Functions; Differential and integral calculus for functions of one variable; power series. The mathematical methods are applied in a large number of examples from mechanics, physics and other areas which are basic to engineering.

Calculus of one variable: Real and complex numbers, vectors, functions, limits, sequences, series, power series, differentiation and integration in one variable, introduction to ordinary differential equations

Differential and integral calculus for functions of one and several variables; vector analysis; ordinary differential equations of first and of higher order, systems of ordinary differential equations; power series. The mathematical methods are applied in a large number of examples from mechanics, physics and other areas which are basic to engineering.

Introduction to the mathematical foundations of engineering sciences, as far as concerning differential and integral calculus.

Calculus in several variables; differential equations

Differential and Integral Calculus for functions of one and several variables, including many examples frommechanics, physics and other areaes.

Introduction to differential calculus and integration in several variables.

Differential and integral calculus for functions of one and several variables; vector analysis; ordinary differential equations of first and of higher order, systems of ordinary differential equations; power series.For each of these topics many examples from mechanics, physics and other areas.

Complex functions of one variable, Cauchy-Riemann equations, Cauchy theorem and integral formula, singularities, residue theorem, special functions, conformal mappings, Riemann mapping theorem.

Basics of complex analysis in theory and applications, in particular the global properties of analytic functions. Introduction to the integral transforms used in signal theory and network analysis.

Symmetry, metrics, and groups

Contents: Linear systems - the Gaussian algorithm, matrices - LU decomposition, determinants, vector spaces, least squares - QR decomposition, linear maps, eigenvalue problem, normal forms - singular value decomposition; numerical aspects.

Introduction to the theory of vector spaces for students of mathematics or physics: Basics, vector spaces, linear transformations, solutions of systems of equations, matrices, determinants, endomorphisms, eigenvalues, eigenvectors.

Introduction to the theory of vector spaces for mathematicians and physicists including solutions of linear equations, linear transformations, determinants, eigenvalues and eigenvectors, bilinear forms, canonical forms for matrices, and selected applications, part II.

Introduction to the theory of vector spaces for mathematicians andphysicists including solutions of linear equations, linear transformations,determinants, eigenvalues and eigenvectors, bilinear forms, canonical forms for matrices, and selected applications, part II.

Group theory: groups, representation of groups, unitary and orthogonal groups, Lorentz group. Lie theory: Lie algebras and Lie groups. Representation theory: representation theory of finite groups, representations of Lie algebras and Lie groups, physical applications (eigenvalue problems with symmetry).