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.

Introduction to the differential and integral calculus in one real variable: fundaments of mathematical thinking, numbers, sequences, basic point set topology, continuity, differentiable functions, ordinary differential equations, Riemann integration.

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.

Introduction to differential and integral calculus in several real variables, vector calculus: differential, partial derivative, implicit functions, inverse function theorem, minima with constraints; Riemann integral, vector fields, differential forms, path integrals, surface integrals, divergence theorem, Stokes' theorem.

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

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.

Conceptual and methodical introduction to theoretical physics by taking the example of classical mechanics. Discussion of Lagrangian and Hamiltonian descriptions as well as symmetries and conserved quantities.

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

Symmetry, metrics, and groups

Fourier series. Linear partial differential equations of mathematical physics. Fourier transform. Special functions and eigenfunction expansions. Distributions. Selected problems from quantum mechanics.

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).

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