Introduction to mathematical modeling and computer simulations / / Vladimir Mityushev, Wojciech Nawalaniec, Natalia Rylko.

• VerfasserIn: Mityushev, Vladimir V.,; Nawalaniec, Wojciech,; Rylko, Natalia,
• TeilnehmendeR: Nawalaniec, Wojciech,; Rylko, Natalia,
• Place / Publishing House: Boca Raton, Florida : : CRC Press,, [2018]; ©2018
• Year of Publication: 2018
• Language: English
• Physical Description: 1 online resource (xvii, 222 pages) :; illustrations
• Notes: "A Chapman & Hall book."

Mathematical Modeling describes a process and an object by use of the mathematical language. A process or an object is presented in a "pure form" in Mathematical Modeling when external perturbations disturbing the study are absent. Computer simulation is a natural continuation of the Mathematical Modeling. Computer simulation can be considered as a computer experiment which corresponds to an experiment in the real world. Such a treatment is rather related to numerical simulations. Symbolic simulations yield more than just an experiment. Mathematical Modeling of stochastic processes is based on the probability theory, in particular, that leads to using of random walks, Monte Carlo methods and the standard statistics tools. Symbolic simulations are usually realized in the form of solution to equations in one unknown, to a system of linear algebraic equations, both ordinary and partial differential equations (ODE and PDE). Various mathematical approaches to stability are discussed in courses of ODE and PDE.

Table of Contents

part, 1 General Principles and Methods -- chapter 1 Principles of Mathematical Modeling / Vladimir Mityushev Wojciech Nawalaniec Natalia Rylko -- chapter 2 Numerical and symbolic computations / Vladimir Mityushev Wojciech Nawalaniec Natalia Rylko -- part, 2 Basic Applications -- chapter 3 Application of calculus to classic mechanics / Vladimir Mityushev Wojciech Nawalaniec Natalia Rylko -- chapter 4 Ordinary differential equations and their applications / Vladimir Mityushev Wojciech Nawalaniec Natalia Rylko -- chapter 5 Stochastic models / Vladimir Mityushev Wojciech Nawalaniec Natalia Rylko -- chapter 6 One-dimensional stationary problems / Vladimir Mityushev Wojciech Nawalaniec Natalia Rylko -- part, 3 Advanced Applications -- chapter 7 Vector analysis / Vladimir Mityushev Wojciech Nawalaniec Natalia Rylko -- chapter 8 Heat equations / Vladimir Mityushev Wojciech Nawalaniec Natalia Rylko -- chapter 9 Asymptotic methods in composites / Vladimir Mityushev Wojciech Nawalaniec Natalia Rylko.