Fluid Dynamics and Linear Elasticity

A First Course in Continuum Mechanics

  • Michael S. Ruderman

Part of the Springer Undergraduate Mathematics Series book series (SUMS)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Michael S. Ruderman
    Pages 1-4
  3. Michael S. Ruderman
    Pages 5-37
  4. Michael S. Ruderman
    Pages 39-64
  5. Michael S. Ruderman
    Pages 65-79
  6. Michael S. Ruderman
    Pages 81-98
  7. Michael S. Ruderman
    Pages 99-129
  8. Michael S. Ruderman
    Pages 131-146
  9. Michael S. Ruderman
    Pages 147-184
  10. Michael S. Ruderman
    Pages 185-203
  11. Back Matter
    Pages 205-291

About this book


​This book provides a concise introduction to continuum mechanics, with a particular emphasis on fluid dynamics, suitable for upper undergraduate students in applied mathematics and related subjects.

Starting with a preliminary chapter on tensors, the main topic of the book begins in earnest with the chapters on continuum kinematics and dynamics. Following chapters cover linear elasticity and both incompressible and compressible fluids. Special topics of note include nonlinear acoustics and the theory of motion of viscous thermal conducting compressible fluids.

Based on an undergraduate course taught for over a decade, this textbook assumes only familiarity with multivariate calculus and linear algebra. It includes many exercises with solutions and can serve as textbook for lecture courses at the undergraduate and masters level.


Continuum mechanics Ideal incompressible fluid Viscous incompressible fluid Ideal compressible fluid Thermal conducting fluid Boundary layers Nonlinear acoustics Shock waves Nonlinear waves in gases

Authors and affiliations

  • Michael S. Ruderman
    • 1
  1. 1.School of Mathematics and StatisticsUniversity of SheffieldSheffieldUK

Bibliographic information