## Menny Akka Ginosar: Catalogue data in Autumn Semester 2021 |

Name | PD Dr. Menny Akka Ginosar |

Field | Dynamic systems |

Address | Professur für Mathematik ETH Zürich, HG J 67 Rämistrasse 101 8092 Zürich SWITZERLAND |

Telephone | +41 44 632 70 24 |

menny.akka@math.ethz.ch | |

URL | https://people.math.ethz.ch/~menashea/ |

Department | Mathematics |

Relationship | Privatdozent |

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

401-0141-00L | Linear Algebra | 5 credits | 3V + 1U | M. Akka Ginosar | |

Abstract | Introduction to Linear Algebra | ||||

Objective | Basic knowledge of linear algebra as a tool for solving engineering problems. Understanding of abstract mathematical formulation of technical and scientific problems. Together with Analysis we develop the basic mathematical knowledge for an engineer. | ||||

Content | Introduction and linear systems of equations, matrices, quadratic matrices, determinants and traces, general vector spaces, linear mappings, bases, change of basis, diagonalization, eigenvalues and eigenvectors, orthogonal transformations, scalar-product, inner product spaces. Calculation with MATLAB will be introduced in the first exercise class. | ||||

Lecture notes | The lecturer will provide course notes. | ||||

Literature | K. Nipp, D. Stoffer, Lineare Algebra, VdF Hochschulverlag ETH G. Strang, Lineare Algebra, Springer Larson, Ron. Elementary linear algebra. Nelson Education, 2016. (Englisch) | ||||

401-0243-00L | Analysis III | 3 credits | 2V + 1U | M. Akka Ginosar | |

Abstract | We will model and solve scientific problems with partial differential equations. Differential equations which are important in applications will be classified and solved. Elliptic, parabolic and hyperbolic differential equations will be treated. The following mathematical tools will be introduced: Laplace and Fourier transforms, Fourier series, separation of variables, methods of characteristics. | ||||

Objective | Learning to model scientific problems using partial differential equations and developing a good command of the mathematical methods that can be applied to them. Knowing the formulation of important problems in science and engineering with a view toward civil engineering (when possible). Understanding the properties of the different types of partial differential equations arising in science and in engineering. | ||||

Content | Classification of partial differential equations Study of the Heat equation general diffusion/parabolic problems using the following tools through Separation of variables as an introduction to Fourier Series. Systematic treatment of the complex and real Fourier Series Study of the wave equation and general hyperbolic problems using Fourier Series, D'Alembert solution and the method of characteristics. Laplace transform and it's uses to differential equations Study of the Laplace equation and general elliptic problems using similar tools and generalizations of Fourier series. Application of Laplace transform for beam theory will be discussed. Time permitting, we will introduce the Fourier transform. | ||||

Lecture notes | Lecture notes will be provided | ||||

Literature | large part of the material follow certain chapters of the following first two books quite closely. S.J. Farlow: Partial Differential Equations for Scientists and Engineers, (Dover Books on Mathematics), 1993 E. Kreyszig: Advanced Engineering Mathematics, John Wiley & Sons, 10. Auflage, 2001 The course material is taken from the following sources: Stanley J. Farlow - Partial Differential Equations for Scientists and Engineers G. Felder: Partielle Differenzialgleichungen. https://people.math.ethz.ch/~felder/PDG/ Y. Pinchover and J. Rubinstein: An Introduction to Partial Differential Equations, Cambridge University Press, 2005 C.R. Wylie and L. Barrett: Advanced Engineering Mathematics, McGraw-Hill, 6th ed, 1995 | ||||

Prerequisites / Notice | Analysis I and II, insbesondere, gewöhnliche Differentialgleichungen. | ||||

401-5370-00L | Ergodic Theory and Dynamical Systems | 0 credits | 1K | M. Akka Ginosar, M. Einsiedler, University lecturers | |

Abstract | Research colloquium | ||||

Objective | |||||

406-0141-AAL | Linear AlgebraEnrolment 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. | 5 credits | 11R | M. Akka Ginosar | |

Abstract | Introduction to Linear Algebra and Numerical Analysis for Engineers. This reading course is based on chapters from the book "Introduction to Linear Algebra" by Gilbert Strang (SIAM 2009), and "A first Course in Numerical Methods" by U. Ascher and C. Greif (SIAM, 2011). | ||||

Objective | To acquire basic knowledge of Linear Algebra and some aspects of related numerical metjhods and the ability to apply basic algorithms to simple problems. | ||||

Content | 1 Introduction, calculations using MATLAB 2 Linear systems I 3 Linear systems II 4 Scalar- & vektorproduct 5 Basics of matrix algebra 6 Linear maps 7 Orthogonal maps 8 Trace & determinant 9 General vectorspaces 10 Metric & scalarproducts 11 Basis, basistransform & similar matrices 12 Eigenvalues & eigenvectors 13 Spectral theorem & diagonalisation 14 Repetition | ||||

Literature | Gilbert Strang, Introduction to Linear Algebra, 4th ed., SIAM & Wellesley-Cambridge Press, 2009. U. Ascher and C. Greif, A first Course in Numerical Methods", SIAM, 2011. | ||||

Prerequisites / Notice | Knowledge of elementary calculus |