Serovajsky S. Mathematical Modelling 2022 torrent

Textbook in PDF format

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.
Foundations of mathematical modeling
Systems with lumped parameters
Approximate solving of differential equations
Mechanical oscillations
Electrical oscillations
Elements of dynamical system theory
Mathematical models in chemistry
Mathematical modelin biology
Mathematical model of economics
Mathematicalmodelsinsocialsciences
Systems with distributed parameters
Mathematical models of transfer processes
Mathematical models of transfer processes
Wave processes
Mathematicalmodelsofstationarysystems
Mathematicalmodelsoffluidandgasmechanics
Mathematicalmodelsofquantummechanicalsystems
Other mathematical models
Variationalprinciples
Discretemodels
Stochasticmodels
Additions
Mathematicalproblemsofmathematicalmodels
Optimalcontrolproblems
Identificationofmathematicalmodels