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Concave functions --- Hamilton-Jacobi equations --- Control theory --- Mathematical optimization

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This book introduces readers to theories that play a crucial role in modern mathematics, such as integration and functional analysis, employing a unifying approach that views these two subjects as being deeply intertwined. This feature is particularly evident in the broad range of problems examined, the solutions of which are often supported by generous hints. If the material is split into two courses, it can be supplemented by additional topics from the third part of the book, such as functions of bounded variation, absolutely continuous functions, and signed measures. This textbook addresses the needs of graduate students in mathematics, who will find the basic material they will need in their future careers, as well as those of researchers, who will appreciate the self-contained exposition which requires no other preliminaries than basic calculus and linear algebra.

Mathematics. --- Measure and Integration. --- Functional Analysis. --- Probability Theory and Stochastic Processes. --- Quantitative Finance. --- Mathematical Applications in the Physical Sciences. --- Mathematical Methods in Physics. --- Functional analysis. --- Finance. --- Distribution (Probability theory). --- Mathematical physics. --- Mathématiques --- Analyse fonctionnelle --- Finances --- Distribution (Théorie des probabilités) --- Physique mathématique --- Calculus --- Mathematics --- Physical Sciences & Mathematics --- Measure theory. --- Economics, Mathematical. --- Probabilities. --- Physics. --- Distribution (Probability theory. --- Physical mathematics --- Physics --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Math --- Science --- Funding --- Funds --- Economics --- Currency question --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Economics, Mathematical . --- Lebesgue measure --- Measurable sets --- Measure of a set --- Algebraic topology --- Integrals, Generalized --- Measure algebras --- Rings (Algebra) --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Mathematical economics --- Econometrics --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Methodology

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This book introduces readers to theories that play a crucial role in modern mathematics, such as integration and functional analysis, employing a unifying approach that views these two subjects as being deeply intertwined. This feature is particularly evident in the broad range of problems examined, the solutions of which are often supported by generous hints. If the material is split into two courses, it can be supplemented by additional topics from the third part of the book, such as functions of bounded variation, absolutely continuous functions, and signed measures. This textbook addresses the needs of graduate students in mathematics, who will find the basic material they will need in their future careers, as well as those of researchers, who will appreciate the self-contained exposition which requires no other preliminaries than basic calculus and linear algebra.

Finance --- Economics --- Functional analysis --- Operational research. Game theory --- Probability theory --- Mathematics --- Measuring methods in physics --- Mathematical physics --- Physics --- kennis --- differentiaalvergelijkingen --- waarschijnlijkheidstheorie --- stochastische analyse --- functies (wiskunde) --- meettechniek --- financiën --- wiskunde --- fysica --- kansrekening

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This book presents important recent applied mathematics research on environmental problems and impacts due to climate change. Although there are inherent difficulties in addressing phenomena that are part of such a complex system, exploration of the subject using mathematical modelling is especially suited to tackling poorly understood issues in the field. It is in this spirit that the book was conceived. It is an outcome of theInternational INDAM Workshop “Mathematical Approach to Climate Change Impacts – MAC2I”, held in Rome in March 2017. The workshop comprised four sessions, on Ecosystems, Hydrology, Glaciology, and Monitoring. The book includes peer-reviewed contributions on research issues discussed during each of these sessions or generated by collaborations among the specialists involved. Accurate parameter determination techniques are explained and innovative mathematical modelling approaches, presented. The book also provides useful material and mathematical problem-solving tools for doctoral programs dealing with the complexities of climate change.

Mathematical physics. --- Geobiology. --- Hydrology. --- Statistics . --- Ecosystems. --- Air pollution. --- Mathematical Physics. --- Biogeosciences. --- Hydrology/Water Resources. --- Statistics, general. --- Atmospheric Protection/Air Quality Control/Air Pollution. --- Climatic changes --- Mathematical models --- Air --- Air contaminants --- Air pollutants --- Air pollution --- Air pollution control --- Air toxics --- Airborne pollutants --- Atmosphere --- Contaminants, Air --- Control of air pollution --- Pollutants, Air --- Toxics, Air --- Pollution --- Air quality --- Atmospheric deposition --- Biocenoses --- Biocoenoses --- Biogeoecology --- Biological communities --- Biomes --- Biotic community ecology --- Communities, Biotic --- Community ecology, Biotic --- Ecological communities --- Ecosystems --- Natural communities --- Ecology --- Population biology --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Aquatic sciences --- Earth sciences --- Hydrography --- Water --- Biology --- Biosphere --- Physical mathematics --- Physics --- Control --- Changes, Climatic --- Changes in climate --- Climate change --- Climate change science --- Climate changes --- Climate variations --- Climatic change --- Climatic fluctuations --- Climatic variations --- Global climate changes --- Global climatic changes --- Climatology --- Climate change mitigation --- Teleconnections (Climatology) --- Environmental aspects

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This book, featuring a truly interdisciplinary approach, provides an overview of cutting-edge mathematical theories and techniques that promise to play a central role in climate science. It brings together some of the most interesting overview lectures given by the invited speakers at an important workshop held in Rome in 2013 as a part of MPE2013 (“Mathematics of Planet Earth 2013”). The aim of the workshop was to foster the interaction between climate scientists and mathematicians active in various fields linked to climate sciences, such as dynamical systems, partial differential equations, control theory, stochastic systems, and numerical analysis. Mathematics and statistics already play a central role in this area. Likewise, computer science must have a say in the efforts to simulate the Earth’s environment on the unprecedented scale of petabytes. In the context of such complexity, new mathematical tools are needed to organize and simplify the approach. The growing importance of data assimilation techniques for climate modeling is amply illustrated in this volume, which also identifies important future challenges. This timely work is mainly addressed to any researcher active in climate science to learn more on qualitative and quantitative methods recently developed for their discipline as well as mathematicians with a strong interest in environmental science. It may also be useful to PhD students in applied mathematics to find excellent research subjects for their thesis.

Mathematics. --- Physical geography. --- System theory. --- Mathematical physics. --- Geophysics. --- Mathematical Applications in the Physical Sciences. --- Systems Theory, Control. --- Earth System Sciences. --- Geophysics and Environmental Physics. --- Applications of Nonlinear Dynamics and Chaos Theory. --- Climatology --- Mathematical models. --- Systems theory. --- Statistical physics. --- Physics --- Mathematical statistics --- Geological physics --- Terrestrial physics --- Earth sciences --- Geography --- Systems, Theory of --- Systems science --- Science --- Physical mathematics --- Statistical methods --- Philosophy --- Mathematics