A modern approach to mathematical modeling, featuring unique applications from the field of mechanics
An Introduction to Mathematical Modeling: A Course in Mechanics is designed to survey the mathematical models that form the foundations of modern science and incorporates examples that illustrate how the most successful models arise from basic principles in modern and classical mathematical physics. Written by a world authority on mathematical theory and computational mechanics, the book presents an account of continuum mechanics, electromagnetic field theory, quantum mechanics, and statistical mechanics for readers with varied backgrounds in engineering, computer science, mathematics, and physics.
The author streamlines a comprehensive understanding of the topic in three clearly organized sections:
Nonlinear Continuum Mechanics introduces kinematics as well as force and stress in deformable bodies; mass and momentum; balance of linear and angular momentum; conservation of energy; and constitutive equations
Electromagnetic Field Theory and Quantum Mechanics contains a brief account of electromagnetic wave theory and Maxwell's equations as well as an introductory account of quantum mechanics with related topics including ab initio methods and Spin and Pauli's principles
Statistical Mechanics presents an introduction to statistical mechanics of systems in thermodynamic equilibrium as well as continuum mechanics, quantum mechanics, and molecular dynamics
Each part of the book concludes with exercise sets that allow readers to test their understanding of the presented material. Key theorems and fundamental equations are highlighted throughout, and an extensive bibliography outlines resources for further study.
Extensively class-tested to ensure an accessible presentation, An Introduction to Mathematical Modeling is an excellent book for courses on introductory mathematical modeling and statistical mechanics at the upper-undergraduate and graduate levels. The book also serves as a valuable reference for professionals working in the areas of modeling and simulation, physics, and computational engineering.
Nyckelord: Mathematical Modeling, nonlinear continuum mechanics, electromagnetic wave theory, , Maxwell’, s equations, introduction to quantum mechanics, an introduction to statistical mechanics of systems in thermodynamic equilibrium, continuum mechanics, electrodynamics, quantum mechanics, statistical mechanics, physics and mathematical science, propagation of waves, transformation of energy in physical systems, kinematics of deformable bodies, mass and momentum, force and stress in deformable bodies, balance of linear and angular momentum, conservation of energy, thermodynamics of continua, constitutive equations, , electromagnetic waves, quantum mechanics, dynamical variables and observables in quantum mechanics, harmonic oscillator and hydrogen atom, Spin and Pauli's principles, atomic and molecular structure, molecular dynamics