In these “BiomathematicsNotes PDF”, you will study the normal functions in living systems. The emphasis is on exposure to nonlinear differential equations with examples such as heartbeat, chemical reactions and nerve impulse transmission. The basic concepts of the probability to understand molecular evolution and genetics have also been applied.
The topics we will cover will be taken from the following list:
Modeling Biological Phenomenon: Population growth, Administration of drugs, Cell division, Systems of linear ordinary differential equations, Heartbeat, Nerve impulse transmission, Chemical reactions, Predator-prey models.
Mathematics of Heart Physiology and Nerve Impulse Transmission: Stability and oscillations: Epidemics, Phase plane and Jacobian matrix, Local stability, Stability, Limit cycles, Forced oscillations; Mathematics of heart physiology: local model, threshold effect, phase plane analysis and heartbeat model, A model of the cardiac pacemaker; Mathematics of nerve impulse transmission: excitability and repetitive firing, travelling waves.
Bifurcation and Chaos: Bifurcation, Bifurcation of a limit cycle, Discrete bifurcation and period-doubling, Chaos, Stability of limit cycles, Poincaré plane.
Modeling Molecular Evolution and Genetics: Modelling Molecular Evolution: Matrix models of base substitutions for DNA sequences, Jukes−Cantor model, Kimura models, Phylogenetic distances; Constructing Phylogenetic Trees: Phylogenetic trees, Unweighted pair-group method with arithmetic means (UPGMA), Neighbor joining method; Genetics: Mendelian genetics, Probability distributions in genetics.
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