Abstract
Often used but less known fundamental concepts have been collected in this chapter. These include certain operations on vectors and matrices, notions and basic properties of directed and undirected graphs, a few theorems from advanced calculus, and also fundamental statements from the theory of ordinary and partial differential equations and stochastic processes. Exercises and problems make the material more easy to digest.
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References
Dickson LE (1913) Finiteness of the odd perfect and primitive abundant numbers with n distinct prime factors. Am J Math 35(4):1913. http://www.jstor.org/stable/2370405
Farkas M (1994) Periodic motions. Springer, New York
Guckenheimer J, Holmes P (1983) Nonlinear oscillations, dynamical systems, and bifurcations of vector fields. Applied mathematical sciences, vol 42. Springer, New York
Harary F (1969) Graph theory. Addison–Wesley, Reading
Horn F, Jackson R (1972) General mass action kinetics. Arch Ratl Mech Anal 47:81–116
Lovász L (2007) Combinatorial problems and exercises. AMS Chelsea Publishing, Providence
Øre O (1962) Theory of graphs, vol 38. AMS Colloquium Publications, Providence
Perko L (1996) Differential equations and dynamical systems. Springer, Berlin
Póta G (1981) On a theorem of overshoot-undershoot kinetics. React Kinet Catal Lett 17(1–2):35–39
Tikhonov AN (1952) Systems of differential equations containing a small parameter at the derivatives. Mat sb 31(73):575–585
Tóth J (1987) Bendixson-type theorems with applications. Z Angew Math Mech 67(1):31–35
Tóth J, Simon LP (2005/2009) Differential equations (Differenciálegyenletek). Typotex, Budapest
Tóth J, Li G, Rabitz H, Tomlin AS (1997) The effect of lumping and expanding on kinetic differential equations. SIAM J Appl Math 57:1531–1556
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Tóth, J., Nagy, A.L., Papp, D. (2018). Mathematical Background. In: Reaction Kinetics: Exercises, Programs and Theorems. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-8643-9_13
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DOI: https://doi.org/10.1007/978-1-4939-8643-9_13
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