Part 1: Introduction to the theory of dynamic systems
The concept of system. Modeling. Direct problem and inverse problem in modeling. Meaning and value of the models. Abstract oriented systems. The specification of the mode of action of a system. Purely algebraic systems and dynamic systems. Linearity in models. Linear specification of the mode of action in differential form. The mode of action in integral form. Interconnection of systems. The structure matrix. Role of the structure matrix in determining the mode of action of a system. Non-linearity, chaotic dynamics and complexity.

Part 2: Multisectoral models of relations between the economic system and the natural environment
The NAMEA. Satellite accounts in green accounting. Multidimensional environmental impact indicators. The Leontief Input-Output model with polluting emissions. The Leontief Input-Output model with de-polluting activities. The price equations. Environmental modeling in general economic equilibrium. CGE models. Social and environmental accounting matrices. Dynamic multisectoral models. Accumulation of capital and environment. Reproducibility of systems and sustainability. Balanced growth of economic and polluting activities and sustainable development.

Part 3: Synthetic indicators of environmental impact and demographic dynamics IPAT. The Ecological Footprint. The Carrying Capacity of natural systems. The ecological deficit. The curve of environmental Kuznets. The demographic system. Maltusian growth models in discrete time and in continuous time. Logical growth models in discrete time and in continuous time. Carrying Capacity, subsistence, capital accumulation and technological development.

Part 4: Aggregate patterns of economic growth with environmental constraints
Intertemporal choices and excellent growth paths. The functional goals. Technological and natural constraints. Solow model with natural resources. The concept of resilience and the model of Common and Perrings. The endogenous growth model of Smulders and Gradus. The DICE model by Nordhaus. The RICE model. Hope's PAGE model and the Stern Review. Intertemporal choices in conditions of uncertainty. Game theory and environmental policies. Collective choices, cooperative games and negotiating processes in multilateral environmental agreements.

PARTE 1
SCARANO G., TEORIA MATEMATICA DEI SISTEMI, DISPENSE DIDATTICHE.
LUNGHINI G., "NOTE SUL CONCETTO DI STRUTTURA", L'INDUSTRIA, 4, 1965.
BERTUGLIA C. S., VAIO F., NON LINEARITÀ, CAOS, COMPLESSITÀ. LA DINAMICHE DEI SISTEMI NATURALI E SOCIALI, BOLLATI BORINGHIERI, TORINO, 2003.
ISRAEL G., MODELLI MATEMATICI, MUZIO, ROMA, 2002.

PARTE 2
D’ANTONIO M., “L’INTERDIPENDENZA TRA ECONOMIA E AMBIENTE. UN’ANALISI APPLICATA ALL’ITALIA”, WORKING PAPERS N.21, DIPARTIMENTO DIECONOMIA, UNIVERSITÀ DEGLI STUDI ROMA TRE, 2001.
SILVESTRI F., LEZIONI DI ECONOMIA DELL’AMBIENTE ED ECOLOGICA, CLUEB, CAP.12.
D’ANTONIO M., ANALISI DELLE INTERDIPENDENZE SETTORIALI. TEORIA E APPLICAZIONI EMPIRICHE, LIGUORI, NAPOLI, 1980, CAPP. 1-2.
PIREDDU G., ECONOMIA DELL’AMBIENTE. UN’INTRODUZIONE IN EQUILIBRIO GENERALE, APOGEO, 2002.
LEONTIEF W., “ENVIRONMENTAL REPERCUSSIONS AND THE ECONOMIC STRUCTURE: AN INPUT-OUTPUT APPROACH”, THE REVIEW OF ECONOMICS AND STATISTICS, VOL. 52, NO. 3 (AUG., 1970), PP. 262-271.
SCARANO G., “CAPITAL ACCUMULATION AND TECHNICAL CONDITIONS ALONG SUSTAINABLE GROWTH PATHS”, 20TH EAEPE CONFERENCE -LABOUR, INSTITUTIONS AND GROWTH IN A GLOBAL KNOWLEDGE BASED ECONOMY. 6-8 NOVEMBER 2008.
UN, EC, IMF, OECD AND WB (2003), INTEGRATED ENVIRONMENTAL AND ECONOMIC ACCOUNTING 2003, ST/ESA/STATSER.F/61/REV.1

PARTE 3
SILVESTRI F., LEZIONI DI ECONOMIA DELL’AMBIENTE ED ECOLOGICA, CLUEB, CAPP. 8, 9.
DE SANTIS G., DEMOGRAFIA ECONOMICA, IL MULINO, BOLOGNA, 1997, CAPP. 1-2.
SCARANO G., “CAPITAL ACCUMULATION, TECHNOLOGICAL PROGRESS AND ENVIRONMENT”, INTERNATIONAL JOURNAL OF GLOBAL ENVIRONMENTAL ISSUES, VOLUME 8, 4, 2008.

PARTE 4
SILVESTRI F., LEZIONI DI ECONOMIA DELL’AMBIENTE ED ECOLOGICA, CLUEB, CAPP. 8
ROMER D., ADVANCED MACROECONOMICS. NEW YORK, NY: MCGRAW-HILL, INC., 2001, CAP. 1.
SOLOW R. M., “INTERGENERATIONAL EQUITY AND EXHAUSTIBLE RESOURCES”, REVIEW OF ECONOMIC STUDIES, VOL. 41, 1974, PP. 29-45.
COMMON M. AND PERRINGS C., 1992. “TOWARDS AN ECOLOGICAL ECONOMICS OF SUSTAINABILITY”, ECOLOGICAL ECONOMICS, 6, PP. 7-34.
SMULDERS S., GRADUS R., “POLLUTION ABATEMENT AND LONG-TERM GROWTH”, EUROPEAN JOURNAL OF POLITICAL ECONOMY, 12, 1996, PP. 505-532.
NORDHAUS W. D., “AN OPTIMAL TRANSITION PATH FOR CONTROLLING GREENHOUSE GASES”, SCIENCE, 258, 1992.
HOPE C., “THE MARGINAL IMPACT OF CO2 FROM PAGE2002: AN INTEGRATED ASSESSMENT MODEL INCORPORATING THE IPCC’S FIVE REASONS FOR CONCERN”, THE INTEGRATED ASSESSMENT JOURNAL, VOL. 6, 2006.

Part 1: Introduction to the theory of dynamic systems
The concept of system. Modeling. Direct problem and inverse problem in modeling. Meaning and value of the models. Abstract oriented systems. The specification of the mode of action of a system. Purely algebraic systems and dynamic systems. Linearity in models. Linear specification of the mode of action in differential form. The mode of action in integral form. Interconnection of systems. The structure matrix. Role of the structure matrix in determining the mode of action of a system. Non-linearity, chaotic dynamics and complexity.

Part 2: Multisectoral models of relations between the economic system and the natural environment
The NAMEA. Satellite accounts in green accounting. Multidimensional environmental impact indicators. The Leontief Input-Output model with polluting emissions. The Leontief Input-Output model with de-polluting activities. The price equations. Environmental modeling in general economic equilibrium. CGE models. Social and environmental accounting matrices. Dynamic multisectoral models. Accumulation of capital and environment. Reproducibility of systems and sustainability. Balanced growth of economic and polluting activities and sustainable development.

Part 3: Synthetic indicators of environmental impact and demographic dynamics IPAT. The Ecological Footprint. The Carrying Capacity of natural systems. The ecological deficit. The curve of environmental Kuznets. The demographic system. Maltusian growth models in discrete time and in continuous time. Logical growth models in discrete time and in continuous time. Carrying Capacity, subsistence, capital accumulation and technological development.

Part 4: Aggregate patterns of economic growth with environmental constraints
Intertemporal choices and excellent growth paths. The functional goals. Technological and natural constraints. Solow model with natural resources. The concept of resilience and the model of Common and Perrings. The endogenous growth model of Smulders and Gradus. The DICE model by Nordhaus. The RICE model. Hope's PAGE model and the Stern Review. Intertemporal choices in conditions of uncertainty. Game theory and environmental policies. Collective choices, cooperative games and negotiating processes in multilateral environmental agreements.

PARTE 1
SCARANO G., TEORIA MATEMATICA DEI SISTEMI, DISPENSE DIDATTICHE.
LUNGHINI G., "NOTE SUL CONCETTO DI STRUTTURA", L'INDUSTRIA, 4, 1965.
BERTUGLIA C. S., VAIO F., NON LINEARITÀ, CAOS, COMPLESSITÀ. LA DINAMICHE DEI SISTEMI NATURALI E SOCIALI, BOLLATI BORINGHIERI, TORINO, 2003.
ISRAEL G., MODELLI MATEMATICI, MUZIO, ROMA, 2002.

PARTE 2
D’ANTONIO M., “L’INTERDIPENDENZA TRA ECONOMIA E AMBIENTE. UN’ANALISI APPLICATA ALL’ITALIA”, WORKING PAPERS N.21, DIPARTIMENTO DIECONOMIA, UNIVERSITÀ DEGLI STUDI ROMA TRE, 2001.
SILVESTRI F., LEZIONI DI ECONOMIA DELL’AMBIENTE ED ECOLOGICA, CLUEB, CAP.12.
D’ANTONIO M., ANALISI DELLE INTERDIPENDENZE SETTORIALI. TEORIA E APPLICAZIONI EMPIRICHE, LIGUORI, NAPOLI, 1980, CAPP. 1-2.
PIREDDU G., ECONOMIA DELL’AMBIENTE. UN’INTRODUZIONE IN EQUILIBRIO GENERALE, APOGEO, 2002.
LEONTIEF W., “ENVIRONMENTAL REPERCUSSIONS AND THE ECONOMIC STRUCTURE: AN INPUT-OUTPUT APPROACH”, THE REVIEW OF ECONOMICS AND STATISTICS, VOL. 52, NO. 3 (AUG., 1970), PP. 262-271.
SCARANO G., “CAPITAL ACCUMULATION AND TECHNICAL CONDITIONS ALONG SUSTAINABLE GROWTH PATHS”, 20TH EAEPE CONFERENCE -LABOUR, INSTITUTIONS AND GROWTH IN A GLOBAL KNOWLEDGE BASED ECONOMY. 6-8 NOVEMBER 2008.
UN, EC, IMF, OECD AND WB (2003), INTEGRATED ENVIRONMENTAL AND ECONOMIC ACCOUNTING 2003, ST/ESA/STATSER.F/61/REV.1

PARTE 3
SILVESTRI F., LEZIONI DI ECONOMIA DELL’AMBIENTE ED ECOLOGICA, CLUEB, CAPP. 8, 9.
DE SANTIS G., DEMOGRAFIA ECONOMICA, IL MULINO, BOLOGNA, 1997, CAPP. 1-2.
SCARANO G., “CAPITAL ACCUMULATION, TECHNOLOGICAL PROGRESS AND ENVIRONMENT”, INTERNATIONAL JOURNAL OF GLOBAL ENVIRONMENTAL ISSUES, VOLUME 8, 4, 2008.

PARTE 4
SILVESTRI F., LEZIONI DI ECONOMIA DELL’AMBIENTE ED ECOLOGICA, CLUEB, CAPP. 8
ROMER D., ADVANCED MACROECONOMICS. NEW YORK, NY: MCGRAW-HILL, INC., 2001, CAP. 1.
SOLOW R. M., “INTERGENERATIONAL EQUITY AND EXHAUSTIBLE RESOURCES”, REVIEW OF ECONOMIC STUDIES, VOL. 41, 1974, PP. 29-45.
COMMON M. AND PERRINGS C., 1992. “TOWARDS AN ECOLOGICAL ECONOMICS OF SUSTAINABILITY”, ECOLOGICAL ECONOMICS, 6, PP. 7-34.
SMULDERS S., GRADUS R., “POLLUTION ABATEMENT AND LONG-TERM GROWTH”, EUROPEAN JOURNAL OF POLITICAL ECONOMY, 12, 1996, PP. 505-532.
NORDHAUS W. D., “AN OPTIMAL TRANSITION PATH FOR CONTROLLING GREENHOUSE GASES”, SCIENCE, 258, 1992.
HOPE C., “THE MARGINAL IMPACT OF CO2 FROM PAGE2002: AN INTEGRATED ASSESSMENT MODEL INCORPORATING THE IPCC’S FIVE REASONS FOR CONCERN”, THE INTEGRATED ASSESSMENT JOURNAL, VOL. 6, 2006.