Search result: Catalogue data in Autumn Semester 2019
Mathematics Bachelor | ||||||
Compulsory Courses | ||||||
Examination Block I In Examination Block I either the course unit 402-2883-00L Physics III or the course unit 402-2203-01L Classical Mechanics must be chosen and registered for an examination. (Students may also enrol for the other of the two course units; within the ETH Bachelor's programme in mathematics, this other course unit cannot be registered in myStudies for an examination nor can it be recognised for the Bachelor's degree.) | ||||||
Number | Title | Type | ECTS | Hours | Lecturers | |
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401-2303-00L | Complex Analysis | O | 6 credits | 3V + 2U | P. Biran | |
Abstract | Complex functions of one variable, Cauchy-Riemann equations, Cauchy theorem and integral formula, singularities, residue theorem, index of closed curves, analytic continuation, special functions, conformal mappings, Riemann mapping theorem. | |||||
Objective | Working knowledge of functions of one complex variables; in particular applications of the residue theorem. | |||||
Literature | B. Palka: "An introduction to complex function theory." Undergraduate Texts in Mathematics. Springer-Verlag, 1991. E.M. Stein, R. Shakarchi: Complex Analysis. Princeton University Press, 2010 Th. Gamelin: Complex Analysis. Springer 2001 E. Titchmarsh: The Theory of Functions. Oxford University Press D. Salamon: "Funktionentheorie". Birkhauser, 2011. (In German) L. Ahlfors: "Complex analysis. An introduction to the theory of analytic functions of one complex variable." International Series in Pure and Applied Mathematics. McGraw-Hill Book Co. K.Jaenich: Funktionentheorie. Springer Verlag R.Remmert: Funktionentheorie I. Springer Verlag E.Hille: Analytic Function Theory. AMS Chelsea Publications | |||||
401-2333-00L | Methods of Mathematical Physics I | O | 6 credits | 3V + 2U | G. Felder | |
Abstract | Fourier series. Linear partial differential equations of mathematical physics. Fourier transform. Special functions and eigenfunction expansions. Distributions. Selected problems from quantum mechanics. | |||||
Objective | ||||||
402-2883-00L | Physics III | W | 7 credits | 4V + 2U | U. Keller | |
Abstract | Introductory course on quantum and atomic physics including optics and statistical physics. | |||||
Objective | A basic introduction to quantum and atomic physics, including basics of optics and equilibrium statistical physics. The course will focus on the relation of these topics to experimental methods and observations. | |||||
Content | Evidence for Quantum Mechanics: atoms, photons, photo-electric effect, Rutherford scattering, Compton scattering, de-Broglie waves. Quantum mechanics: wavefunctions, operators, Schrodinger's equation, infinite and finite square well potentials, harmonic oscillator, hydrogen atoms, spin. Atomic structure: Perturbation to basic structure, including Zeeman effect, spin-orbit coupling, many-electron atoms. X-ray spectra, optical selection rules, emission and absorption of radiation, including lasers. Optics: Fermat's principle, lenses, imaging systems, diffraction, interference, relation between geometrical and wave descriptions, interferometers, spectrometers. Statistical mechanics: probability distributions, micro and macrostates, Boltzmann distribution, ensembles, equipartition theorem, blackbody spectrum, including Planck distribution | |||||
Lecture notes | Lecture notes will be provided electronically during the course. | |||||
Literature | Quantum mechanics/Atomic physics/Molecules: "The Physics of Atoms and Quanta", H. Hakan and H. C. Wolf, ISBN 978-3-642-05871-4 Optics: "Optics", E. Hecht, ISBN 0-321-18878-0 Statistical mechanics: "Statistical Physics", F. Mandl 0-471-91532-7 | |||||
402-2203-01L | Classical Mechanics | W | 7 credits | 4V + 2U | M. Gaberdiel | |
Abstract | A conceptual introduction to theoretical physics: Newtonian mechanics, central force problem, oscillations, Lagrangian mechanics, symmetries and conservation laws, spinning top, relativistic space-time structure, particles in an electromagnetic field, Hamiltonian mechanics, canonical transformations, integrable systems, Hamilton-Jacobi equation. | |||||
Objective | Fundamental understanding of the description of Mechanics in the Lagrangian and Hamiltonian formulation. Detailed understanding of important applications, in particular, the Kepler problem, the physics of rigid bodies (spinning top) and of oscillatory systems. | |||||
252-0851-00L | Algorithms and Complexity | O | 4 credits | 2V + 1U | J. Lengler, A. Steger | |
Abstract | Introduction: RAM machine, data structures; Algorithms: sorting, median, matrix multiplication, shortest paths, minimal spanning trees; Paradigms: divide & conquer, dynamic programming, greedy algorithms; Data Structures: search trees, dictionaries, priority queues; Complexity Theory: P and NP, NP-completeness, Cook's theorem, reductions. | |||||
Objective | After this course students know some basic algorithms as well as underlying paradigms. They will be familiar with basic notions of complexity theory and can use them to classify problems. | |||||
Content | Die Vorlesung behandelt den Entwurf und die Analyse von Algorithmen und Datenstrukturen. Die zentralen Themengebiete sind: Sortieralgorithmen, Effiziente Datenstrukturen, Algorithmen für Graphen und Netzwerke, Paradigmen des Algorithmenentwurfs, Klassen P und NP, NP-Vollständigkeit, Approximationsalgorithmen. | |||||
Lecture notes | Ja. Wird zu Beginn des Semesters verteilt. |
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