In mathematics, an implicit equation is a relation of the form R ( x 1 , … , x n ) = 0 {\displaystyle R(x_{1},\ldots ,x_{n})=0} , where R {\displaystyle R} is a function of several variables (often a polynomial). For example, the implicit equation of the unit circle is x 2...

In mathematics, more specifically in multivariable calculus, the implicit function theorem is a tool that allows relations to be converted to functions of several real variables. It does so by representing the relation as the graph of a function. There may not be a single function whose graph can represent the entire relation, but there may be such a function on a restriction of the domain of the relation. The implicit function theorem gives a sufficient condition to ensure that there is such a function. More precisely, given a system of m equations fi (x1, ..., xn, y1, ..., ym) = 0, i = 1...

The Course of Theoretical Physics is a ten-volume series of books covering theoretical physics that was initiated by Lev Landau and written in collaboration with his student Evgeny Lifshitz starting in the late 1930s. It is said that Landau composed much of the series in his head while in an NKVD prison in 1938-1939. However, almost all of the actual writing of the early volumes was done by Lifshitz, giving rise to the witticism, "not a word of Landau and not a thought of Lifshitz". The first eight volumes were finished in the 1950s, written in Russian and translated into English in the late 1950s...

Fundamentals of Physics is a calculus-based physics textbook by David Halliday, Robert Resnick, and Jearl Walker. The textbook is currently in its tenth edition (published 2013). The current version is a revised version of the original 1960 textbook Physics for Students of Science and Engineering by Halliday and Resnick, which was published in two parts (Part I containing Chapters 1-25 and covering mechanics and thermodynamics; Part II containing Chapters 26-48 and covering electromagnetism, optics, and introducing quantum physics). A 1966 revision of the first edition of Part I changed the title...

The Larmor formula is used to calculate the total power radiated by a non relativistic point charge as it accelerates. This is used in the branch of physics known as electrodynamics and is not to be confused with the Larmor precession from classical nuclear magnetic resonance. It was first derived by J. J. Larmor in 1897, in the context of the wave theory of light. When any charged particle (such as an electron, a proton, or an ion) accelerates, it radiates away energy in the form of electromagnetic waves. For velocities that are small relative to the speed of light, the total power radiated...

Fundamentals of Physics is a calculus-based physics textbook by David Halliday, Robert Resnick, and Jearl Walker. The textbook is currently in its tenth edition (published 2013). The current version is a revised version of the original 1960 textbook Physics for Students of Science and Engineering by Halliday and Resnick, which was published in two parts (Part I containing Chapters 1-25 and covering mechanics and thermodynamics; Part II containing Chapters 26-48 and covering electromagnetism, optics, and introducing quantum physics). A 1966 revision of the first edition of Part I changed the title...