## Menny Akka Ginosar: Catalogue data in Autumn Semester 2019 |

Name | Dr. Menny Akka Ginosar |

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 | Lecturer |

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

Literature | K. Nipp, D. Stoffer, Lineare Algebra, VdF Hochschulverlag ETH G. Strang, Lineare Algebra, Springer | ||||

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: * Separation of variables * Fourier series * Fourier transform * Laplace transform Study of the wave equation and general hyperbolic problems using similar tools and the method of characteristics. 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. | ||||

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

Literature | 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/ | ||||

Prerequisites / Notice | Analysis I and II. In particular, knowing how to solve ordinary differential equations is an important prerequisite. | ||||

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 | ||||

406-0242-AAL | Analysis IIEnrolment 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 | M. Akka Ginosar | |

Abstract | Mathematical tools of an engineer | ||||

Objective | Mathematics as a tool to solve engineering problems, mathematical formulation of problems in science and engineering. Basic mathematical knowledge of an engineers. | ||||

Content | Multi variable calculus: gradient, directional derivative, chain rule, Taylor expansion, Lagrange multipliers. Multiple integrals: coordinate transformations, path integrals, integrals over surfaces, divergence theorem, applications in physics. Ordinary differential equations. | ||||

Literature | Textbooks in English: - J. Stewart: Multivariable Calculus, Thomson Brooks/Cole - V. I. Smirnov: A course of higher mathematics. Vol. II. Advanced calculus - W. L. Briggs, L. Cochran: Calculus: Early Transcendentals: International Edition, Pearson Education - M. Akveld, R. Sperb, Analysis II, vdf - L. Papula: Mathematik für Ingenieure 2, Vieweg Verlag | ||||

406-0243-AAL | Analysis I and IIEnrolment 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. | 14 credits | 30R | M. Akka Ginosar | |

Abstract | Mathematical tools for the engineer | ||||

Objective | Mathematics as a tool to solve engineering problems. Mathematical formulation of technical and scientific problems. Basic mathematical knowledge for engineers. | ||||

Content | Complex numbers. Calculus for functions of one variable with applications. Simple Mathematical models in engineering. Multi variable calculus: gradient, directional derivative, chain rule, Taylor expansion, Lagrange multipliers. Multiple integrals: coordinate transformations, path integrals, integrals over surfaces, divergence theorem, applications in physics. Ordinary differential equations. | ||||

Literature | Textbooks in English: - J. Stewart: Calculus, Cengage Learning, 2009, ISBN 978-0-538-73365-6. - J. Stewart: Multivariable Calculus, Thomson Brooks/Cole. - V. I. Smirnov: A course of higher mathematics. Vol. II. Advanced calculus. - W. L. Briggs, L. Cochran: Calculus: Early Transcendentals: International Edition, Pearson Education. ISBN 978-0-321-65193-8. Textbooks in German: - M. Akveld, R. Sperb: Analysis I, vdf - M. Akveld, R. Sperb: Analysis II, vdf - L. Papula: Mathematik für Ingenieure und Naturwissenschaftler, Vieweg Verlag - L. Papula: Mathematik für Ingenieure 2, Vieweg Verlag |