# Vasile Catrinel Gradinaru: Catalogue data in Autumn Semester 2016

Name | Dr. Vasile Catrinel Gradinaru |

Address | Seminar für Angewandte Mathematik ETH Zürich, HG GO 52.2 Rämistrasse 101 8092 Zürich SWITZERLAND |

Telephone | +41 44 632 34 48 |

vasile.gradinaru@sam.math.ethz.ch | |

URL | http://www.sam.math.ethz.ch/~gvasile |

Department | Mathematics |

Relationship | Lecturer |

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

401-0141-00L | Linear Algebra and Numerical Analysis | 5 credits | 3V + 1U | V. C. Gradinaru, R. Käppeli | |

Abstract | Introduction to Linear Algebra and Numerical Analysis with emphasis on both abstract concepts and algorithms. | ||||

Objective | To acquire basic knowledge of Linear Algebra and Numerical Methods. Enhanced capability for abstract and algorithmic thinking based on mathematical concepts and models. Ability to select appropriate numerical linear algebra methods, to apply them properly and to implement them efficiently in MATLAB. | ||||

Content | 1. Linear systems of equations 2. Vector and matrix calculus 3. Subspaces and bases 4. The Euclidean space Rn 5. Numerical linear algebra with MATLAB 6. Linear mappings [optional] 7. Diagonalization (eigenproblems) | ||||

Lecture notes | Für weitere Informationen: http://www.sam.math.ethz.ch/~grsam/HS16/LABAUG/index.html | ||||

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

401-0151-00L | Linear Algebra | 4 credits | 3G + 2U | V. C. Gradinaru, R. Käppeli | |

Abstract | Contents: Linear systems - the Gaussian algorithm, matrices - LU decomposition, determinants, vector spaces, least squares - QR decomposition, linear maps, eigenvalue problem, normal forms - singular value decomposition; numerical aspects; introduction to MATLAB. | ||||

Objective | Einführung in die Lineare Algebra für Ingenieure unter Berücksichtigung numerischer Aspekte | ||||

Lecture notes | K. Nipp / D. Stoffer, Lineare Algebra, vdf Hochschulverlag, 5. Auflage 2002 | ||||

Literature | K. Nipp / D. Stoffer, Lineare Algebra, vdf Hochschulverlag, 5. Auflage 2002 | ||||

401-3667-66L | Case Studies Seminar (Autumn Semester 2016) | 3 credits | 2S | V. C. Gradinaru, R. Hiptmair, M. Reiher | |

Abstract | In the CSE Case Studies Seminar invited speakers from ETH, from other universities as well as from industry give a talk on an applied topic. Beside of attending the scientific talks students are asked to give short presentations (10 minutes) on a published paper out of a list. | ||||

Objective | |||||

406-0141-AAL | Linear Algebra and Numerical AnalysisEnrolment 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 | R. Käppeli, V. C. Gradinaru | |

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 | * Linear systems of equations: Gaussian elimination, row echelon form, theory abiut existence and uniqueness of solutions (Strang Ch. 2 and 3.4) * Mathematical modelling by linear systems (e.g. networks, trusses) (Strang, parts of Ch. 8) * Column space, null space and rank of matrices (Strang 3.2, 3.3) * linear combinations, linear (in)dependence, bases, dimension theorem for matrices (Strang 3.5, 3.6) * inner product, orthogonality, length in Euclidean space (Strang 4.1, 4.2) * Least squares solutions and orthogonalization (Gram-Schmidt and QR) (Strang 4.3, 4.4) * Linear mappings, matrix representation and change of basis (Strang Ch. 7) * Determinants and diagonalization of matrices (eigenvalues and eigenvectors) (Strang 6.1, 6.2, 6.5, 6.6) * Diagonalization applied to linear differential and difference equations. (Strang 6.3) * Numerical methods for solving linear systems of equations (Ascher/Greif 5.1, MATLAB Documentation of \) * Interpolation with polynomials and splines (Ascher/Greif Ch. 10 and 11) | ||||

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 |