# Search result: Catalogue data in Autumn Semester 2017

Interdisciplinary Sciences Bachelor | ||||||

Biochemical-Physical Direction | ||||||

1. Semester (Biochemical-Physical Direction) | ||||||

Compulsory Subjects First Year Examinations | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |
---|---|---|---|---|---|---|

551-0105-00L | Fundamentals of Biology IA | O | 5 credits | 5G | M. Aebi, E. Hafen, M. Peter | |

Abstract | The course provides an introduction to the basics of molecular- and cell biology and genetics. | |||||

Objective | Introduction to modern biology and to principal biological concepts. | |||||

Content | The course is divided into several chapters: 1. Basic principles of Evolution. 2. Chemistry of Life: Water; Carbon and molecular diversity; biomolecules 3. The cell: structure; membrane structure and function, cell cycle 4. Metabolism: Respiration; Photosynthesis; Fermentation 5. Inheritance: meiosis and sexual reproduction; Mendelian genetics, chromosomal basis of inheritance, molecular basis of inheritance, from gene to protein, regulation of gene expression; genomes and their evolution | |||||

Lecture notes | None. | |||||

Literature | The text-book "Biology" (Campbell, Reece) (10th edition) is the basis of the course. The structure of the course is largely identical with that of the text-book. | |||||

Prerequisites / Notice | Certain sections of the text-book must be studied by self-instruction. | |||||

401-0271-00L | Mathematical Foundations I: Analysis A | W | 5 credits | 3V + 2U | L. Kobel-Keller | |

Abstract | 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. | |||||

Objective | Introduction to calculus in one dimension. Building simple models and analysing them mathematically. | |||||

Content | 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. | |||||

Literature | G. B. Thomas, M. D. Weir, J. Hass: Analysis 1, Lehr- und Übungsbuch, Pearson-Verlag D. W. Jordan, P. Smith: Mathematische Methoden für die Praxis, Spektrum Akademischer Verlag R. Sperb/M. Akveld: Analysis I (vdf) L. Papula: Mathematik für Ingenieure und Naturwissenschaftler (3 Bände), Vieweg further reading suggestions will be indicated during the lecture | |||||

401-1261-07L | Analysis I | W | 10 credits | 6V + 3U | M. Einsiedler | |

Abstract | 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. | |||||

Objective | The ability to work with the basics of calculus in a mathematically rigorous way. | |||||

Literature | H. Amann, J. Escher: Analysis I https://link.springer.com/book/10.1007/978-3-7643-7756-4 J. Appell: Analysis in Beispielen und Gegenbeispielen https://link.springer.com/book/10.1007/978-3-540-88903-8 R. Courant: Vorlesungen über Differential- und Integralrechnung https://link.springer.com/book/10.1007/978-3-642-61988-5 O. Forster: Analysis 1 https://link.springer.com/book/10.1007/978-3-658-00317-3 H. Heuser: Lehrbuch der Analysis https://link.springer.com/book/10.1007/978-3-322-96828-9 K. Königsberger: Analysis 1 https://link.springer.com/book/10.1007/978-3-642-18490-1 W. Walter: Analysis 1 https://link.springer.com/book/10.1007/3-540-35078-0 V. Zorich: Mathematical Analysis I (englisch) https://link.springer.com/book/10.1007/978-3-662-48792-1 A. Beutelspacher: "Das ist o.B.d.A. trivial" https://link.springer.com/book/10.1007/978-3-8348-9599-8 H. Schichl, R. Steinbauer: Einführung in das mathematische Arbeiten https://link.springer.com/book/10.1007/978-3-642-28646-9 | |||||

401-0231-10L | Analysis I | W | 8 credits | 4V + 3U | T. H. Willwacher | |

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

Objective | Einfuehrung in die Grundlagen der Analysis | |||||

Lecture notes | Konrad Koenigsberger, Analysis I. Christian Blatter: Ingenieur-Analysis (Kapitel 1-3) | |||||

529-0001-00L | Introduction to Computer Science | O | 4 credits | 2V + 2U | P. H. Hünenberger | |

Abstract | Introduction to UNIX, data representation, introduction to C++ programming, errors, algorithms, computer architecture, sorting and searching, databases, numerical algorithms, types of algorithms, simulation, data communication & networks, chemical structures, operating systems, programming languages, software engineering. | |||||

Objective | Discuss fundamentals of computer architecture, languages, algorithms and programming with an eye to their application in the area of chemistry, biology and material science. | |||||

Content | Minimal introduction to UNIX, Data representation and processing, algorithms and programming in C++, Errors, programming guidelines, efficiency, computer architecture, algorithms for sorting and searching, databases, numerical algorithms, types of algorithms, simulation, data communication & networks, chemical structures, operating systems, programming languages, style, software engineering. | |||||

Lecture notes | Available (in English), distributed at first lecture | |||||

Literature | See: www.csms.ethz.ch/education/InfoI | |||||

Prerequisites / Notice | Since the exercises on the computer do convey and test essentially different skills as those being conveyed during the lectures and tested at the written exam, the results of the exercises are taken into account when evaluating the results of the exam. For more information about the lecture: www.csms.ethz.ch/education/InfoI | |||||

529-0011-02L | General Chemistry (Inorganic Chemistry) I | O | 3 credits | 2V + 1U | A. Togni | |

Abstract | Introduction to the chemistry of ionic equilibria: Acids and bases, redox reactions, formation of coordination complexes and precipitation reactions | |||||

Objective | Understanding and describing ionic equilibria from both a qualitative and a quantitative perspective | |||||

Content | Chemical equilibrium and equilibrium constants, mono- and polyprotic acids and bases in aqueous solution, calculation of equilibrium concentrations, acidity functions, Lewis acids, acids in non-aqueous solvents, redox reactions and equilibria, Galvanic cells, electrode potentials, Nernst equation, coordination chemistry, stepwise formation of metal complexes, solubility | |||||

Lecture notes | Copies of the course slides as well as other documents will be provided as pdf files via the moodle platform. | |||||

Literature | C. E. Housecroft & E. C. Constable: Chemistry, An Introduction to Organic, Inorganic and Physical Chemistry, 4th Edition, Prentice Hall / Pearson, 2010, ISBN 978-0-273-71545-0 | |||||

529-0011-03L | General Chemistry (Organic Chemistry) I | O | 3 credits | 2V + 1U | H. Wennemers | |

Abstract | Introduction to Organic Chemistry. Classical structure theory, stereochemistry, chemical bonds and bonding, symmetry, nomenclature, organic thermochemistry, conformational analysis, basics of chemical reactions. | |||||

Objective | Introduction to the structures of organic compounds as well as the structural and energetic basis of organic chemistry. | |||||

Content | Introduction to the history of organic chemistry, introduction to nomenclature, learning of classical structures and stereochemistry: isomerism, Fischer projections, CIP rules, point groups, molecular symmetry and chirality, topicity, chemical bonding: Lewis bonding model and resonance theory in organic chemistry, description of linear and cyclic conjugated molecules, aromaticity, Huckel rules, organic thermochemistry, learning of organic chemistry reactions, intermolecular interactions. | |||||

Lecture notes | Unterlagen werden als PDF über die ILIAS-Plattform zur Verfügung gestellt | |||||

Literature | C. E. Housecroft & E. C. Constable: Chemistry, An Introduction to Organic, Inorganic and Physical Chemistry, 4th Edition, Prentice Hall / Pearson, 2010, ISBN 978-0-273-71545-0 | |||||

529-0011-01L | General Chemistry (Physical Chemistry) I | O | 3 credits | 2V + 1U | H. J. Wörner | |

Abstract | Atomic structure and structure of matter; Atomic orbitals and energy levels; Quantum mechanical atom model; Chemical bonding; Equations of state. | |||||

Objective | Introduction to Physical Chemistry | |||||

Content | Atomic structure and structure of matter: atomic theory, elementary particles, atomic nuclei, radioactivity, nuclear reactions. Atomic orbitals and energy levels: ionisation energies, atomic spectroscopy, term values and symbols. Quantum mechanical atom model: wave-particle duality, the uncertainty principle, Schrödinger's equation, the hydrogen atom, construction of the periodic table of the elements. Chemical bonding: ionic bonding, covalent bonding, molecular orbitals. Equations of state: ideal gases | |||||

Lecture notes | See homepage of the lecture. | |||||

Literature | See homepage of the lecture. | |||||

Prerequisites / Notice | Voraussetzungen: Maturastoff. Insbesondere Integral- und Differentialrechnung. | |||||

Additional First Year Compulsory Subjects | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

529-0011-04L | Practical Course General Chemistry Latest online enrolment is 18 September 2017. Information about the practical course will be given on the first day. | O | 8 credits | 12P | H. V. Schönberg, E. C. Meister | |

Abstract | Qualitative analysis (determination of cations and anions), acid-base-equilibria (pH- values, titrations, buffer), precipitation equilibria (gravimetry, potentiometry, conductivity), redoxreactions (syntheses, redox-titrations, galvanic elements), metal complexes (syntheses, complexometric titration) analysis of measured values, states of aggregation (vapour pressure, conductivity, calorimetry) | |||||

Objective | Qualitative analysis (simple cation and anion separation process, determination of cations and anions), acid-base-equilibria (strengths of acids and bases, pH- and pKa-values, titrations, buffer systems, Kjeldahl determination), precipitation equilibria (gravimetry, potentiometry, conductivity), oxidation state and redox behaviour (syntheses), redox-titrations, galvanic elements), metal complexes (syntheses of complexes, ligand exchange reactions, complexometric titration) analysis of measured values (measuring error, average value, error analysis), states of aggregation (vapour pressure), characteristics of electrolytes (conductivity measurements), thermodynamics (calorimetry) | |||||

Content | The general aim for the students of the practical course in general chemistry is an introduction in the scientific work and to get familiar with simple experimental procedures in a chemical laboratory. In general, first experiences with the principal reaction behaviour of a variety of different substances will be made. The chemical characteristics of these will be elucidated by a series of quantitative experiments alongside with the corresponding qualitative analyses. In order to get an overview of classes of substances as well as some general phenomena in chemistry suitable experiments have been chosen. In the second part of the practical course, i.e. physical chemistry, the behaviour of substances in their states of aggregation as well as changes of selected physical values will be recorded and discussed. | |||||

Lecture notes | http://www.gruetzmacher.ethz.ch/education/labcourses | |||||

Prerequisites / Notice | Compulsory: online enrolment latest one week after start of the semester | |||||

3. Semester (Biochemical-Physical Direction) | ||||||

Compulsory Subjects Examination Block | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

401-0373-00L | Mathematics III: Partial Differential Equations | W | 4 credits | 2V + 1U | F. Da Lio | |

Abstract | Examples of partial differential equations. Linear partial differential equations. Introduction to Separation of Variables method. Fourier Series, Fourier Transform, Laplace Transform and applications to the resolution to some partial differential equations (Laplace Equation, Heat Equation, Wave Equation). | |||||

Objective | The main objective is that the students get a basic knowledge of the classical tools to solve explicitly linear partial differential equations. | |||||

Content | ## Examples of partial differential equations - Classification of PDEs - Superposition principle ## One-dimensional wave equation - D'Alembert's formula - Duhamel's principle ## Fourier series - Representation of piecewise continuous functions via Fourier series - Examples and applications ## Separation of variables - Resolution of wave and heat equation - Homogeneous and inhomogeneous boundary conditions, Dirichlet and Neumann boundary conditions ## Laplace equation - Resolution of the Laplace equation on rectangle, disk and annulus - Poisson formula - Mean value theorem and maximum principle ## Fourier transform - Derivation and Definition - Inverse Fourier transformation and inversion formula - Interpretation and properties of the Fourier transform - Resolution of the heat equation ## Laplace transform - Definition, motivation and properties - Inverse Laplace transform of rational functions - Application to ordinary differential equations | |||||

Lecture notes | There are available some Lecture Notes in English and also in German of the Professor. These can be found following the links provided under the tab 'Lernmaterialien'. The Professor will use also the following book: S.J. Farlow, Partial Differential Equations for Scientists and Engineers, Dover Books on Mathematics, NY. | |||||

Literature | 1) N. Hungerbühler, Einführung in partielle Differentialgleichungen für Ingenieure, Chemiker und Naturwissenschaftler, vdf Hochschulverlag, 1997. 2) S.J. Farlow, Partial Differential Equations for Scientists and Engineers, Dover Books on Mathematics, NY. 3) E. Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons (only Chapters 1,2,6,11) 4) T. Westermann: Partielle Differentialgleichungen, Mathematik für Ingenieure mit Maple, Springer-Lehrbuch 1997. | |||||

Prerequisites / Notice | It is required a minimal background of: 1) multivariables functions (Riemann integrals in two or three variables, change of variables in the integrals through the Jacobian, partial derivatives, differentiability, Jacobian) 2) numerical and functional sequences and series, basic knowledge of ordinary differential equations. | |||||

401-0353-00L | Analysis III | W | 4 credits | 2V + 1U | A. Figalli | |

Abstract | In this lecture we treat problems in applied analysis. The focus lies on the simplest cases of three fundamental types of partial differential equations of second order: the Laplace equation, the heat equation and the wave equation. | |||||

Objective | ||||||

Content | 1.) Klassifizierung von PDE's - linear, quasilinear, nicht-linear - elliptisch, parabolisch, hyperbolisch 2.) Quasilineare PDE - Methode der Charakteristiken (Beispiele) 3.) Elliptische PDE - Bsp: Laplace-Gleichung - Harmonische Funktionen, Maximumsprinzip, Mittelwerts-Formel. - Methode der Variablenseparation. 4.) Parabolische PDE - Bsp: Wärmeleitungsgleichung - Bsp: Inverse Wärmeleitungsgleichung - Methode der Variablenseparation 5.) Hyperbolische PDE - Bsp: Wellengleichung - Formel von d'Alembert in (1+1)-Dimensionen - Methode der Variablenseparation 6.) Green'sche Funktionen - Rechnen mit der Dirac-Deltafunktion - Idee der Green'schen Funktionen (Beispiele) 7.) Ausblick auf numerische Methoden - 5-Punkt-Diskretisierung des Laplace-Operators (Beispiele) | |||||

Literature | Y. Pinchover, J. Rubinstein, "An Introduction to Partial Differential Equations", Cambridge University Press (12. Mai 2005) Zusätzliche Literatur: Erwin Kreyszig, "Advanced Engineering Mathematics", John Wiley & Sons, Kap. 8, 11, 16 (sehr gutes Buch, als Referenz zu benutzen) Norbert Hungerbühler, "Einführung in die partiellen Differentialgleichungen", vdf Hochschulverlag AG an der ETH Zürich. G. Felder:Partielle Differenzialgleichungen. https://people.math.ethz.ch/~felder/PDG/ | |||||

Prerequisites / Notice | Prerequisites: Analysis I and II, Fourier series (Komplexe Analysis) | |||||

402-0043-00L | Physics I | W | 4 credits | 3V + 1U | T. Esslinger | |

Abstract | Introduction to the concepts and tools in physics with the help of demonstration experiments: mechanics of point-like and ridged bodies, periodic motion and mechanical waves. | |||||

Objective | The concepts and tools in physics, as well as the methods of an experimental science are taught. The student should learn to identify, communicate and solve physical problems in his/her own field of science. | |||||

Content | Mechanics (motion, Newton's laws, work and energy, conservation of momentum, rotation, gravitation, fluids) Periodic Motion and Waves (periodic motion, mechanical waves, acoustics). | |||||

Lecture notes | The lecture follows the book "Physics" by Paul A. Tipler. | |||||

Literature | Paul A. Tipler and Gene P. Mosca, Physics (for Scientists and Engineers), W. H. Freeman and Company | |||||

Prerequisites / Notice | Prerequisites: Mathematics I & II | |||||

402-1701-00L | Physics I | W | 7 credits | 4V + 2U | A. Wallraff | |

Abstract | This course gives a first introduction to Physics with an emphasis on classical mechanics. | |||||

Objective | Acquire knowledge of the basic principles regarding the physics of classical mechanics. Skills in solving physics problems. | |||||

529-0422-00L | Physical Chemistry II: Introduction to Chemical Reaction Kinetics | O | 4 credits | 3V + 1U | F. Merkt | |

Abstract | Introduction to Chemical Reaction Kinetics. Fundamental concepts: rate laws, elementary reactions and composite reactions, molecularity, reaction order. Experimental methods in reaction kinetics. Simple chemical reaction rate theories. Reaction mechanisms and complex kinetic systems, approximation techniques, chain reactions, explosions and detonations. Homogeneous catalysis and enzyme kinetics. | |||||

Objective | Introduction to Chemical Reaction Kinetics | |||||

Content | Fundamental concepts: rate laws, elementary reactions and composite reactions, molecularity, reaction order. Experimental methods in reaction kinetics up to new developments in femtosecond kinetics. Simple chemical reaction rate theories: temperature dependence of the rate constant and Arrhenius equation, collision theory, reaction cross-section, transition state theory. Reaction mechanisms and complex kinetic systems, approximation techniques, chain reactions, explosions and detonations. Homogeneous catalysis and enzyme kinetics. Kinetics of charged particles. Diffusion and diffusion-controlled reactions. Photochemical kinetics. Heterogeneous reactions and heterogeneous catalysis. | |||||

Literature | - M. Quack und S. Jans-Bürli: Molekulare Thermodynamik und Kinetik, Teil 1, Chemische Reaktionskinetik, VdF, Zürich, 1986. - G. Wedler: Lehrbuch der Physikalischen Chemie, Verlag Chemie, Weinheim, 1982. | |||||

Prerequisites / Notice | Voraussetzungen: - Mathematik I und II - Allgemeine Chemie I und II - Physikalische Chemie I | |||||

529-0221-00L | Organic Chemistry I | O | 3 credits | 2V + 1U | E. M. Carreira, J. W. Bode | |

Abstract | Chemical reactivity and classes of compounds. Eliminations, fragmentations, chemistry of aldehydes and ketones (hydrates, acetals, imines, enamines, nucleophilic addition of organometallic compounds, reactions with phosphorus and sulfur ylides; reactions of enolates as nucleophiles) and of carboxylic acid derivatives. Aldol reactions. | |||||

Objective | Acquisition of a basic repertoire of synthetic methods including important reactions of aldehydes, ketones, carboxylic acids and carboxylic acid derivatives, as well as eliminations and fragmentations. Particular emphasis is placed on the understanding of reaction mechanisms and the correlation between structure and reactivity. A deeper understanding of the concepts presented during the lecture is reached by solving the problems handed out each time and discussed one week later in the exercise class. | |||||

Content | Chemical reactivity and classes of compounds. Eliminations, fragmentations, chemistry of aldehydes and ketones (hydrates, acetals, imines, enamines, nucleophilic addition of organometallic compounds, reactions with phosphorus and sulfur ylides; reactions of enolates as nucleophiles) and of carboxylic acid derivatives. Aldol reactions. | |||||

Lecture notes | A pdf file of the printed lecture notes is provided online. Supplementary material may be provided online. | |||||

Literature | No set textbooks. Optional literature will be proposed at the beginning of the class and in the lecture notes. | |||||

Electives For the Bachelor in Interdisciplinary Sciences students can in principle choose from all subjects taught at the Bachelor level at ETH Zurich. At the beginning of the 2. year an individual study programme is established for every student in discussion with the Director of Studies in interdisciplinary sciences. For details see Programme Regulations 2010. | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

252-0027-00L | Introduction to Programming | W | 7 credits | 4V + 2U | T. Gross | |

Abstract | Introduction to fundamental concepts of modern programming and operational skills for developing high-quality programs, including large programs as in industry. The course introduces software engineering principles with an object-oriented approach based. | |||||

Objective | Many people can write programs. The "Introduction to Programming" course goes beyond that basic goal: it teaches the fundamental concepts and skills necessary to perform programming at a professional level. As a result of successfully completing the course, students master the fundamental control structures, data structures, reasoning patterns and programming language mechanisms characterizing modern programming, as well as the fundamental rules of producing high-quality software. They have the necessary programming background for later courses introducing programming skills in specialized application areas. | |||||

Content | Basics of object-oriented programming. Objects and classes. Pre- and postconditions, class invariants, Design by Contract. Fundamental control structures. Assignment and References. Basic hardware concepts. Fundamental data structures and algorithms. Recursion. Inheritance and interfaces, introduction to event-driven design and concurrent programming. Basic concepts of Software Engineering such as the software process, specification and documentation, reuse and quality assurance. | |||||

Lecture notes | The lecture slides are available for download on the course page. | |||||

Literature | See the course page for up-to-date information. | |||||

Prerequisites / Notice | There are no special prerequisites. Students are expected to enroll in the other courses offered to first-year students of computer science. | |||||

252-0847-00L | Computer Science | W | 5 credits | 2V + 2U | B. Gärtner | |

Abstract | This lecture is an introduction to programming based on the language C++. We cover fundamental types, control statements, functions, arrays, and classes. The concepts will be motivated and illustrated through algorithms and applications. | |||||

Objective | The goal of this lecture is an algorithmically oriented introduction to programming. | |||||

Content | This lecture is an introduction to programming based on the language C++. We cover fundamental types, control statements, functions, arrays, and classes. The concepts will be motivated and illustrated through algorithms and applications. | |||||

Lecture notes | Lecture notes in English and Handouts in German will be distributed electronically along with the course. | |||||

Literature | Andrew Koenig and Barbara E. Moo: Accelerated C++, Addison-Wesley, 2000. Stanley B. Lippman: C++ Primer, 3. Auflage, Addison-Wesley, 1998. Bjarne Stroustrup: The C++ Programming Language, 3. Auflage, Addison-Wesley, 1997. Doina Logofatu: Algorithmen und Problemlösungen mit C++, Vieweg, 2006. Walter Savitch: Problem Solving with C++, Eighth Edition, Pearson, 2012 | |||||

401-0373-00L | Mathematics III: Partial Differential Equations | W | 4 credits | 2V + 1U | F. Da Lio | |

Abstract | Examples of partial differential equations. Linear partial differential equations. Introduction to Separation of Variables method. Fourier Series, Fourier Transform, Laplace Transform and applications to the resolution to some partial differential equations (Laplace Equation, Heat Equation, Wave Equation). | |||||

Objective | The main objective is that the students get a basic knowledge of the classical tools to solve explicitly linear partial differential equations. | |||||

Content | ## Examples of partial differential equations - Classification of PDEs - Superposition principle ## One-dimensional wave equation - D'Alembert's formula - Duhamel's principle ## Fourier series - Representation of piecewise continuous functions via Fourier series - Examples and applications ## Separation of variables - Resolution of wave and heat equation - Homogeneous and inhomogeneous boundary conditions, Dirichlet and Neumann boundary conditions ## Laplace equation - Resolution of the Laplace equation on rectangle, disk and annulus - Poisson formula - Mean value theorem and maximum principle ## Fourier transform - Derivation and Definition - Inverse Fourier transformation and inversion formula - Interpretation and properties of the Fourier transform - Resolution of the heat equation ## Laplace transform - Definition, motivation and properties - Inverse Laplace transform of rational functions - Application to ordinary differential equations | |||||

Lecture notes | There are available some Lecture Notes in English and also in German of the Professor. These can be found following the links provided under the tab 'Lernmaterialien'. The Professor will use also the following book: S.J. Farlow, Partial Differential Equations for Scientists and Engineers, Dover Books on Mathematics, NY. | |||||

Literature | 1) N. Hungerbühler, Einführung in partielle Differentialgleichungen für Ingenieure, Chemiker und Naturwissenschaftler, vdf Hochschulverlag, 1997. 2) S.J. Farlow, Partial Differential Equations for Scientists and Engineers, Dover Books on Mathematics, NY. 3) E. Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons (only Chapters 1,2,6,11) 4) T. Westermann: Partielle Differentialgleichungen, Mathematik für Ingenieure mit Maple, Springer-Lehrbuch 1997. | |||||

Prerequisites / Notice | It is required a minimal background of: 1) multivariables functions (Riemann integrals in two or three variables, change of variables in the integrals through the Jacobian, partial derivatives, differentiability, Jacobian) 2) numerical and functional sequences and series, basic knowledge of ordinary differential equations. | |||||

401-1151-00L | Linear Algebra I | W | 7 credits | 4V + 2U | M. Akveld | |

Abstract | Introduction to the theory of vector spaces for mathematicians and physicists: Basics, vector spaces, linear transformations, solutions of systems of equations and matrices, determinants, endomorphisms, eigenvalues and eigenvectors. | |||||

Objective | - Mastering basic concepts of Linear Algebra - Introduction to mathematical methods | |||||

Content | - Basics - Vectorspaces and linear maps - Systems of linear equations and matrices - Determinants - Endomorphisms and eigenvalues | |||||

Literature | - H. Schichl and R. Steinbauer: Einführung in das mathematische Arbeiten. Springer-Verlag 2012. Link: http://link.springer.com/book/10.1007%2F978-3-642-28646-9 - G. Fischer: Lineare Algebra. Springer-Verlag 2014. Link: http://link.springer.com/book/10.1007/978-3-658-03945-5 - K. Jänich: Lineare Algebra. Springer-Verlag 2004. Link: http://link.springer.com/book/10.1007/978-3-662-08375-8 - S. H. Friedberg, A. J. Insel and L. E. Spence: Linear Algebra. Pearson 2003. Link - R. Pink: Lineare Algebra I und II. Lecture notes. Link: https://people.math.ethz.ch/%7epink/ftp/LA-Zusammenfassung-20150901.pdf | |||||

401-2303-00L | Complex Analysis | W | 6 credits | 3V + 2U | R. Pandharipande | |

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 with functions of one complex variables; in particular applications of the residue theorem | |||||

Literature | 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. B. Palka: "An introduction to complex function theory." Undergraduate Texts in Mathematics. Springer-Verlag, 1991. R.Remmert: Theory of Complex Functions. Springer Verlag |

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