Foundations of Continuum Mechanics and Transport Laws

Continuum Mechanics and Transport Phenomena are the mathematical bedrock for understanding how materials behave and how energy and mass move through systems, essential for fields like fluid dynamics and materials science. This course provides a rigorous, text-based introduction to the core principles, helping you build a solid foundation in the conservation laws and constitutive relations necessary to analyze complex engineering problems. What you'll learn: * Understand the concept of a continuum and master the use of tensor notation for describing mechanical states and fields. * Derive the fundamental conservation equations for mass, momentum (Navier-Stokes), and energy in differential form. * Apply constitutive relations (like Newtonian fluids and Hookean solids) to close the system of governing equations. * Analyze classic transport phenomena problems, including steady-state conduction, viscous flow, and Fickian diffusion. * Practice solving simplified transport equations using analytical and mathematical methods. * Configure boundary and initial conditions essential for solving real-world continuum mechanics problems. We begin with mathematical prerequisites, including vectors and tensors, before diving into kinematic definitions and the derivation of the conservation laws. The final sections focus on applying these governing equations to analyze momentum, heat, and mass transfer problems. This comprehensive introductory course is designed for absolute beginners in engineering, physics, or applied mathematics; no prior knowledge of continuum mechanics is required. Start building your foundational expertise in transport science today.