Mathematics for biologists 1989/90, 1990/91, 1992/93. For 1st year biology students. Average program. Official name: Istituzioni di Matematiche per biologi.

ELEMENTARY METHODS What is mathematics? Fundamental rules The logarithm Trigonometric functions Polar coordinates in plane and space Complex numbers n-th roots of complex numbers The language of set theory Peano's axioms and the principle of induction Some logic Operations on sets with infinitely many operandss The cartesian product Resolution of systems of linear equations with Gauss elimination Binomial numbers Euclidean algorithm FUNCTIONS AND RELATIONS Functions Relations Equivalence relations REAL NUMBERS sqrt(2) is irrational Real numbers SEQUENCES AND SERIES Sequences of real numbers Sequences tending to infinity The Bolzano-Weierstrass theorem Convergence criteria for sequences Limsup and liminf Sequences of complex numbers Numerical series Convergence criteria specific for series ANALYTIC GEOMETRY Linear subspaces of R^n Linear independence, bases and dimension Affine subspaces of R^n The scalar product Linear mappings and matrices Determinants and vector product CONTINUOUS FUNCTIONS Triangular inequality in R^n Limit of f(x) for x tending to x_0 Continuous functions defined on a subset of R^m Polynomial functions The existence of zeros for continuous functions Existence of the maximum of a continuous function defined on a compact set Pointwise and uniform convergence of sequences of functions Logarithms (theory) DIFFERENTIAL CALCULUS IN ONE VARIABLE The equation y = y_0+a(x-x_0) The derivative The derivatives of trigonometric functions The derivative of the exponential and the logarithm Relative maxima and minima and Rolle's theorem The marvelous theorem of calculus Analytic study of the graph of a function Taylor series of a polynomial Taylor series of a differentiable function De l'Hopital's rules Inversion of trigonometric functions INTEGRATION Measures Measurable sets and Caratheodory's theorem Measurable functions The integral Fundamental inequality of integration theory Lebesgue measure Fundamental theorem of calculus Calculating integrals by means of the fundamental theorem Integration by parts Transformation rules for the integral