Table of Contents

​​​​I Introduction to Linear Algebra and Differential Geometry.- 1 Vector Space and Linear Maps.- 2 Tensor Algebra.- 3 Skew-symmetric Tensors and Exterior Algebra.- 4 Euclidean and Symplectic Vector Spaces.- 5 Duality and Euclidean Tensors.- 6 Differentiable Manifolds.- 7 One-Parameter Groups of Diffeomorphisms.- 8 Exterior Derivative and Integration.- 9 Absolute Differential Calculus.-​ 10 An Overview of Dynamical Systems.- II Mechanics.- 11 Kinematics of a Point Particle.- 12 Kinematics of Rigid Bodies.- 13 Principles of Dynamics.- 14 Dynamics of a Material Point.- 15 General Principles of Rigid Body Dynamics.- 16 Dynamics of a Rigid Body.- 17 Lagrangian Dynamics.- 18 Hamiltonian Dynamics.- 19 Hamilton-Jacobi Theory.- 20 Completely Integrable Systems.- 21 Elements of Statistical Mechanics of Equilibrium.- 22 Impulsive Dynamics.- 23 Introduction to Fluid Mechanics.- A First-Order PDE.- B Fourier’s Series.- References.- Index.

About the Author

Antonio Romano has been the author or coauthor of numerous books on mechanics and Mathematica, and he has taught courses in mechanics for 35 years at "Il Fredrico" University in Naples.

Reviews

From the reviews:“By centering his presentation around the major aspects and omitting less important details, the author succeeds in providing a concise though lucid introduction into the mathematical areas … it in particular, can be recommended to students who wish to learn these mathematical concepts without indulging too much in formal and technical points. … The average graduate student … will be well served by Romano’s book. It enjoys many qualities that render this book a promising candidate for becoming a standard text in physics classrooms.” (H. Hogreve, Mathematical Reviews, October, 2013)“The author presents a high-level textbook based mainly on differential geometry methods; at the same time, he tries to follow a historical process that leads to an easier understanding of the development of mechanics. … The book is written in a very clear and systematic manner; each chapter is followed by many exercises … . The volume represents a real contribution to the field, being useful not only to students but to all readers who wish to have a correct and well-written information, too.” (Petre P. Teodorescu, Zentralblatt MATH, Vol. 1263, 2013)