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CBE8801: 2018Au outline.pdf Outline 1. A few mathematical preliminaries (a) Complex numbers (b) Matrices and determinants References: • E. A. Coddington, “An introduction to ordinary differential equations,” Dover, New York (1989). Chapter 1. • J. Bak and D. J. Newman, “Complex Analysis (3rd ed.),” Springer, New York (2010). Chapter 1. Find pdf files through the university library here. 2. Ordinary differential equations (a) 1st order ODE i. ii. iii. iv. v. vi. Integration factor Separation of variables Exact equations A system of 1st order ODE’s Numerical methods Qualitative theory of ordinary differential equations A. One-dimensional systems B. Two-dimensional systems vii. Stochastic simulation of chemical reactions (b) 2nd order ODE i. ii. iii. iv. Constant coefficients Variable coefficients Regular singularity Sturm-Liouville theory A. Vector space B. Fourier series C. Orthogonal polynomials References: (a) General reference for ODE’s • E. A. Coddington, “An introduction to ordinary differential equations,” Dover, New York (1989). Chapters 2-4. • F. J. Farlow, “An introduction to differential equations and their applications,” Dover, New York (2006). • F. J. Murray and K. S. Miller, “Existence theorems for ordinary differential equations,” Dover, New York (2007). (b) Numerical methods for ODE’s — 1— CBE8801: 2018Au outline.pdf • W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. R. Flannery, “Numerical Recipes, The art of Scientific Computing” 2nd edition. Cambridge University Press (1992). Chapters 16 and 17. Both Fortran and C versions are available. • W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. R. Flannery, “Numerical Recipes, The art of Scientific Computing” 3rd edition. Cambridge University Press (2007). Chapters 17 and 18. This edition includes more recent developments. Softwares are written in C++. (c) Qualitative theory of ODE’s • F. J. Farlow, “An introduction to differential equations and their applications,” Dover, New York (2006). Chapters 6 and 8. • Armin Fuchs, “Nonlinear dynamics in complex systems,” Springer, New York (2013). Find pdf files through the university library here. • S. H. Strogatz, “Nonlinear dynamics and chaos (2nd ed.),” Westview Press, Colorado (2015). Access E-book through the university library here. (d) Stochastic simulation of chemical reactions • D. T. Gillespie, “A general method for numerically simulating the stochastic time evolution of coupled chemical reactions,” Journal of Computational Physics, vol. 22, pp. 403–434 (1976). (e) Sturm-Liouville theory • M. A. Al-Gwaiz, “Sturm-Liouville theory and its applications,” Springer-Verlag, London, (2008). Chapters 1-6. Find pdf files through the university library here. 3. Numerical methods for partial differential equations 4. Stochastic differential equations — 2—