Using Lagrangian mechanics, it may be shown that the motion of a pendulum can be described by the dimensionless nonlinear equation
22.
In the case of a nonlinear equation, it will only rarely be possible to obtain the general solution in closed form.
23.
His recent research interests include nonlinear conservation laws, nonlinear waves, nonlinear equations of mixed type, free boundary problems, and geometric problems.
24.
In general, solving these nonlinear equations presents a formidable challenge because of the huge range over which the free concentrations may vary.
25.
The full nonlinear equations emerge when the energy-momentum of the gravitons themselves are included in the stress-energy tensor in a unique self-consistent way.
26.
Nonlinear equations and functions are of interest to physicists and mathematicians because they can be used to represent many natural phenomena, including chaos.
27.
Enforcing these conditions leads to a set of nonlinear equations which have been solved and tabulated up to order 131 in the polynomial.
28.
The linear equation had a confidence interval of ? 8 bpm and the nonlinear equation had a tighter range of ? 5 bpm.
29.
Finally, in 1740, Thomas Simpson described Newton's method as an iterative method for solving general nonlinear equations using calculus, essentially giving the description above.
30.
Schnabel's research interests include numerical computation, numerical solution of unconstrained and constrained optimization problems, solution of systems of nonlinear equations, and nonlinear least squares.
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