Continuum Mechanics - The Birthplace of Mathematical Models

Continuum Mechanics: The Origins of Partial Differential Equations successfully makes the topic accessible to advanced undergraduate mathematics majors by aligning the mathematical notation and language with related courses in multivariable calculus, linear algebra, and differential equations; making connections with other areas of applied mathematics where parial differential equations arise; introducing thermodynamics and the implications of the entropy inequality for constitutive relations; and treating multiconstituent continua to illustrate how important phenomena such as diffusion and porous-media flow obey continuum-mechanical principles.§Begining with geometric, algebraic, and analytical foundations it moves on to a range of topics in kinematics that serve as the descriptive language for continuum motions. Next, balance laws are addressed, followed by an exploiration of constitutive theory from two vantage points: common constitutive laws that are encountered in heat flow, fluid dynamics, and solid mechanics; and an elementary treatment of constiututive relations from a more formal perspective.§Finally, the book introduces an approach to multiconstiuent continua based on mixture theory. This serves as a streamnlined way to introduce diffusion, which is a topic of immense importance in environmental science and engineering and enables a rational derivation of the field equations most commonly used to model flows in porous media.