Authors introduced advanced applications of partial differential equations in plasma physics using analytical methods based on Boltzmann-Maxwell equations. The book creates theoretical tools for predicting and controlling plasma behavior in many outstanding applications. In the study was introduced a new mathematical model for calculating the thermodynamic forces, kinetic coefficients, and flux variables as two new scientific achievements. Secondly, with reasonable accuracy, was determined the thermodynamic equilibrium time of electrons under an external force. Authors clarify the difference between an equilibrium velocity distribution function and a perturbed one. The book introduces the extended Gibbs equation, which predicts ratios between various contributions to the internal energy change for diamagnetic and paramagnetic plasmas. A standard laboratory argon plasma model is used to apply the results. It advances our understanding of plasma physics and holds immense potential for practical applications in aerospace engineering, plasma technology, and materials science. This book lays the groundwork for future innovations and technological advancements in plasma.