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
Fourier series, Fourier transformation, (3 hours)Discuss the use of Fourier transformation in
X-ray crystallography and in optics
Mathematics for Biological Scientists, M. Aitken, B. Broadhursts, S. Haldky, Garland Science
Introduction to Mathematics for Life Scientists, E. Batschelet, Springer Verlag, 3rd edition
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)
6 credits - Lecture
Name(s) of other Academic units to whom the course may be relevant