Search results with tag "The hyperbolic"
3.6 The hyperbolic identities - mathcentre.ac.uk
mathcentre.ac.uk3.6 The hyperbolic identities Introduction The hyperbolic functions satisfy a number of identities. These allow expressions involving the hyperbolic functions to be written in different, yet equivalent forms. Several commonly used identities are given on this leaflet. 1. Hyperbolic identities coshx = e x+e−x 2, sinhx = ex −e− 2 tanhx ...
3.6 The hyperbolic identities - mathcentre.ac.uk
www.mathcentre.ac.uk3.6 The hyperbolic identities Introduction The hyperbolic functions satisfy a number of identities. These allow expressions involving the hyperbolic functions to be written in different, yet equivalent forms. Several commonly used identities are given on this leaflet. 1. Hyperbolic identities coshx = e x+e−x 2, sinhx = ex −e− 2 tanhx ...
The two-dimensional heat equation - Trinity University
ramanujan.math.trinity.eduThe hyperbolic trigonometric functions The hyperbolic cosine and sine functions are coshy = ey + e y 2; sinhy = ey e y 2: They satisfy the following identities: cosh2 y sinh2 y = 1; d dy coshy = sinhy; d dy sinhy = coshy: One can show that the general solution to the ODE Y00 2Y = 0 can (also) be written as Y = Acosh( y) + B sinh( y): Daileda ...