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Mathematical Preliminaries
Published in K.T. Chau, Theory of Differential Equations in Engineering and Mechanics, 2017
where P0 ≠ 0, P1(x), …, Pn(x) are polynomials of x and n is positive integer, w = f(x) is called an algebraic function. On the other hand, any function which cannot be expressed as a solution of (1.1) is called a transcendental function. Transcendental functions include exponential functions, trigonometric functions (or circular functions such as sine and cosine), hyperbolic functions (such as sinh $ {{sinh }} $ and cosh) $ {{cosh }}) $ , and logarithmic functions.
Power Series Solutions and Special Functions
Published in Steven G. Krantz, Differential Equations, 2015
A transcendental function is one that is not a polynomial or a rational function. The elementary transcendental functions are the ones that we encounter in calculus class: sine, cosine, logarithm, exponential, and their inverses and combinations using arithmetic/algebraic operations.
Power Series Solutions and Special Functions
Published in Steven G. Krantz, Differential Equations, 2020
A transcendental function is one that is not a polynomial or a rational function or a root. The elementary transcendental functions are the ones that we encounter in calculus class: sine, cosine, logarithm, exponential, and their inverses and combinations using arithmetic/algebraic operations.
Automated generation of hybrid automata for multi-rigid-body mechanical systems and its application to the falsification of safety properties
Published in Mathematical and Computer Modelling of Dynamical Systems, 2018
E.M. Navarro-López, M.D. O’Toole
Creating computational models of MRB systems is not straightforward. The governing dynamic equations are piecewise smooth and contain discontinuities and jumps in the state space resulting from changing friction and impacts. Moreover, the governing equations themselves may be non-linear and contain transcendental functions. The possible occurrence of multiple contacts further expounds the problem.