Introduction to partial differential equations. Differential equations which are important in applications are classified and solved. Elliptic, parabolic and hyperbolic differential equations are treated. The following mathematical tools are introduced: Laplace transforms, Fourier series, separation of variables, methods of characteristics.

Introduction to calculus in one dimension. Building simple models and analysing them mathematically.Functions of one variable: the notion of a function, of the derivative, the idea of a differential equation, complex numbers, Taylor polynomials and Taylor series. The integral of a function of one variable.

Basics about multidimensional analysis.Ordinary differential equations as mathematical models to describe processes (continuation from Analysis A).Numerical, analytical and geometrical aspects of differential equations.

This course equips doctoral students with knowledge and tools to recognize, discuss and address ethical issues of their research.

Mathematics I covers mathematical concepts and techniques necessary to model, solve and discuss scientific problems - notably through ordinary differential equations.The main focus of Mathematics II is multivariable calculus.

Continuation of the topics of Mathematics I, with main focus on multivariable calculus.

Continuation of the topics of Mathematics I, with main focus on multivariable calculus.