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

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.

Calculus in several variables; differential equations

Introduction to differential calculus and integration in several variables.

The lecture gives an overview of the physics at high-energycolliders. After the introduction of the theoretical concepts, themost important applications are described in detail: the production ofjets, heavy quarks, and electroweak gauge bosons. The experimentalprogram at the Large Hadron Collider at CERN is also discussed, withspecial emphasis on the postulated Higgs particle.

Introduction to differential geometry and differential topology. Contents: Curves, (hyper-)surfaces in R^n, geodesics, curvature, Theorema Egregium, Theorem of Gauss-Bonnet. Hyperbolic space. Differentiable manifolds, immersions and embeddings, Sard's Theorem, mapping degree and intersection number, vector bundles, vector fields and flows, differential forms, Stokes' Theorem.

Introduction to Riemannian geometry in combination with some elements of modern metric geometry. Contents: Riemannian manifolds, Levi-Civita connection, geodesics, Hopf-Rinow Theorem, curvature, second fundamental form, Riemannian submersions and coverings, Hadamard-Cartan Theorem, triangle and volume comparison, relations between curvature and topology, spaces of Riemannian manifolds.

Selected topics from Riemannian geometry in the large, including the geometry of open (complete non-compact) Riemannian manifolds of non-negative sectional curvature and Perelman's proof of the Cheeger-Gromoll soul conjecture, as well as the Besson-Courtois-Gallot barycenter method and the proofs of the minimal entropy theorem and the Mostow rigidity theorem for rank one locally symmetric spaces.

Seminar for PhD students

Introduction to particle sources and accelerators.Theory of particle interaction with matter and signal formation.Basics and concepts of particle detectors.Momentum reconstruction, calorimetry and particle identification techniques.Simulation methods, readout electronics, trigger and data acquisition.Examples of key experiments.

The program covers theoretical and experimental aspects of flavorphysics. Topics include the Cabibbo-Kobayashi-Maskawa matrix,particle anti-particle mixing and CP violation in B and K mesondecays.Effective field theories and their application to rare B mesondecays are presented. Experimental aspects at B factories andhadron colliders are discussed.

Introduction to Geometric Measure Theory from a metric viewpoint. Contents: Lipschitz maps, differentiability, area and coarea formula, rectifiable sets, introduction to the (de Rham-Federer-Fleming) theory of currents, currents in metric spaces after Ambrosio-Kirchheim, normal currents, relation to BV functions, slicing, compactness theorem for integral currents and applications.

During semester breaks 6-12 students stay for 3 weeks at PSIand participate in a hands-on course on experimental particle physics, wherea small but real experiment is performed in common, includingdesign, construction, running and analysis.The exact date is determined by the PSI beam schedule.

No description available.