning linear differential equations and linear discrete-time systems; a sketch of the general theory of nonlinear systems and the stability of equilibria; an introduction to numerical methods for differential equations, and some applications to the solution of nonlinear equations and static optimization. The second part of the book discusses stabilization problems, including optimal stabilization, linear-quadratic optimization and other problems of dynamic optimization, including a proof of the Maximum Principle for general optimal control problems. All these mathematical subjects are illustrated with detailed discussions of economic models. Audience: This text is recommended as auxiliary material for undergraduate and graduate level MBA students, while at the same time it can also be used as a reference by specialists. |
| differential equations in economics: Quantitative Economics with R Vikram Dayal, 2020-02-03 This book provides a contemporary treatment of quantitative economics, with a focus on data science. The book introduces the reader to R and RStudio, and uses expert Hadley Wickham’s tidyverse package for different parts of the data analysis workflow. After a gentle introduction to R code, the reader’s R skills are gradually honed, with the help of “your turn” exercises. At the heart of data science is data, and the book equips the reader to import and wrangle data, (including network data). Very early on, the reader will begin using the popular ggplot2 package for visualizing data, even making basic maps. The use of R in understanding functions, simulating difference equations, and carrying out matrix operations is also covered. The book uses Monte Carlo simulation to understand probability and statistical inference, and the bootstrap is introduced. Causal inference is illuminated using simulation, data graphs, and R code for applications with real economic examples, covering experiments, matching, regression discontinuity, difference-in-difference, and instrumental variables. The interplay of growth related data and models is presented, before the book introduces the reader to time series data analysis with graphs, simulation, and examples. Lastly, two computationally intensive methods—generalized additive models and random forests (an important and versatile machine learning method)—are introduced intuitively with applications. The book will be of great interest to economists—students, teachers, and researchers alike—who want to learn R. It will help economics students gain an intuitive appreciation of applied economics and enjoy engaging with the material actively, while also equipping them with key data science skills. |
| differential equations in economics: Differential Equations on Measures and Functional Spaces Vassili Kolokoltsov, 2019-06-20 This advanced book focuses on ordinary differential equations (ODEs) in Banach and more general locally convex spaces, most notably the ODEs on measures and various function spaces. It briefly discusses the fundamentals before moving on to the cutting edge research in linear and nonlinear partial and pseudo-differential equations, general kinetic equations and fractional evolutions. The level of generality chosen is suitable for the study of the most important nonlinear equations of mathematical physics, such as Boltzmann, Smoluchovskii, Vlasov, Landau-Fokker-Planck, Cahn-Hilliard, Hamilton-Jacobi-Bellman, nonlinear Schroedinger, McKean-Vlasov diffusions and their nonlocal extensions, mass-action-law kinetics from chemistry. It also covers nonlinear evolutions arising in evolutionary biology and mean-field games, optimization theory, epidemics and system biology, in general models of interacting particles or agents describing splitting and merging, collisions and breakage, mutations and the preferential-attachment growth on networks. The book is intended mainly for upper undergraduate and graduate students, but is also of use to researchers in differential equations and their applications. It particularly highlights the interconnections between various topics revealing where and how a particular result is used in other chapters or may be used in other contexts, and also clarifies the links between the languages of pseudo-differential operators, generalized functions, operator theory, abstract linear spaces, fractional calculus and path integrals. |
| differential equations in economics: Backward Stochastic Differential Equations Jianfeng Zhang, 2017-08-22 This book provides a systematic and accessible approach to stochastic differential equations, backward stochastic differential equations, and their connection with partial differential equations, as well as the recent development of the fully nonlinear theory, including nonlinear expectation, second order backward stochastic differential equations, and path dependent partial differential equations. Their main applications and numerical algorithms, as well as many exercises, are included. The book focuses on ideas and clarity, with most results having been solved from scratch and most theories being motivated from applications. It can be considered a starting point for junior researchers in the field, and can serve as a textbook for a two-semester graduate course in probability theory and stochastic analysis. It is also accessible for graduate students majoring in financial engineering. |
| differential equations in economics: Introduction to Difference Equations Samuel Goldberg, 1986-01-01 Exceptionally clear exposition of an important mathematical discipline and its applications to sociology, economics, and psychology. Topics include calculus of finite differences, difference equations, matrix methods, and more. 1958 edition. |
| differential equations in economics: Mathematical Economics Kelvin Lancaster, 2012-10-10 Graduate-level text provides complete and rigorous expositions of economic models analyzed primarily from the point of view of their mathematical properties, followed by relevant mathematical reviews. Part I covers optimizing theory; Parts II and III survey static and dynamic economic models; and Part IV contains the mathematical reviews, which range fromn linear algebra to point-to-set mappings. |
| differential equations in economics: Game Theory and Partial Differential Equations Pablo Blanc, Julio Daniel Rossi, 2019-07-22 Extending the well-known connection between classical linear potential theory and probability theory (through the interplay between harmonic functions and martingales) to the nonlinear case of tug-of-war games and their related partial differential equations, this unique book collects several results in this direction and puts them in an elementary perspective in a lucid and self-contained fashion. |
| differential equations in economics: Mathematical Economics Vasily E. Tarasov, 2020-06-03 This book is devoted to the application of fractional calculus in economics to describe processes with memory and non-locality. Fractional calculus is a branch of mathematics that studies the properties of differential and integral operators that are characterized by real or complex orders. Fractional calculus methods are powerful tools for describing the processes and systems with memory and nonlocality. Recently, fractional integro-differential equations have been used to describe a wide class of economical processes with power law memory and spatial nonlocality. Generalizations of basic economic concepts and notions the economic processes with memory were proposed. New mathematical models with continuous time are proposed to describe economic dynamics with long memory. This book is a collection of articles reflecting the latest mathematical and conceptual developments in mathematical economics with memory and non-locality based on applications of fractional calculus. |
| differential equations in economics: Mathematical Methods and Models for Economists Angel de la Fuente, 2000-01-28 A textbook for a first-year PhD course in mathematics for economists and a reference for graduate students in economics. |
| differential equations in economics: Mathematical Modeling in Economics, Ecology and the Environment N.V. Hritonenko, Yuri P. Yatsenko, 2013-04-17 The problems of interrelation between human economics and natural environment include scientific, technical, economic, demographic, social, political and other aspects that are studied by scientists of many specialities. One of the important aspects in scientific study of environmental and ecological problems is the development of mathematical and computer tools for rational management of economics and environment. This book introduces a wide range of mathematical models in economics, ecology and environmental sciences to a general mathematical audience with no in-depth experience in this specific area. Areas covered are: controlled economic growth and technological development, world dynamics, environmental impact, resource extraction, air and water pollution propagation, ecological population dynamics and exploitation. A variety of known models are considered, from classical ones (Cobb Douglass production function, Leontief input-output analysis, Solow models of economic dynamics, Verhulst-Pearl and Lotka-Volterra models of population dynamics, and others) to the models of world dynamics and the models of water contamination propagation used after Chemobyl nuclear catastrophe. Special attention is given to modelling of hierarchical regional economic-ecological interaction and technological change in the context of environmental impact. Xlll XIV Construction of Mathematical Models ... |
| differential equations in economics: Linear Algebra for Economists Fuad Aleskerov, Hasan Ersel, Dmitri Piontkovski, 2011-08-18 This textbook introduces students of economics to the fundamental notions and instruments in linear algebra. Linearity is used as a first approximation to many problems that are studied in different branches of science, including economics and other social sciences. Linear algebra is also the most suitable to teach students what proofs are and how to prove a statement. The proofs that are given in the text are relatively easy to understand and also endow the student with different ways of thinking in making proofs. Theorems for which no proofs are given in the book are illustrated via figures and examples. All notions are illustrated appealing to geometric intuition. The book provides a variety of economic examples using linear algebraic tools. It mainly addresses students in economics who need to build up skills in understanding mathematical reasoning. Students in mathematics and informatics may also be interested in learning about the use of mathematics in economics. |
| differential equations in economics: Mathematics of Economics and Business Frank Werner, Yuri N. Sotskov, 2006-04-18 1. Introduction -- 2. Sequences, series, finance -- 3. Relations, mappings, functions of a real variable -- 4. Differentiation -- 5. Integration -- 6. Vectors -- 7. Matrices and determinants -- 8. Linear equations and inequalities -- 9. Linear programming -- 10. Eigenvalue problems and quadratic forms -- 11. Functions of several variables -- 12. Differential equations and difference equations. |
| differential equations in economics: Differential Equations For Dummies Steven Holzner, 2008-06-03 The fun and easy way to understand and solve complex equations Many of the fundamental laws of physics, chemistry, biology, and economics can be formulated as differential equations. This plain-English guide explores the many applications of this mathematical tool and shows how differential equations can help us understand the world around us. Differential Equations For Dummies is the perfect companion for a college differential equations course and is an ideal supplemental resource for other calculus classes as well as science and engineering courses. It offers step-by-step techniques, practical tips, numerous exercises, and clear, concise examples to help readers improve their differential equation-solving skills and boost their test scores. |
| differential equations in economics: Basic Mathematics for Economics, Business and Finance EK Ummer, 2012-03-15 This book can help overcome the widely observed math-phobia and math-aversion among undergraduate students in these subjects. The book can also help them understand why they have to learn different mathematical techniques, how they can be applied, and how they will equip the students in their further studies. The book provides a thorough but lucid exposition of most of the mathematical techniques applied in the fields of economics, business and finance. The book deals with topics right from high school mathematics to relatively advanced areas of integral calculus covering in the middle the topics of linear algebra; differential calculus; classical optimization; linear and nonlinear programming; and game theory. Though the book directly caters to the needs of undergraduate students in economics, business and finance, graduate students in these subjects will also definitely find the book an invaluable tool as a supplementary reading. The website of the book – ww.emeacollege.ac.in/bmebf – provides supplementary materials and further readings on chapters on difference equation, differential equations, elements of Mathematica®, and graphics in Mathematica®, . It also provides materials on the applications of Mathematica®, as well as teacher and student manuals. |
| differential equations in economics: Mathematics for Economists with Applications James Bergin, 2015-01-09 Mathematics for Economists with Applications provides detailed coverage of the mathematical techniques essential for undergraduate and introductory graduate work in economics, business and finance. Beginning with linear algebra and matrix theory, the book develops the techniques of univariate and multivariate calculus used in economics, proceeding to discuss the theory of optimization in detail. Integration, differential and difference equations are considered in subsequent chapters. Uniquely, the book also features a discussion of statistics and probability, including a study of the key distributions and their role in hypothesis testing. Throughout the text, large numbers of new and insightful examples and an extensive use of graphs explain and motivate the material. Each chapter develops from an elementary level and builds to more advanced topics, providing logical progression for the student, and enabling instructors to prescribe material to the required level of the course. With coverage substantial in depth as well as breadth, and including a companion website at www.routledge.com/cw/bergin, containing exercises related to the worked examples from each chapter of the book, Mathematics for Economists with Applications contains everything needed to understand and apply the mathematical methods and practices fundamental to the study of economics. |
| differential equations in economics: Modelling with Differential and Difference Equations Glenn Fulford, Peter Forrester, Arthur Jones, 1997-06-12 Any student wishing to solve problems via mathematical modelling will find that this book provides an excellent introduction to the subject. |
What exactly is a differential? - Mathematics Stack Exchange
Jul 13, 2015 · The differential of a function $f$ at $x_0$ is simply the linear function which produces the best linear approximation of $f(x)$ in a neighbourhood of $x_0$.
calculus - What is the practical difference between a differential …
See this answer in Quora: What is the difference between derivative and differential?. In simple words, the rate of change of function is called as a derivative and differential is the actual …
What is a differential form? - Mathematics Stack Exchange
Mar 4, 2020 · At this point, however, I think that the best way to approach the daunting concept of differential forms is to realize that differential forms are defined to be the thing that makes …
calculus - The second differential versus the differential of a ...
Jul 8, 2018 · Now if you want to, you can partially evaluate the second differential $ \mathrm d ^ 2 y $ when $ \mathrm d ^ 2 x = 0 $, getting a partial second differential showing only the …
Best Book For Differential Equations? - Mathematics Stack Exchange
For mathematics departments, some more strict books may be suitable. But whatever book you are using, make sure it has a lot of solved examples. And ideally, it should also include some …
How To Solve a Trigonometric Differential Equation
Dec 23, 2018 · $\begingroup$ Well, I saw this equation in a fb group named JulioProfe some time ago. I found the exercise interesting and decided to take it back a few days ago, I don't know …
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Jul 6, 2015 · $\begingroup$ Differential topology deals with the study of differential manifolds without using tools related with a metric: curvature, affine connections, etc. Differential …
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Nov 3, 2016 · Of course, defining $$ \mathrm{d}x= \lim_{\Delta x \to 0}\Delta x $$ is the same as defining $$ dx=0, $$ which makes no sense.
tensors - How to differentiate a differential form? - Mathematics …
Mar 18, 2013 · There is a formula of computing exterior derivative of any differential form (which is assumed to be smooth). In your case, if $\sigma$ is a 1-form, and $$ \sigma = \sum_{j=1}^n …
"Differential" of a measure - Mathematics Stack Exchange
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What exactly is a differential? - Mathematics Stack Exchange
Jul 13, 2015 · The differential of a function $f$ at $x_0$ is simply the linear function which produces the best linear approximation of $f(x)$ in a neighbourhood of $x_0$.
calculus - What is the practical difference between a differential …
See this answer in Quora: What is the difference between derivative and differential?. In simple words, the rate of change of function is called as a derivative and differential is the actual …
What is a differential form? - Mathematics Stack Exchange
Mar 4, 2020 · At this point, however, I think that the best way to approach the daunting concept of differential forms is to realize that differential forms are defined to be the thing that makes …
calculus - The second differential versus the differential of a ...
Jul 8, 2018 · Now if you want to, you can partially evaluate the second differential $ \mathrm d ^ 2 y $ when $ \mathrm d ^ 2 x = 0 $, getting a partial second differential showing only the …
Best Book For Differential Equations? - Mathematics Stack Exchange
For mathematics departments, some more strict books may be suitable. But whatever book you are using, make sure it has a lot of solved examples. And ideally, it should also include some …
How To Solve a Trigonometric Differential Equation
Dec 23, 2018 · $\begingroup$ Well, I saw this equation in a fb group named JulioProfe some time ago. I found the exercise interesting and decided to take it back a few days ago, I don't know …
soft question - Differential topology versus differential geometry ...
Jul 6, 2015 · $\begingroup$ Differential topology deals with the study of differential manifolds without using tools related with a metric: curvature, affine connections, etc. Differential …
real analysis - Rigorous definition of "differential" - Mathematics ...
Nov 3, 2016 · Of course, defining $$ \mathrm{d}x= \lim_{\Delta x \to 0}\Delta x $$ is the same as defining $$ dx=0, $$ which makes no sense.
tensors - How to differentiate a differential form? - Mathematics …
Mar 18, 2013 · There is a formula of computing exterior derivative of any differential form (which is assumed to be smooth). In your case, if $\sigma$ is a 1-form, and $$ \sigma = \sum_{j=1}^n …
"Differential" of a measure - Mathematics Stack Exchange
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