Book description
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:
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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.
