BB 619 - Mathematics for Biologists

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
  • 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)
Pre-requisite : N/A
Total credits : 6 credits - Lecture
Type :
Duration : Autumn 2022
Name(s) of other Academic units to whom the course may be relevant : N/A