This book is part of the series “Mathematics and Physics Applied to Science and Technology.” It combines rigorous mathematics with general physical principles to model practical engineering systems with a detailed derivation and interpretation of results. The book presents the mathematical theory of partial differential equations and methods of solution satisfying initial and boundary conditions. It includes applications to acoustic, elastic, water, electromagnetic and other waves, to the diffusion of heat, mass and electricity, and to their interactions. The author covers simultaneously rigorous mathematics, general physical principles and engineering applications with practical interest. The book provides interpretation of results with the help of illustrations throughout and discusses similar phenomena, such as the diffusion of heat, electricity and mass. The book is intended for graduate students and engineers working with mathematical models and can be applied to problems in mechanical, aerospace, electrical and other branches of engineering.
Part 1: Vector Fields with applications to Thermodynamics and
Irreversibility.
1. Classes of Equations and Similarity Solutions. 1.1.
Hierarchy of Partial Differential Equations. 1.2 General Integral and
Arbitrary Functions. 1.3. Unforced P.D.E. with First-Order Derivatives. 1.4.
Quasi-Linear and Forced First-Order P.D.E.S. 1.5. Differentials of
First-Degree in Three Variables. 1.6. P.D.E.s with Constant Coefficients and
All Derivatives of Same Order. 1.7. Harmonic and Biharmonic Functions on the
Plane. 1.8. Forced Linear P.D.E. with Derivatives of Constant Order. 1.9.
Forced Harmonic and Biharmonic Equations. 1.10. Conclusion.
2.
Thermodynamics, Irreversibility, Compressible Flow and Shocks. 2.1. Work,
Heat, Entropy and Temperature. 2.2. Functions of State and Constitutive
Properties. 2.3. Three Principles and Four Processes of Thermodynamics. 2.4.
Entropy Production and Diffusive Properties. Part 2: Compressible Flow with
applications to Engines, Shocks and Nozzles.
2. Thermodynamics,
Irreversibility, Compressible Flow and Shocks. 2.5 Equation of State and
Thermodynamic Cycles. 2.6 Adiabatic Compressible Fluid Flow. 2.7. Vortex
Sheet and the Normal Shock (Rankine 1870; Huginot 1887). 2.8. Oblique Shock
(Busemann 1931) and Adiabatic Turn (Prandtl, Meyer 1908). 2.9. The Choked
or Shocked Nozzle. 2.10. Conclusion.
Luis Manuel Braga da Costa Campos was the coordinator of the Scientific Area of Applied and Aerospace Mechanics in the Department of Mechanical Engineering and also the director (and founder) of the Center for Aeronautical and Space Science and Technology until retirement in 2020.
L. A. R. Vilela is currently completing an Integrated Masters degree in Aerospace Engineering at Instituto Superior Técnico (IST) of Lisbon University.
