Mathematics

The course begins with a consideration of number sets and measurable quantities in biology: from natural numbers, through generalization of elementary operations, we gradually arrive at studying the real number field. The next leap is the complex numbers: a bridge between algebra and geometry, they allow solving any algebraic equations (fundamental theorem of algebra).

After offering a detailed introduction of the concept of a function, we continue with a rigorous but intuitive study of the notions of a circle and a limit. Limits of elementary functions and techniques for calculating limits of any functions are then discussed. Finally, the concepts of continuity and derivability, as well as extremal points and local/global minimum and maximum of a real variable real function are addressed.

The course continues with the study of the Riemann integral: from the calculation of the primitives of a function (indefinite integral), we move on to the notion of measuring the area subtended by the graph of a real function with real variable (definite integral) and its relation to the primitives of that function (fundamental theorem of calculus). Improper integrals and the concept of convergence are then addressed. The course closes with an introduction to ordinary differential equations, with a focus on solving techniques for first-order ones (autonomous, separable variable, homogeneous, Bernoulli, linear with constant coefficients).