hyperbolic functions engineering mathematics complete course cover

Hyperbolic functions are a set of functions that are widely used in engineering mathematics to model various physical phenomena. The hyperbolic functions are related to the standard trigonometric functions (sine, cosine, tangent, etc.) and are defined in terms of the exponential function.

In mathematics, there are six hyperbolic functions: sinh, cosh, tanh, coth, sech, and csch. These functions are defined as follows:

• The hyperbolic sine function (sinh) is defined as sinh(x) = (e^x – e^(-x))/2.
• The hyperbolic cosine function (cosh) is defined as cosh(x) = (e^x + e^(-x))/2.
• The hyperbolic tangent function (tanh) is defined as tanh(x) = sinh(x)/cosh(x) = (e^x – e^(-x))/(e^x + e^(-x)).
• The hyperbolic cotangent function (coth) is defined as coth(x) = cosh(x)/sinh(x) = (e^x + e^(-x))/(e^x – e^(-x)).
• The hyperbolic secant function (sech) is defined as sech(x) = 1/cosh(x) = 2/(e^x + e^(-x)).
• The hyperbolic cosecant function (csch) is defined as csch(x) = 1/sinh(x) = 2/(e^x – e^(-x)).

Hyperbolic functions have many applications in engineering mathematics, including:

• The calculation of electromagnetic fields in transmission lines, waveguides, and antennas.
• The modeling of fluid flow in pipes and channels.
• The analysis of vibrating systems, such as mechanical systems and electrical circuits.
• The design and analysis of control systems, such as in robotics and aerospace engineering.
• The solution of differential equations that arise in many areas of engineering and science.

In summary, hyperbolic functions are important tools in engineering mathematics that enable engineers to model and analyze complex systems in a variety of fields.