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The theory will be proposed verbally, and not mathematically, because it is not clear that traditional mathematical tools are immediately suitable for its mathematization.
Mathematical tools are, in many cases, shared.
The mathematical tools are based on the kernel estimators technique.
Adequate mathematical tools are provided to tackle the related problems.
The common mathematical tools are integral inequality and free-weighting matrix method.
Heuristic rules and mathematical tools are mainly used to achieve our target.
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Therefore development of new mathematical tools is necessary.
But, until recently, mathematical tools were not well suited to investigate emergence, or other properties of out-of-equilibrium dynamical systems.
Moreover, the availability of reliable and comprehensive mathematical tools is recognized as a key to develop cost effective and highly performing innovative powertrains.
From then on, some classical mathematical tools were used successfully to study these singular equations, such as Mawhin's continuation theorem in the coincidence degree theory [17], the method of upper and lower solutions [8], some fixed point theorems in cones [2], the Poincaré-Birkhoff theorem [14], the phase-plane analysis and topological degree methods [12], and so on.
The matrices that are its main mathematical tool are usually taught as a simplifying notation, and Professor Strang covers this idea.
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