| Geometric Concepts and Generalities | |
| Surfaces and Curves in Three Dimensions | p. 1 |
| Methods of Solution of dx/P = dy/Q = dz/R | p. 7 |
| Orthogonal Trajectories of a System of Curves on a Surface | p. 11 |
| Pfaffian Differential Equation in R[superscript 3] | p. 13 |
| Newton's Mechanics, Lagrangians, Hamiltonian, Hamilton-Jacobi Equation, and Liouville's Theorem | p. 15 |
| Partial Differential Equations of First Order | |
| Classification | p. 23 |
| Linear PDEFO for Functions Defined in [Omega] [is a subset of] R[superscript 2] | p. 25 |
| Quasi-linear PDEFO for Functions Defined in [Omega] [is a subset of] R[superscript 2] | p. 27 |
| Quasi-linear PDEFO for Functions Defined in [Omega] [is a subset of] R[superscript n] | p. 34 |
| Physical Applications I | |
| Mechanics | p. 37 |
| Angular Momentum in Quantum Mechanics | p. 44 |
| Heat Propagation between Two Superconducting Cables | p. 51 |
| Classical Statistical Mechanics in Equilibrium | p. 54 |
| Renormalization Group's Equations | p. 56 |
| Particle Multiplicity Distribution in High Energy Physics | p. 59 |
| Hamiltonian Perturbation Approach in Accelerator Physics | p. 61 |
| Perturbation Approach for the One-dimensional Constant of Motion | p. 64 |
| Constant of Motion for a Relativistic Particle under Periodic Perturbation | p. 65 |
| Nonlinear Partial Differential Equations of First Order | |
| Non-linear PDEFO for Functions Defined in [Omega] [is a subset of] R[superscript 2] | p. 68 |
| Non-linear PDEFO for Functions Defined in [Omega] [is a subset of] R[superscript n] | p. 83 |
| Physical Applications II | |
| Motion of a Classical Particle | p. 90 |
| Hamilton-Jacobi equation for a one-dimensional Harmonic oscillator | p. 90 |
| The Lagrangian obtained directly from the Hamiltonian | p. 92 |
| Relativistic particle moving in a Coulomb field | p. 93 |
| Motion of a test particle in a Schwarzchild's space | p. 97 |
| Interaction of a periodic gravitational wave with a test particle | p. 100 |
| Trajectory of a Ray of Light | p. 103 |
| Solution of the Eikonal equation for a refraction index depending on z | p. 104 |
| Solution of the Eikonal equation for a refraction index radially depending | p. 105 |
| Characteristic Surfaces of Linear Partial Differential Equation of Second Order | |
| Characteristic Surfaces of a Linear PDESO Defined in R[superscript n] | p. 108 |
| Characteristic Surfaces of a Linear PDESO Defined in R[superscript 2] | p. 111 |
| Index | p. 115 |
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