What inspired Maxwell's four equations?
The experimental and theoretical work of Faraday, who was not mathematically inclined, but still a gifted self taught physicist. Maxwell essentially put into equations the ideas of Faraday and Oerster/Ampere . Faraday had the idea of directed fields and lines of force. The only mathematics to describe these ideas was William Rowan Hamilton's Quaternions and especially the vector part of quaternions. Vectors described the directied forces and lines.
Maxwell found out about quaternions and vectors and thus his four equations involve vectors. Maxwell, ignored the scalar part of quaternions and he did not like the quaternions rules for vectors which gave the product of parallel vectors a negative sign.
Oliver Heaviside and Willard Gibbs, changed Hamilton's Rule and defined their "Vector Analysis" to have a positive sign. This is the rule currently used in physics today. Unfortunately, this rule makes Gibbs vectors non-associative (II)J = J but I(IJ) = -J. Hamilton's Quaternions define and Division Algebra.
Create a matrix of the coefficients of each equation. The solutions to the equations should make up the rightmost column of the matrix. Then, row reduce the matrix until you are able to rewrite the equations and solve them. The matrix should be a 4x5 matrix (4 rows and 5 columns) for four equations with four variables. This is known as a system of equations.
It is widely, but not universally, accepted that the Bible was divinely inspired. 2 Timothy 3:16 may be speaking of the Old Testament, when it says, "All scripture is given by inspiration of God ..." since the New Testament canon had not yet been defined. A later view is that the New Testament was inspired by the Holy Spirit. A medieval artwork shows a dove, symbol of the Holy Spirit, whispering into the ear of…
This can happen in different ways: a) More variables than equations. For instance, a single equation with two variables (such as x + y = 15), two equations with three variables, two equations with four variables, etc. b) To of the equations describe the same line, plane, or hyper-plane - this, in turn, will result in that you "really" have less equations than it seems. For example: y = 2x + 3 2y = 4x…
The answer will depend on what kinds of equations: there are linear equations, polynomials of various orders, algebraic equations, trigonometric equations, exponential ones and logarithmic ones. There are single equations, systems of linear equations, systems of linear and non-linear equations. There are also differential equations which are classified by order and by degree. There are also partial differential equations.
What are the release dates for HGTV Design Star - 2006 The Final Four Bring Sets Inspired by '80s Sitcom the Facts of Life to This Century?
There are four kinematic equations. Assuming acceleration is constant, the equations are: vf = vo + a*t xf = xo + vo*t + (1/2) a*t^2 vf^2 = vo^2 + 2*a*(xf-xo) d = (vf + vo)/2 * t On the variables: f indicates final value, o indicates original or initial value. v = velocity a = acceleration x = position d = distance t = time ^ indicates an exponent (i.e. t^2 is t squared) *…
Laurent Veron has written: 'Singularities of solutions of second order quasilinear equations' -- subject(s): Differential equations, Elliptic, Differential equations, Nonlinear, Differential equations, Parabolic, Elliptic Differential equations, Nonlinear Differential equations, Numerical solutions, Parabolic Differential equations, Singularities (Mathematics)