Section 1 Physiological and pharmacological modelling. Introduction. The input-output principle. Steady-states: Alveolar ventillation aamp, PaCO2. Gas laws. Flux aamp, the Fick principle. Fick aamp, cardiac output, dilution methods. Fick aamp, cerebral blood flow. Apnoeic oxygenation. Nitrogen washout and preoxygeneration. Time constants. Step change in ventilation. Air embolism. Pharmacokinetic models. Drug-receptor interaction. Drug antagonism. Oscillating systems. Damped oscillations. Forced oscillation. Modelling arterial pressure waves. Section 2 - Mathematical background. Numbers. Functions. Pattern functions aamp, transformation. Constant function. Linear. Rectangular hyperbolic functions. Polynomial functions. Inverse functions. Exponential aamp, logarithmic functions. Sinusoidal functions. Functions of more than one variable. The derivative aamp, differentiation. Maxima aamp, minima. Integration. Differential equations. Numerical methods for differential equations. Section 3 - Probability aamp, statistics. Probability models and simulation. Waiting times in a Poisson process. Passing the fellowship, the binomial distribution. Measuring SVP, the normal distribution. Modelling with random variables. Sums of random variables. Probability. Conditional probability aamp, Bayes theorem. Summary measures, location and dispersion. The normal distribution. Statistical inference. Sample mean. Estimation aamp, confidence. Sample variance. Significance testing. Samples of unknown mean and variance. Categorial data. Related variables, linear regression. Related variables, correlation. Distribution-free methods. Stochastic IOP. Queues. Bibliography. Index.