Name | Prof. Dr. Ana Cannas da Silva |

Address | Dep. Mathematik ETH Zürich, HG G 27.4 Rämistrasse 101 8092 Zürich SWITZERLAND |

Telephone | +41 44 632 85 90 |

ana.cannas@math.ethz.ch | |

URL | http://www.math.ethz.ch/~acannas |

Department | Mathematics |

Relationship | Adjunct Professor |

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

401-0131-00L | Linear Algebra | 7 credits | 4V + 2U | A. Cannas da Silva, O. Sorkine Hornung | |

Abstract | Introduction to linear algebra (vector spaces, linear transformations, matrices), inner product, determinants, matrix decompositions (LU, QR, eigenvalue and singular value decomposition). | ||||

Learning objective | - Understand and apply fundamental concepts of linear algebra - Learn about applications of linear algebra | ||||

Content | Linear Algebra: Linear systems of equations, vectors and matrices, norms and scalar products, LU decomposition, vector spaces and linear transformations, least squares problems, QR decomposition, determinants, eigenvalues and eigenvectors, singular value decomposition, applications. | ||||

Lecture notes | Extracts from the lecture notes "Lineare Algebra" (by Gutknecht) in German, with English expressions for all technical terms. | ||||

Literature | Recommendations on the course website | ||||

Prerequisites / Notice | The relevant high school material is reviewed briefly at the beginning. | ||||

401-0261-G0L | Analysis I | 8 credits | 5V + 3U | A. Cannas da Silva, U. Lang | |

Abstract | 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. | ||||

Learning objective | Introduction to the mathematical foundations of engineering sciences, as far as concerning differential and integral calculus. | ||||

Lecture notes | U. Stammbach: Analysis I/II | ||||

Prerequisites / Notice | The exercises and online quizzes are an integral part of this course. | ||||

401-5580-00L | Symplectic Geometry Seminar | 0 credits | 2K | P. Biran, A. Cannas da Silva | |

Abstract | Research colloquium | ||||

Learning objective | |||||

406-0252-AAL | Mathematics II Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement. Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit. | 7 credits | 15R | A. Cannas da Silva | |

Abstract | Continuation of the topics of Mathematics I. Main focus: multivariable calculus and partial differential equations. | ||||

Learning objective | Mathematics is of ever increasing importance to the Natural Sciences and Engineering. The key is the so-called mathematical modelling cycle, i.e. the translation of problems from outside of mathematics into mathematics, the study of the mathematical problems (often with the help of high level mathematical software packages) and the interpretation of the results in the original environment. The goal of Mathematics I and II is to provide the mathematical foundations relevant for this paradigm. Differential equations are by far the most important tool for modelling and are therefore a main focus of both of these courses. | ||||

Content | - Multivariable Differential Calculus: functions of several variables, partial differentiation, curves and surfaces in space, scalar and vector fields, gradient, curl and divergence. - Multivariable Integral Calculus: multiple integrals, line and surface integrals, work and flux, Green, Gauss and Stokes theorems, applications. - Partial Differential Equations: separation of variables, Fourier series, heat equation, wave equation, Laplace equation, Fourier transform. | ||||

Literature | - Thomas, G. B.: Thomas' Calculus, Parts 2 (Pearson Addison-Wesley). - Kreyszig, E.: Advanced Engineering Mathematics (John Wiley & Sons). | ||||

406-0253-AAL | Mathematics I & II Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement. Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit. | 13 credits | 28R | A. Cannas da Silva | |

Abstract | Mathematics I covers mathematical concepts and techniques necessary to model, solve and discuss scientific problems - notably through ordinary differential equations. Main focus of Mathematics II: multivariable calculus and partial differential equations. | ||||

Learning objective | Mathematics is of ever increasing importance to the Natural Sciences and Engineering. The key is the so-called mathematical modelling cycle, i.e. the translation of problems from outside of mathematics into mathematics, the study of the mathematical problems (often with the help of high level mathematical software packages) and the interpretation of the results in the original environment. The goal of Mathematics I and II is to provide the mathematical foundations relevant for this paradigm. Differential equations are by far the most important tool for modelling and are therefore a main focus of both of these courses. | ||||

Content | 1. Linear Algebra and Complex Numbers: systems of linear equations, Gauss-Jordan elimination, matrices, determinants, eigenvalues and eigenvectors, cartesian and polar forms for complex numbers, complex powers, complex roots, fundamental theorem of algebra. 2. Single-Variable Calculus: review of differentiation, linearisation, Taylor polynomials, maxima and minima, antiderivative, fundamental theorem of calculus, integration methods, improper integrals. 3. Ordinary Differential Equations: separable ordinary differential equations (ODEs), integration by substitution, 1st and 2nd order linear ODEs, homogeneous systems of linear ODEs with constant coefficients, introduction to 2-dimensional dynamical systems. 4. Multivariable Differential Calculus: functions of several variables, partial differentiation, curves and surfaces in space, scalar and vector fields, gradient, curl and divergence. 5. Multivariable Integral Calculus: multiple integrals, line and surface integrals, work and flow, Green, Gauss and Stokes theorems, applications. 6. Partial Differential Equations: separation of variables, Fourier series, heat equation, wave equation, Laplace equation, Fourier transform. | ||||

Literature | - Bretscher, O.: Linear Algebra with Applications (Pearson Prentice Hall). - Thomas, G. B.: Thomas' Calculus, Part 1 - Early Transcendentals (Pearson Addison-Wesley). - Thomas, G. B.: Thomas' Calculus, Parts 2 (Pearson Addison-Wesley). - Kreyszig, E.: Advanced Engineering Mathematics (John Wiley & Sons). | ||||

Prerequisites / Notice | Prerequisites: familiarity with the basic notions from Calculus, in particular those of function and derivative. Assistance: Tuesdays and Wednesdays 17-19h, in Room HG E 41. |