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 (Cobbยญ 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 ..
1. Principles of Model Construction -- I. Models of Controlled Economic Systems -- 2. Aggregate Models of Economic Dynamics -- 3. Modelling of Technological Change -- 4. Multi-Sector Linear Economic Models -- 5. Models of Controlled Technological Renovation -- 6. Optimization Models of Economic Renovation -- II. Models in Ecology and Environment -- 7. Mathematical Models of Biological Communities -- 8. Models of Air Pollution Propagation -- 9. Models of Water Pollution Propagation -- III. Models of Economic-Ecological Systems. -- 10. Modeling of Environmental Impact and Resource Extraction -- 11. Models of World Dynamics: Structure and Results -- 12. Models for Pollution Propagation Control In Air And Water
Calculus of variations
Mathematical Modeling and Industrial Mathematics
Calculus of Variations and Optimal Control; Optimization