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El. knyga: Mathematical Modeling in Economics, Ecology and the Environment

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Updated to textbook form by popular demand, this second edition discusses diverse mathematical models used in economics, ecology, and the environmental sciences with emphasis on control and optimization. It is intended for graduate and upper-undergraduate course use, however, applied mathematicians, industry practitioners, and a vast number of interdisciplinary academics will find the presentation highly useful.
Core topics of this text are:
· Economic growth and technological development
· Population dynamics and human impact on the environment
· Resource extraction and scarcity
· Air and water contamination
· Rational management of the economy and environment
· Climate change and global dynamics
The step-by-step approach taken is problem-based and easy to follow. The authors aptly demonstrate that the same models may be used to describe different economic and environmental processes and that similar investigation techniques are applicable to analyze various models. Instructors will appreciate the substantial flexibility that this text allows while designing their own syllabus. Chapters are essentially self-contained and may be covered in full, in part, and in any order.

Appropriate one- and two-semester courses include, but are not limited to, Applied Mathematical Modeling, Mathematical Methods in Economics and Environment, Models of Biological Systems, Applied Optimization Models, and Environmental Models. Prerequisites for the courses are Calculus and, preferably, Differential Equations.



With comprehensive treatment of applied mathematical modeling in economics, population biology, and environmental science, this popular publication has been updated to textbook format for its second edition, which emphasizes control and optimization.

Recenzijos

From the book reviews:

This book contains a wealth of information on many of the models used in describing economic and environmental changes. this is a very well written and very thorough introduction to mathematical modeling in economics and the environment. It is a valuable first source on basic modeling that is accessible to a graduate student level or professional audience. (Mary Flagg, MAA Reviews, October, 2014)

1 Introduction: Principles and Tools of Mathematical Modeling
1(24)
1.1 Role and Stages of Mathematical Modeling
1(5)
1.1.1 Stages of Mathematical Modeling
2(3)
1.1.2 Mathematical Modeling and Computer Simulation
5(1)
1.2 Choice of Models
6(3)
1.2.1 Deterministic and Stochastic Models
6(1)
1.2.2 Continuous and Discrete Models
7(1)
1.2.3 Linear and Nonlinear Models
8(1)
1.3 Review of Selected Mathematical Tools
9(16)
1.3.1 Derivatives and Integrals
10(2)
1.3.2 Vector Algebra and Calculus
12(1)
1.3.3 Differential Equations
13(3)
1.3.4 Integral Equations
16(3)
1.3.5 Optimization and Optimal Control
19(2)
Exercises
21(1)
References
22(3)
Part I Mathematical Models in Economics
2 Aggregate Models of Economic Dynamics
25(28)
2.1 Production Functions and Their Types
25(8)
2.1.1 Properties of Production Functions
26(1)
2.1.2 Characteristics of Production Functions
26(1)
2.1.3 Major Types of Production Functions
27(2)
2.1.4 Two-Factor Production Functions
29(4)
2.2 Solow--Swan Model of Economic Dynamics
33(4)
2.2.1 Model Description
34(1)
2.2.2 Analysis of Model
35(2)
2.3 Optimization Versions of Solow--Swan Model
37(8)
2.3.1 Optimization over Finite Horizon (Solow--Shell Model)
38(4)
2.3.2 Infinite-Horizon Optimization (Solow--Ramsey Model)
42(2)
2.3.3 Central Planner, General Equilibrium, and Nonlinear Utility
44(1)
2.4 Appendix: Maximum Principle
45(8)
2.4.1 Scalar Controls
47(1)
2.4.2 Discounted Optimization
47(1)
2.4.3 Interior Controls
48(1)
2.4.4 Transversality Conditions
49(1)
2.4.5 Maximum Principle and Dynamic Programming
49(1)
Exercises
50(1)
References
51(2)
3 Modeling of Technological Change
53(26)
3.1 Major Concepts of Technological Change
53(3)
3.1.1 Exogenous Autonomous Technological Change
54(1)
3.1.2 Embodied and Disembodied Technological Change
55(1)
3.1.3 Endogenous Technological Change
55(1)
3.1.4 Technological Change as Separate Sector of Economy
56(1)
3.2 Models with Autonomous Technological Change
56(7)
3.2.1 Solow--Swan Model
58(2)
3.2.2 Solow--Shell Model
60(2)
3.2.3 Solow--Ramsey Model
62(1)
3.3 Models with Endogenous Technological Change
63(10)
3.3.1 Induced Technological Change
63(1)
3.3.2 One-Sector Model with Physical and Human Capital
64(4)
3.3.3 Two-Sector Model with Physical and Human Capital (Uzawa--Lucas Model)
68(2)
3.3.4 Knowledge-Based Models of Economic Growth
70(3)
3.4 Modeling of Technological Innovations
73(6)
3.4.1 Inventions, Innovations, and Spillovers
73(1)
3.4.2 Substitution Models of Technological Innovations
74(2)
3.4.3 Diffusion and Evolution Models of Technological Innovation
76(1)
3.4.4 General Purpose Technologies and Technological Breakthroughs
77(1)
Exercises
77(1)
References
78(1)
4 Models with Heterogeneous Capital
79(26)
4.1 Macroeconomic Vintage Capital Models
80(7)
4.1.1 Solow Vintage Capital Model
80(2)
4.1.2 Vintage Models with Scrapping of Obsolete Capital
82(2)
4.1.3 Two-Sector Vintage Model
84(1)
4.1.4 Optimization Problems in Vintage Models
85(2)
4.2 Vintage Capital Models of a Firm
87(4)
4.2.1 Malcomson Model
87(3)
4.2.2 Aggregate Production Functions
90(1)
4.3 Vintage Models with Distributed Investments
91(5)
4.3.1 Optimization Problems
93(1)
4.3.2 Relations to Differential Models of Equipment Replacement
94(2)
4.4 Discrete and Continuous Models of Machine Replacement
96(9)
4.4.1 Multi-machine Replacement Model in Discrete Time
96(3)
4.4.2 One-Machine Replacement in Discrete and Continuous Time
99(2)
Exercises
101(1)
References
102(3)
5 Optimization of Economic Renovation
105(28)
5.1 Optimal Replacement of One Machine
105(6)
5.1.1 Necessary Condition for an Extremum
106(1)
5.1.2 Qualitative Analysis of Optimal Replacement Policy
107(4)
5.2 Profit-Maximizing Firm Under Resource Restrictions
111(6)
5.2.1 Necessary Condition for an Extremum
112(2)
5.2.2 Structure of Optimal Trajectories
114(2)
5.2.3 Economic Interpretation
116(1)
5.3 Nonlinear Utility Optimization in Ramsey Vintage Model
117(6)
5.3.1 Reduction to One-Sector Optimization Problem
118(2)
5.3.2 Interior Solutions
120(1)
5.3.3 Balanced Growth
120(2)
5.3.4 Economic Interpretation: Turnpike Properties
122(1)
5.4 Appendix: Optimal Control in Vintage Capital Models
123(10)
5.4.1 Statement of Optimization Problem
124(1)
5.4.2 Variational Techniques
125(1)
5.4.3 Method of Lagrange Multipliers
126(3)
5.4.4 Extremum Conditions
129(1)
Exercises
129(1)
References
130(3)
Part II Models in Ecology and Environment
6 Mathematical Models of Biological Populations
133(24)
6.1 Models of Single Species Dynamics
133(7)
6.1.1 Malthusian Growth Model
134(1)
6.1.2 Von Bertalanffy Model
135(1)
6.1.3 Verhulst--Pearl Model
136(2)
6.1.4 Controlled Version of Verhulst--Pearl Model
138(1)
6.1.5 Verhulst--Volterra Model with Hereditary Effects
138(2)
6.2 Models of Two Species Dynamics
140(9)
6.2.1 Lotka--Volterra Model of Two Interacting Species
140(2)
6.2.2 Lotka--Volterra Predator--Prey Model
142(3)
6.2.3 Control in Predator--Prey Model
145(1)
6.2.4 Generalized Predator--Prey Models
146(1)
6.2.5 Predator--Prey Model with Individual Migration
147(2)
6.3 Age-Structured Models of Population Dynamics
149(8)
6.3.1 McKendrick Linear Population Model
149(1)
6.3.2 MacCamy Nonlinear Population Model
150(1)
6.3.3 Euler--Lotka Linear Integral Model of Population Dynamics
151(2)
Exercises
153(3)
References
156(1)
7 Modeling of Heterogeneous and Controlled Populations
157(22)
7.1 Linear Size-Structured Population Models
157(2)
7.1.1 Model of Managed Size-Structured Population
158(1)
7.1.2 Connection Between Age- and Size-Structured Models
158(1)
7.1.3 Model of Size-Structured Population with Natural Reproduction
159(1)
7.2 Nonlinear Population Models
159(6)
7.2.1 Age-Structured Model with Intraspecies Competition
160(1)
7.2.2 Bifurcation Analysis
160(2)
7.2.3 Nonlinear Size-Structured Model
162(1)
7.2.4 Steady-State Analysis
163(2)
7.3 Population Models with Control and Optimization
165(14)
7.3.1 Age-Structured Population Models with Control
165(2)
7.3.2 Elements of Analysis
167(5)
7.3.3 Nonlinear Age-Structured Models of Controlled Harvesting
172(1)
7.3.4 Size-Structured Models with Controls
173(2)
Exercises
175(1)
References
176(3)
8 Models of Air Pollution Propagation
179(18)
8.1 Fundamentals of Environmental Pollutions
179(1)
8.2 Models of Air Pollution Transport and Diffusion
180(5)
8.2.1 Model of Pollution Transport
181(1)
8.2.2 Model of Pollution Transport and Diffusion
182(1)
8.2.3 Steady-State Analysis: One-Dimensional Stationary Distribution of Pollutant
183(1)
8.2.4 Models of Pollution Transport, Diffusion, and Chemical Reaction
184(1)
8.2.5 Control Problems of Pollution Propagation in Atmosphere
185(1)
8.3 Modeling of Plant Location
185(4)
8.3.1 Adjoint Method
186(3)
8.4 Control of Plant Pollution Intensity
189(3)
8.4.1 Stationary Control of Air Pollution Intensity
189(2)
8.4.2 Dynamic Control of Air Pollution Intensity
191(1)
8.5 Structure of Applied Air Pollution Models
192(5)
8.5.1 Interaction with Earth Surface
193(1)
8.5.2 Interaction of Different Air Pollutants
194(1)
8.5.3 Air Contamination in Cities
194(1)
Exercises
195(1)
References
196(1)
9 Models of Water Pollution Propagation
197(24)
9.1 Structure and Classification of Water Pollution Models
197(3)
9.1.1 Structure of Models
198(1)
9.1.2 Classification of Models
198(2)
9.2 Three-Dimensional Model
200(4)
9.2.1 Models of Adsorption and Sedimentation
200(1)
9.2.2 Equation of Transport of Dissolved Pollutants
201(1)
9.2.3 Equation of Transport of Suspended Pollutants
202(1)
9.2.4 Equations of Surface Water Dynamics
203(1)
9.2.5 Modeling of Pollutant Transport in Underground Water
204(1)
9.3 Two-Dimensional Horizontal Model
204(3)
9.3.1 Equation of Ground Deposit Accumulation
204(1)
9.3.2 Equation of Transport of Dissolved Pollutants
205(1)
9.3.3 Equation of Transport of Suspended Pollutants
206(1)
9.3.4 Equations of Water Dynamics
206(1)
9.4 One-Dimensional Pollution Model and Its Analytic Solutions
207(5)
9.4.1 Link Between Convective Diffusion Equation and Heat Equation
207(1)
9.4.2 Mathematical Preliminary: Heat Equation
208(1)
9.4.3 Instantaneous Source of Pollutant
209(1)
9.4.4 Pollutant Source with Constant Intensity
210(2)
9.5 Compartmental Models and Control Problems
212(9)
9.5.1 Equations of Water Balance
212(1)
9.5.2 Equations of Suspension Balance
212(1)
9.5.3 Equations of Pollution Propagation
213(1)
9.5.4 Control Problems of Water Pollution Propagation
214(1)
Exercises
215(1)
References
216(5)
Part III Models of Economic-Environmental Systems
10 Modeling of Nonrenewable Resources
221(20)
10.1 Aggregate Models of Nonrenewable Resources
221(13)
10.1.1 Models of Optimal Resource Extraction
222(1)
10.1.2 Linear Model with No Resource Extraction Cost
222(2)
10.1.3 Models with Resource Extraction Cost
224(5)
10.1.4 Hotelling's Rule of Resource Extraction
229(2)
10.1.5 Modifications of Hotelling's Model
231(1)
10.1.6 Stochastic Models of Resource Extraction
232(2)
10.2 Dasgupta--Heal Model of Economic Growth with Exhaustible Resource
234(7)
10.2.1 Optimality Conditions
235(1)
10.2.2 Analysis of Model
236(3)
10.2.3 Interpretation of Results
239(1)
Exercises
239(1)
References
240(1)
11 Modeling of Environmental Protection
241(22)
11.1 Mutual Influence of Economy and Environment
241(6)
11.1.1 Climate Change and Environmental Strategies
241(2)
11.1.2 Modeling of Economic Impact on Environment
243(1)
11.1.3 Modeling of the Environmental Impact on Economy and Society
244(2)
11.1.4 Modeling of Mitigation and Adaptation
246(1)
11.2 Model with Pollution Emission and Abatement
247(5)
11.2.1 Optimality Conditions
249(1)
11.2.2 Analysis of Model
249(2)
11.2.3 Interpretation of Results
251(1)
11.3 Model with Pollution Accumulation and Abatement
252(2)
11.3.1 Analysis of Model
252(2)
11.3.2 Interpretation of Results
254(1)
11.4 Model with Pollution Abatement and Environmental Adaptation
254(9)
11.4.1 Optimality Conditions
256(1)
11.4.2 Steady-State Analysis
257(1)
11.4.3 Discussion of Results
258(2)
Exercises
260(1)
References
261(2)
12 Models of Global Dynamics: From Club of Rome to Integrated Assessment
263(22)
12.1 Global Trends and Their Modeling
263(6)
12.1.1 Global Environmental Trends
264(1)
12.1.2 Global Demographic Trends
265(1)
12.1.3 Population and Environment
265(1)
12.1.4 Modeling of Global Change
266(1)
12.1.5 Simplified Models of Human--Environmental Interaction
267(1)
12.1.6 Aggregate Indicators in Global Models
268(1)
12.2 Models of World Dynamics
269(7)
12.2.1 Forrester Model
270(2)
12.2.2 Meadows Models
272(3)
12.2.3 Mesarovic--Pestel Model
275(1)
12.2.4 Limitations of World Dynamics Models
275(1)
12.3 Integrated Assessment Models: Structure and Results
276(5)
12.3.1 Deterministic Models of Climate and Economy (DICE, RICE, WITCH)
277(1)
12.3.2 Deterministic Energy--Economy Models (Global 2100, CETA, MERGE, ECLIPSE)
278(1)
12.3.3 Scenario-Based Integrated Models (IMAGE, TARGETS)
279(1)
12.3.4 Probabilistic Integrated Models (PAGE, ICAM)
280(1)
12.3.5 Limitations of Integrated Assessment Models
281(1)
12.4 Global Modeling: A Look Ahead
281(4)
Exercises
282(1)
References
283(2)
Index 285
Natali Hritonenko is an award-winning professor of mathematics at Prairie View A&M University. She has traveled the world sharing her research results through numerous presentations and collaborating on groundbreaking research projects with a diverse team of leading experts. During her prolific career, Dr. Hritonenko has authored 7 books and well over 100 papers, and is also on the editorial board of 9 international interdisciplinary journals. Her real passion, however, is teaching and she aims to bring the fascinating and versatile nature of mathematics to her students, while also revealing to them the insights that mathematics can bring to any subject.

Dr. Yuri Yatsenko has published seven books and over 200 papers. He earned his MS and PhD from Kiev State University and a Doctor of Science from the USSR Academy of Sciences (Moscow). During his career, he has been a professor in five different countries and taught mathematics, statistics, economics, information systems, and computer sciences in four languages. For five years, he held senior positions in data analytics and operations research at international companies in USA and Canada. He joined Houston Baptist University in 2002 and is currently engaged in intensive collaboration with several European and Asian universities. His areas of expertise include modeling and optimization of economic, industrial, and environmental processes, technological change, innovations, operations research, and computational methods.
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