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Inverse Trigonometric Functions 2 3.10 Trigonometric Equations and Inequalities 3 3.11 The Secant, Cosecant, and Cotangent Functions 2 3.12 Equivalent Representations of Trigonometric Functions 2 3.13 Trigonometry and Polar Coordinates 2 3.14 Polar Function Graphs 2 3.15 Rates of Change in Polar Functions 2
A formula for computing the trigonometric identities for the one-third angle exists, but it requires finding the zeroes of the cubic equation 4x 3 − 3x + d = 0, where is the value of the cosine function at the one-third angle and d is the known value of the cosine function at the full angle.
They also occur in the solutions of many linear differential equations (such as the equation defining a catenary), cubic equations, and Laplace's equation in Cartesian coordinates. Laplace's equations are important in many areas of physics , including electromagnetic theory , heat transfer , fluid dynamics , and special relativity .
Solving an equation symbolically means that expressions can be used for representing the solutions. For example, the equation x + y = 2x – 1 is solved for the unknown x by the expression x = y + 1, because substituting y + 1 for x in the equation results in (y + 1) + y = 2(y + 1) – 1, a true statement. It is also possible to take the ...
Order of accuracy — rate at which numerical solution of differential equation converges to exact solution; Series acceleration — methods to accelerate the speed of convergence of a series Aitken's delta-squared process — most useful for linearly converging sequences; Minimum polynomial extrapolation — for vector sequences; Richardson ...
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. [ 21 ] [ 22 ] [ 23 ] Differential equations play a prominent role in engineering , physics , economics , biology , and other disciplines.
The notation convention chosen here (with W 0 and W −1) follows the canonical reference on the Lambert W function by Corless, Gonnet, Hare, Jeffrey and Knuth. [3]The name "product logarithm" can be understood as this: Since the inverse function of f(w) = e w is called the logarithm, it makes sense to call the inverse "function" of the product we w as "product logarithm".