# Search result: Catalogue data in Spring Semester 2021

Mathematics Bachelor | ||||||

First Year Compulsory Courses | ||||||

First Year Examination Block 2 | ||||||

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

401-1262-07L | Analysis II | O | 10 credits | 6V + 3U | G. Felder | |

Abstract | 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. | |||||

Objective | ||||||

Content | Calculus in several variables; curves and surfaces in R^n; extrema with constraints; integration in n dimensions; vector calculus. | |||||

Literature | H. Amann, J. Escher: Analysis II https://link.springer.com/book/10.1007/3-7643-7402-0 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/10.1007/978-3-642-61973-1 O. Forster: Analysis 2 https://link.springer.com/book/10.1007/978-3-658-02357-7 H. Heuser: Lehrbuch der Analysis https://link.springer.com/book/10.1007/978-3-322-96826-5 K. Königsberger: Analysis 2 https://link.springer.com/book/10.1007/3-540-35077-2 W. Walter: Analysis 2 https://link.springer.com/book/10.1007/978-3-642-97614-8 V. Zorich: Mathematical Analysis II (englisch) https://link.springer.com/book/10.1007/978-3-662-48993-2 | |||||

401-1152-02L | Linear Algebra II | O | 7 credits | 4V + 2U | M. Akka Ginosar | |

Abstract | Eigenvalues and eigenvectors, Jordan normal form, bilinear forms, euclidean and unitary vector spaces, selected applications. | |||||

Objective | Basic knowledge of the fundamentals of linear algebra. | |||||

Literature | Siehe Lineare Algebra I | |||||

Prerequisites / Notice | Linear Algebra I | |||||

401-1652-10L | Numerical Analysis I | O | 6 credits | 3V + 2U | C. Schwab | |

Abstract | This course will give an introduction to numerical methods, aimed at mathematics majors. It covers numerical linear algebra, quadrature, interpolation and approximation methods as well as their error analysis and implementation. | |||||

Objective | Knowledge of the fundamental numerical methods as well as `numerical literacy': application of numerical methods for the solution of application problems, mathematical foundations of numerical methods, and basic mathematical methods of the analysis of stability, consistency and convergence of numerical methods, MATLAB implementation. | |||||

Content | Rounding errors, solution of linear systems of equations, nonlinear equations, interpolation (polynomial as well as trigonometric), least squares problems, extrapolation, numerical quadrature, elementary optimization methods. | |||||

Lecture notes | Lecture Notes and reading list will be available. | |||||

Literature | Lecture Notes (german or english) will be made available to students of ETH BSc MATH. Quarteroni, Sacco and Saleri, Numerische Mathematik 1 + 2, Springer Verlag 2002 (in German). There is an English version of this text, containing both German volumes, from the same publisher. If you feel more comfortable with English, you can follow this text as well. Content and Indexing are identical in the German and the English text. | |||||

Prerequisites / Notice | Admission Requirements: Completed course Linear Algebra I, Analysis I in ETH BSc MATH Parallel enrolment in Linear Algebra II, Analysis II in ETH BSc MATH Weekly homework assignments involving MATLAB programming are an integral part of the course. Turn-in of solutions will be graded. | |||||

402-1782-00L | Physics II | O | 7 credits | 4V + 2U | R. Wallny | |

Abstract | Introduction to theory of waves, electricity and magnetism. This is the continuation of Physics I which introduced the fundamentals of mechanics. | |||||

Objective | basic knowledge of mechanics and electricity and magnetism as well as the capability to solve physics problems related to these subjects. |

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