Course content

• Elementary calculus : (12 hours)
• Functions : Idea of functions using examples from Biology. Concentration of proteins as a function of time. Periodic functions.
• Differentiation: Introduce change in concentration,change in length etc as derivatives. Slope and derivative. Derivatives of simple functions. Pressure,entropy, force etc as derivatives of free energy .Techniques of differentiation.
• Plotting functions: Maximum and minimum points.
• Sketching simple functions : Exponential, Gaussian,Logarithm etc.
• Techniques of Integration: Integration as area under a curve. Integrating simple expressions. Use of Integration techniques in biology.
• Descriptive statistics and Data display (6 Hours)
• Measurement scales. Continuous and discrete data
• Summarizing data set: Histograms, Pie Charts, otherways of representing data Mean, variance, standard deviation Errors, fitting a function to experimental data,linear and non-linear fits.
• Vectors, Co-ordinate systems: (3 hours)
• Scalars and vectors. Spherical polar coordinates,Cylindrical coordinates. Use of these coordinate systems to study 3-dimensional configuration ofproteins
• Differential Equations : (8 hours)
• Ordinary/partial differential equations: Rate equations,Diffusion, Solving differential equations, Applications in biology. Calculus of growth and decay processes.
• Probability: (8 hours)
• Relevance of stochasticity in biology.
• Thermalfluctuations, Mutations, Bacterial motion.
• Introduction to probability, Probability distributions,Moments Binomial distribution , Gaussian distribution ,Poisson distribution Examples from biology (Luria-Delbruck fluctuation test, Knudson 302222s two-hit hypothesis)
• Conditional probability Master equations. Modeling gene expression, polymerization of actin/microtubules
• Fourier series, Fourier transformation, (3 hours)Discuss the use of Fourier transformation in X-ray crystallography and in optics

References

• Mathematics for Biological Scientists, M. Aitken, B. Broadhursts, S. Haldky, Garland Science (2009)
• Introduction to Mathematics for Life Scientists, E. Batschelet, Springer Verlag, 3rd edition (2003)
• Physical Biology of the Cell, R Phillips, J Kondev, J. Theriot, Garland Science (2009)
• Calculus for Life Sciences, R. De Sapio, W. H. Freeman and Co. (1976)
• Random Walks in Biology, H. C. Berg, Princeton university press (1993)