textbook-theory · English
Difference Equations to Differential Equations — Section 6.7: Hyperbolic Functions
Section 6.7 of Dan Sloughter's open calculus textbook introduces the six hyperbolic functions (sinh, cosh, tanh, coth, sech, csch), derives their derivatives and integrals from exponential definitions, and develops inverse hyperbolic functions with logarithmic closed forms. The section demonstrates how hyperbolic substitutions simplify integrals such as those involving sqrt(1+x^2) and sqrt(x^2-1), providing an alternative to trigonometric substitution methods. Practice problems covering differentiation, integration, and graphing are included.
hyperbolic functionscalculusdifferentiationintegration