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• Part 1 Introduction. Part 2 Theory. Part 3 The data, variables and equations. Part 4 Estimating and testing single equations. Part 5 The stochastic equations of the US model. Part 6 The stochastic equations of the ROW model. Part 7 Estimating and testing complete models. Part 8 Estimating and testing the US model. Part 9 Testing the MC model. Part 10 Analyzing properties of models. Part 11 Analyzing properties of the US model. Part 12 Analyzing properties of the MC model. Appendices: tables for the US model
• tables for the ROW model.
• (source: Nielsen Book Data)

In this book Ray Fair expounds techniques for estimating and analyzing macroeconometric models. He takes advantage of the remarkable decrease in computational costs that has occurred since the early 1980s by implementing such sophisticated techniques as stochastic simulation. "Testing Macroeconometric Models" also incorporates the assumption of rational expectations in the estimation, solution, and testing of the models. And it presents the latest versions of Fair's models of the economies of the United States and other countries. After estimating and testing the US model, Fair analyzes its properties - including those which are relevant to economic policymakers: the optimal monetary policy instrument, the effect of a government spending reduction on the government deficit, whether monetary policy is becoming less effective over time, and the sensitivity of policy effects to the assumption of rational expectations. Ray Fair has conducted research on structural macroeconomic models for more than 20 years. With interest increasing in the area, this book should be a useful reference for macroeconomists.
(source: Nielsen Book Data)

• kn. 1. Teorii͡a i metodologii͡a issledovanii͡a mnogourovnevoĬ ėkonomiki
• kn. 2. Prognozy razvitii͡a narodnogo khozi͡aĬstva i varianty ėkonomicheskoĬ politiki
• t. 3. Prioritety strukturnoĬ politiki i opyt reform

• Discrete-Time Markov Chain
• Branching Processes and Hidden Markov Model
• Poisson Processes and its Extensions
• Continuous-Time Markov Modeling
• Applications and Biology and Ecology

This book provides the essential theoretical tools for stochastic modeling. The authors address the most used models in applications such as Markov chains with discrete-time parameters, hidden Markov chains, Poisson processes, and birth and death processes. This book also presents specific examples with simulation methods that apply the topics to different areas of knowledge. These examples include practical applications, such as modeling the COVID-19 pandemic and animal movement modeling. This book is concise and rigorous, presenting the material in an easily accessible manner that allows readers to learn how to address and solve problems of a stochastic nature.

• 1. Integration with Respect to Stochastic Measures.
• 2. Path Properties of Stochastic Measures.
• 3. Equations Driven by Stochastic Measures.
• 4. Approximation of Solutions of the Equations.
• 5. Integration and Evolution Equations in Hilbert Spaces.
• 6. Symmetric Integrals.
• 7. Averaging Principle.
• 8. Solutions to Exercises.
• (source: Nielsen Book Data)

This book is devoted to the study of stochastic measures (SMs). An SM is a sigma-additive in probability random function, defined on a sigma-algebra of sets. SMs can be generated by the increments of random processes from many important classes such as square-integrable martingales and fractional Brownian motion, as well as alpha-stable processes. SMs include many well-known stochastic integrators as partial cases. General Stochastic Measures provides a comprehensive theoretical overview of SMs, including the basic properties of the integrals of real functions with respect to SMs. A number of results concerning the Besov regularity of SMs are presented, along with equations driven by SMs, types of solution approximation and the averaging principle. Integrals in the Hilbert space and symmetric integrals of random functions are also addressed. The results from this book are applicable to a wide range of stochastic processes, making it a useful reference text for researchers and postgraduate or postdoctoral students who specialize in stochastic analysis.
(source: Nielsen Book Data)

This book carefully considers hydrological models which are essential for predicting floods, droughts, soil moisture estimation, land use change detection, geomorphology and water structures. The book highlights recent advances in the area of hydrological modelling in the Ganga Basin and other internationally important river basins. The impact of climate change on water resources is a global concern. Water resources in many countries are already stressed, and climate change along with burgeoning population, rising standard of living and increasing demand are adding to the stress. Furthermore, river basins are becoming less resilient to climatic vagaries. Fundamental to addressing these issues is hydrological modelling which is covered in this book. Integrated water resources management is vital to ensure water and food security. Integral to the management is groundwater and solute transport, and this book encompasses tools that will be useful to mitigate the adverse consequences of natural disasters.
(source: Nielsen Book Data)

• Foundations of mathematical modelling. Lecture. 1.1 Cognition and modelling. 1.2 Natural sciences and Mathematics. 1.3 Content or form? 1.4 Copernicus or Ptolemy? 1.5 Mathematical model of a body falling. 1.6 Principles of mathematical model determining. 1
• .7. Classification of mathematical models. Appendix.
• 1. Probe movement.
• 2. Missile flight. 3 Glider flight. Notes. I. Systems with lumped parameters.
• 2. Approximate solving of differential equations. Lecture. 2.1 Conception of approximate solution. 2.2 Euler method. 2.3 Probe movement. 2.4 Missile flight. 2
• .5. Glider flight. Appendix.
• 1. Runge-Kutta method.
• 2. Two-body problem.
• 3. Predator-pray model. Notes.
• 3. Mechanical Oscillations. Lecture. 3
• .1. Determination of the pendulum oscillation equation. 3.2 Solving of the pendulum oscillation equation. 3.3 Pendulum oscillation energy. 3.4 Oscillation of a pendulum with friction. 3.5 Equilibrium position of the pendulum. 3.6 Forced oscillations of the pendulum. Appendix.
• 1. Spring oscillation.
• 2. Large pendulum oscillations.
• 3. Problems of nonlinear oscillation theory. Notes. 4 Electrical Oscillations. Lecture. 4.1 Electrical circuit. 4.2 Energy of circuit. 4.3 Circuit with resistance. 4.4 Forced circuit oscillations. Appendix.
• 1. Forced oscillations of spring.
• 2. Circuit with nonlinear capacity. 3 Van der Pol circuit. Notes.
• 5. Elements of dynamical system theory. Lecture. 5
• .1. Evolutionary processes and differential equations. 5.2 General notions of dynamic systems theory. 5.3 Change in species number with excess food. 5.4 Oscillations of pendulum. 5.5 Stability of the equilibrium position. 5.6 Limit cycle. Appendix.
• 1. Exponential growth systems.
• 2. Brussellator.
• 3. System with two limit cycle. Notes.
• 6. Mathematical models in chemistry. Lecture. 6
• .1. Chemical kinetics equations. 6
• .2. Monomolecular reaction. 6
• .3. Bimolecular reaction. 6
• .4. Lotka reaction system. Appendix.
• 1. Brusselator.
• 2. Oregonator.
• 3. Chemical niche.
• 4. Laser healing model. Notes.
• 7. Mathematical model in biology. Lecture. 7
• .1. One species evolution. 7
• .2. Biological competition model. 7.3 Predator-prey model. 7.4 Symbiosis model. Appendix.
• 1. Models of chemical and physical competition.
• 2. Fluctuations in yield and fertility.
• 3. Ecological niche model.
• 4. SIR model for spread of disease.
• 5. Antibiotic resistance model. Notes.
• 8. Mathematical model of economics. Lecture.
• 1. One company evolution.
• 2. Economic competition model.
• 3. Economic niche model.
• 4. Free market model.
• 5. Monopolized market model. Appendix.
• 1. Ecological niche model.
• 2. Inflation model.
• 3. Model of economic cooperation.
• 4. Racketeer - entrepreneur model.
• 5. Solow model of economic growth. Notes.
• 9. Mathematical models in social sciences. Lecture. 9
• .1. Political competition. 9
• .2. Political niche. 9
• .3. Bipartisan system. 9
• .4. Trade union activity. 9.5 Allied relations. Appendix.
• 1. Competition models.
• 2. Niche models.
• 3. Predator-prey models. Notes. II. Systems with distributed parameters.
• 10. Mathematical models of transfer processes. Lecture. 10.1 Heat equation. 10.2 First boundary value problem for the homogeneous heat equation. 10.3 Non-homogeneous heat equation. Appendix.
• 1. Generalizations of the heat equation.
• 2. Second boundary value problem for the heat equation.
• 3. Diffusion equation. Notes.
• 11. Mathematical models of transfer processes. Lecture.
• 1. Heat equation and similarity theory.
• 2. Goods transfer equation.
• 3. Finite difference method for the heat equation.
• 4. Diffusion of chemical reactants.
• 5. Stefan problem for the heat equation. Appendix.
• 1. Overview of transfer processes.
• 2. Finite difference method. Implicit scheme.
• 3. Competitive species migration.
• 4. Hormone treatment of the tumor with hormone resistance. Notes.
• 12. Wave processes. Lecture. 12
• .1. Vibration of string. 12
• .2. Vibrations of string with fixed ends. 12.3 Infinitely long string. 12
• .4. Electrical vibrations in wires. Appendix.
• 1. Energy of vibrating string.
• 2. Mathematical models of wave processes.
• 3. Beam vibrations.
• 4. Maxwell equations.
• 5. Finite difference method for the vibrating string equation. Notes.
• 13. Mathematical models of stationary systems. Lecture. 13
• .1. Stationary heat transfer 13
• .2. Spherical and cylindrical coordinates. 13.3 Vector fields. 13
• .4. Electrostatic field. 13.5 Gravity field. Appendix.
• 1. Stationary fluid flow.
• 2. Steady oscillations.
• 3. Bending a thin elastic plate.
• 4. Variable separation method for the Laplace equation in a circle.
• 5. Establishment method. Notes.
• 14. Mathematical models of fluid and gas mechanics. Lecture. 14
• .1. Vibration string equation. 14
• .2. Ideal fluid movement. 14
• .3. Ideal fluid under the gravity field. 14
• .4. Viscous fluid movement. Appendix.
• 1. Burgers equation.
• 2. Surface wave movement.
• 3. Boundary layer model.
• 4. Acoustic problem.
• 5. Thermal convection.
• 6. Problems of magnetohydrodynamics. Notes.
• 15. Mathematical models of quantum mechanical systems. Lecture. 15
• .1. Quantum mechanics problems. 15
• .2. Wave function. 15
• .3. Schroedinger equation. 15
• .4. Particle movement under an external field. 15
• .5. Potential barrier. Appendix.
• 1. Wave function normalization.
• 2. Particle movement in a well with infinitely high walls. Notes. III. Other mathematical models.
• 16. Variational principles. Lecture.
• 1. Brachistochrone problem.
• 2. Lagrange problem.
• 3. Shortest curve.
• 4. Body falling problem and the concept of action.
• 5. Principle of least action.
• 6. Vibrations of string. Appendix.
• 1. Law of conservation of energy.
• 2. Fermat's principle and light refraction.
• 3. River crossing problem.
• 4. Pendulum oscillations.
• 5. Approximate solution of minimization problems. Notes.
• 17. Discrete models. Lecture. 17
• .1. Discrete population dynamics models. 17
• .2. Discrete heat transfer model. 17
• .3. Transportation problem. 17
• .4. Traveling salesman problem. 17
• .5. Prisoner's Dilemma. Appendix.
• 1. Discrete model of epidemic propagation.
• 2. Potential method for solving a transportation problem.
• 3. Production planning.
• 4. Concepts of game theory. Notes.
• 18. Stochastic models. Lecture. 18
• .1. Stochastic model of pure birth. 18
• .2. Monte Carlo method. 18
• .3. Stochastic model of population death. 18
• .4. Stochastic Malthus model. Appendix.
• 1. Malthus model with random population growth.
• 2. Models with random parameters.
• 3. Discrete model of selling goods.
• 4. Passage of a neutron through a plate. Notes. IV. Additions.
• 19. Mathematical problems of mathematical models. Lecture. 19
• .1. Cauchy problem properties for differential equations. 19
• .2. Properties of boundary value problems. 19
• .3. Boundary value problems for the heat equation. 19
• .4. Hadamard's example and well-posedness of problems. 19
• .5. Classical and generalized solution of problems. Appendix.
• 1. Nonlinear boundary value problems.
• 2. Euler's elastic problem.
• 3. Benard problem.
• 4. Generalized model of stationary heat transfer.
• 5. Sequential model of stationary heat transfer. Notes.
• 20. Optimal control problems. Lecture. 20
• .1. Maximizing the shell fight range. 20
• .2. Maximizing the missile fight range. 20
• .3. General optimal control problem. 20
• .4. Solving of the maximization problem of the missile fight range. 20
• .5. Time-optimal control problem. Appendix.
• 1. Maximizing the probe's ascent height.
• 2. Approximate methods for solving optimality conditions.
• 3. Gradient methods. Notes.
• 21. Identification of mathematical models. Lecture. 21
• .1. Problem of determining the system parameters. 21
• .2. Inverse problems and their solving. 21
• .3. Heat equation with data at the final time. 21
• .4. Differentiation of functionals and gradient methods. 21
• .5. Solving of the heat equation with reversed time. Appendix.
• 1. Boundary inverse problem for the heat equation.
• 2. Inverse problem for the falling of body.
• 3. Inverse gravimetry problem.
• 4. Well-posedness of optimal control problems. Notes. Epilogue. Bibliography. Index.
• (source: Nielsen Book Data)

Mathematical Modelling sets out the general principles of mathematical modelling as a means comprehending the world. Within the book, the problems of physics, engineering, chemistry, biology, medicine, economics, ecology, sociology, psychology, political science, etc. are all considered through this uniform lens. The author describes different classes of models, including lumped and distributed parameter systems, deterministic and stochastic models, continuous and discrete models, static and dynamical systems, and more. From a mathematical point of view, the considered models can be understood as equations and systems of equations of different nature and variational principles. In addition to this, mathematical features of mathematical models, applied control and optimization problems based on mathematical models, and identification of mathematical models are also presented. Features Each chapter includes four levels: a lecture (main chapter material), an appendix (additional information), notes (explanations, technical calculations, literature review) and tasks for independent work; this is suitable for undergraduates and graduate students and does not require the reader to take any prerequisite course, but may be useful for researchers as well Described mathematical models are grouped both by areas of application and by the types of obtained mathematical problems, which contributes to both the breadth of coverage of the material and the depth of its understanding Can be used as the main textbook on a mathematical modelling course, and is also recommended for special courses on mathematical models for physics, chemistry, biology, economics, etc.
(source: Nielsen Book Data)

28 faszinierende Modelle laden zum Nachbauen und Experimentieren ein: Sie rechnen, zeichnen Ellipsen und andere Figuren, faktorisieren Zahlen, ls̲en Gleichungssysteme, synthetisieren Funktionen, messen Flc̃heninhalte oder sehen einfach nur spannend aus. Das Buch wendet sich gleichermassen an Schülerinnen und Schüler, Lehrende, Hobbyisten, Enthusiasten und an alle, die Mathematik mg̲en. Es ist eine Fundgrube für Mathematik-AGs und andere MINT-Angebote. Zu jedem Modell ist eine Liste der bent̲igten fischertechnik-Einzelteile angegeben. Für begrenzte Zeit stellt die Firma fischertechnik einen Baukasten zu diesem Buch zur Verfügung.

• Chapter 1: Introduction
• Chapter 2: Constructing a Rasch Scale
• Chapter 3: Evaluating a Rasch Scale
• Chapter 4: Maintaining a Rasch Scale
• Chapter 5: Using a Rasch Scale
• Chapter 6: Conclusion.
• (source: Nielsen Book Data)

This book introduces current perspectives on Rasch measurement theory with an emphasis on developing Rasch-based scales. Authors George Engelhard Jr and Jue Wang introduce Rasch measurement theory step by step, with chapters on scale construction, evaluation, maintenance, and use. Points are illustrated and techniques are demonstrated through an extended example: The Food Insecurity Experience (FIE) Scale.
(source: Nielsen Book Data)

• Introduction
• Three Simple Models
• What can be Learnt from Simple Models?
• Reality Check for Simple Models
• A Physical Simple Model
• What are Simple Models Worth for?
• Complex Models to Understand Complex Social Situations
• Modelling Epidemics
• Why Weather/Climate Forecasts can be Trusted
• We are not Social Atoms
• Social Data are Soaked by Social Complexity
• Machines that Learn How to Model
• Starting from Data to Hunt Causes
• A Moral Thermometer?
• Where do Indicators Lead us?. Which Numbers for the Future?
• Conclusion
• Acknowledgements
• Annexes.

More than 300 years ago, Isaac Newton created a mathematical model of the solar system that predicted the existence of a yet unknown planet: Neptune. Today, driven by the digital revolution, modern scientists are creating complex models of society itself to shed light on topics as far-ranging as epidemic outbreaks and economic growth. But how do these scientists gather and interpret their data? How accurate are their models? Can we trust the numbers? With a rare background in physics, economics and sociology, the author is able to present an insider's view of the strengths, weaknesses and dangers of transforming our lives into numbers. After reading this book, you'll understand how different numerical models work and how they are used in practice. The author begins by exploring several simple, easy-to-understand models that form the basis for more complex simulations. What follows is an exploration of the myriad ways that models have come to describe and define our world, from epidemiology and climate change to urban planning and the world chess championship. Highly engaging and nontechnical, this book will appeal to any readers interested in understanding the links between data and society and how our lives are being increasingly captured in numbers.

• Preface
• Static condensation optimal port/interface reduction and error estimation for structural health monitoring, by Kathrin Smetana
• Parametric Models for Coupled System, by Hermann G. Matthies and Roger Ohayon
• Model order reduction of linear switched systems with constrained switching, by Ion Victor Gosea, Igor Pontes Duff, Peter Benner and Athanasios C. Antoulas
• Reduced order model using data-driven and equation-free methods, by Soledad Le Clainche and Jos´e M. Vega
• An adaptive way of choosing signicant snapshots for the Proper Orthogonal Decomposition, by Steffen Kastian, Stefanie Reese
• Fully online ROMs and collocation based on LUPOD, by Maria-Luisa Rapún, Filippo Terragni, José M. Vega
• A posteriori Error Estimation in Model Order Reduction of Elastic Multibody Systems with Large Rigid Motion, by Ashish Bhatt, J¨org Fehr, Dennis Grunert and Bernard Haasdonk
• A Reduced Order Approach for the Embedded Shifted Boundary FEM and a Heat Exchange System on Parametrized Geometries, by Efthymios N. Karatzas, Giovanni Stabile, Nabil Atallah, Guglielmo Scovvazzi and Gianluigi Rozza
• POD-Based Augmented Lagrangian Method for State Constrained Heat-Convection Phenomena, by Jonas Siegfried Jehle, Luca Mechelli and Stefan Volkwein
• Coupling of incompressible free-surface flow, acoustic fluid and flexible structure via a modal basis, by Florian Toth and Manfred Kaltenbacher
• Model Order Reduction of Coupled, Parameterized Elastic Bodies for Shape Optimization, by Benjamin Fröhlich, Florian Geiger, Jan Gade, Manfred Bischoff and Peter Eberhard
• A Novel Penalty Based Reduced Order Modelling Approach for Dynamic Analysis of Joint Structures with Localized Non-linearities, by Jie Yuan, Loic Salles, Luca Pesaresi, Chian Wong and Sophoclis Patsias
• POD-DEIM Model Order Reduction for the Monodomain Reaction-Diffusion Sub-Model of the Neuro-Muscular System, by Nehzat Emamy, Pascal Litty, Thomas Klotz, Miriam Mehl and Oliver Röhrle
• Index-aware MOR for Gas Transport Networks, by Nicodemus Banagaaya, Sara Grundel and Peter Benner
• Polynomial Tensor-Based Stability Identification of Milling Process: Application to Reduced Thin-Walled Workpiece, by Chigbogu G. Ozoegwu.

This volume contains the proceedings of the IUTAM Symposium on Model Order Reduction of Coupled System, held in Stuttgart, Germany, May 22-25, 2018. For the understanding and development of complex technical systems, such as the human body or mechatronic systems, an integrated, multiphysics and multidisciplinary view is essential. Many problems can be solved within one physical domain. For the simulation and optimization of the combined system, the different domains are connected with each other. Very often, the combination is only possible by using reduced order models such that the large-scale dynamical system is approximated with a system of much smaller dimension where the most dominant features of the large-scale system are retained as much as possible. The field of model order reduction (MOR) is interdisciplinary. Researchers from Engineering, Mathematics and Computer Science identify, explore and compare the potentials, challenges and limitations of recent and new advances.

• Fuzzy Kernel-Based Clustering and Support Vector Machine Algorithm in Analyzing Cerebral Infarction Dataset.- A predator-prey model with fear factor, Allee effect and periodic harvesting.- Mathematical Modeling of Rock Massif Dynamics under Explosive Sources of Disturbances.- Residual Power Series Approach for Solving Linear Fractional Swift-Hohenberg Problems.- Kernel-based Fuzzy Clustering for Sinusitis Dataset.
• (source: Nielsen Book Data)

This book presents a collection of original research papers from the 2nd International Conference on Mathematical and Related Sciences, held in Antalya, Turkey, on 27 - 30 April 2019 and sponsored/supported by Duzce University, Turkey; the University of Jordan; and the Institute of Applied Mathematics, Baku State University, Azerbaijan. The book focuses on various types of mathematical methods and models in applied sciences; new mathematical tools, techniques and algorithms related to various branches of applied sciences; and important aspects of applied mathematical analysis. It covers mathematical models and modelling methods related to areas such as networks, intelligent systems, population dynamics, medical science and engineering, as well as a wide variety of analytical and numerical methods. The conference aimed to foster cooperation among students, researchers and experts from diverse areas of mathematics and related sciences and to promote fruitful exchanges on crucial research in the field. This book is a valuable resource for graduate students, researchers and educators interested in applied mathematics and interactions of mathematics with other branches of science to provide insights into analysing, modelling and solving various scientific problems in applied sciences. .
(source: Nielsen Book Data)

• Classical string theory
• Quantization of bosonic strings
• Conformal field theory
• Scattering amplitudes and vertex operators
• Strings in background fields
• Superstrings and supersymmetry
• D-branes
• Compactification and supersymmetry breaking
• Loop corrections to string effective couplings
• Duality connections and nonperturbative effects
• Compactifications with fluxes
• Black holes and entropy in string theory
• The bulk/boundary (holographic) correspondence
• Applications of the holographic correspondence
• String theory and matrix models
• Appendix A : Two-dimensional complex geometry
• Appendix B : Differential forms
• Appendix C : Conformal transformations and curvature
• Appendix D: Theta and other elliptic functions
• Appendix E : Toroidal lattice sums
• Appendix F : Toroidal Kaluza-Klein reduction
• Appendix G : The Reissner-Nordström black hole
• Appendix H : Electric-magnetic duality in D = 4
• Appendix I : Supersymmetric actions in ten and eleven dimensions
• Appendix J : N = 1,2, four-dimensional supergravity coupled to matter
• Appendix K : BPS multiplets in four dimensions
• Appendix L : The geometry of anti-de Sitter space

The essential introduction to modern string theory-now fully expanded and revised String Theory in a Nutshell is the definitive introduction to modern string theory. Written by one of the world's leading authorities on the subject, this concise and accessible book starts with basic definitions and guides readers from classic topics to the most exciting frontiers of research today. It covers perturbative string theory, the unity of string interactions, black holes and their microscopic entropy, the AdS/CFT correspondence and its applications, matrix model tools for string theory, and more. It also includes 600 exercises and serves as a self-contained guide to the literature. This fully updated edition features an entirely new chapter on flux compactifications in string theory, and the chapter on AdS/CFT has been substantially expanded by adding many applications to diverse topics. In addition, the discussion of conformal field theory has been extensively revised to make it more student-friendly. The essential one-volume reference for students and researchers in theoretical high-energy physics Now fully expanded and revised Provides expanded coverage of AdS/CFT and its applications, namely the holographic renormalization group, holographic theories for Yang-Mills and QCD, nonequilibrium thermal physics, finite density physics, and entanglement entropy Ideal for mathematicians and physicists specializing in theoretical cosmology, QCD, and novel approaches to condensed matter systems An online illustration package is available to professors.
(source: Nielsen Book Data)

This book focuses on structural changes and economic modeling. It presents papers describing how to model structural changes, as well as those introducing improvements to the existing before-structural-changes models, making it easier to later on combine these models with techniques describing structural changes. The book also includes related theoretical developments and practical applications of the resulting techniques to economic problems. Most traditional mathematical models of economic processes describe how the corresponding quantities change with time. However, in addition to such relatively smooth numerical changes, economical phenomena often undergo more drastic structural change. Describing such structural changes is not easy, but it is vital if we want to have a more adequate description of economic phenomena - and thus, more accurate and more reliable predictions and a better understanding on how best to influence the economic situation.
(source: Nielsen Book Data)

• Frontmatter
• Contents
• Foreword / Schilling, Alexander
• 1 Historical Context
• 2 The Representation of Architecture
• 3 Typology
• 4 Function
• 5 Model Construction Site
• 6 Presentation and Views
• Outlook
• Conclusion

Architectural models are used at various stages of a project. As working models they support the design process: they are made up from time to time using simple materials, such as cardboard, without any attempt at accuracy, and continue to be adjusted and added to as the ideas and the design progress. The point here is to swiftly check a design idea, to allow it to be continued or dismissed. Presentational models are more involved; at this stage the design has been completed and the purpose of the model is to convey the ideas to the potential user in a clear and easy-to-understand way. The book Architecture and Model Building includes outstanding examples explaining the possibilities of this medium and, at the same time, provides comprehensive information on materials and techniques.
(source: Nielsen Book Data)

• chapter 1 The Process of Mathematical Modeling / Mayer Humi
• chapter 2 Modeling with Ordinary Differential Equations / Mayer Humi
• chapter 3 Solutions of Systems of ODEs / Mayer Humi
• chapter 4 Stability Theory / Mayer Humi
• chapter 5 Bifurcations and Chaos / Mayer Humi
• chapter 6 Perturbations / Mayer Humi
• chapter 7 Modeling with Partial Differential Equations / Mayer Humi
• chapter 8 Solutions of Partial Differential Equations / Mayer Humi
• chapter 9 Variational Principles / Mayer Humi
• chapter 10 Modeling Fluid Flow / Mayer Humi
• chapter 11 Modeling Geophysical Phenomena / Mayer Humi
• chapter 12 Stochastic Modeling / Mayer Humi
• chapter 13 Answers to Problems / Mayer Humi.

Introduction to Mathematical Modeling helps students master the processes used by scientists and engineers to model real-world problems, including the challenges posed by space exploration, climate change, energy sustainability, chaotic dynamical systems and random processes. Primarily intended for students with a working knowledge of calculus but minimal training in computer programming in a first course on modeling, the more advanced topics in the book are also useful for advanced undergraduate and graduate students seeking to get to grips with the analytical, numerical, and visual aspects of mathematical modeling, as well as the approximations and abstractions needed for the creation of a viable model.
(source: Nielsen Book Data)