# Search result: Catalogue data in Autumn Semester 2020

Mechanical Engineering Master | ||||||

Master's Thesis | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |
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151-1001-00L | Master's Thesis Mechanical Engineering Students who fulfill the following criteria are allowed to begin with their Master's Thesis: a. successful completion of the bachelor program; b. fulfilling of any additional requirements necessary to gain admission to the master programme; c. successful completion of the semester project and industrial internship; d. achievement of 28 ECTS in the category "Core Courses". The Master's Thesis must be approved in advance by the tutor and is supervised by a professor of ETH Zurich. To choose a titular professor as a supervisor, please contact the D-MAVT Student Administration. | O | 30 credits | 64D | Professors | |

Abstract | Master's programs are concluded by the master's thesis. The thesis is aimed at enhancing the student's capability to work independently toward the solution of a theoretical or applied problem. The subject of the master's thesis, as well as the project plan and roadmap, are proposed by the tutor and further elaborated with the student. | |||||

Objective | The thesis is aimed at enhancing the student's capability to work independently toward the solution of a theoretical or applied problem. | |||||

Course Units for Additional Admission Requirements The courses below are only available for MSc students with additional admission requirements. | ||||||

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

406-0173-AAL | Linear Algebra 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. | E- | 6 credits | 13R | N. Hungerbühler | |

Abstract | Linear algebra is an indispensable tool of engineering mathematics. The course is an introduction to basic methods and fundamental concepts of linear algebra and its applications to engineering sciences. | |||||

Objective | After completion of this course, students are able to recognize linear structures and to apply adequate tools from linear algebra in order to solve corresponding problems from theory and applications. In addition, students have a basic knowledge of the software package Matlab. | |||||

Content | Systems of linear equations, Gaussian elimination, solution space, matrices, LR decomposition, determinants, structure of linear spaces, normed vector spaces, inner products, method of least squares, QR decomposition, introduction to MATLAB, applications. Linear maps, kernel and image, coordinates and matrices, coordinate transformations, norm of a matrix, orthogonal matrices, eigenvalues and eigenvectors, algebraic and geometric multiplicity, eigenbasis, diagonalizable matrices, symmetric matrices, orthonormal basis, condition number, linear differential equations, Jordan decomposition, singular value decomposition, examples in MATLAB, applications. Reading: Gilbert Strang "Introduction to linear algebra", Wellesley-Cambridge Press: Chapters 1-6, 7.1-7.3, 8.1, 8.2, 8.6 A Practical Introduction to MATLAB: http://www.math.ethz.ch/~grsam/Numerik_MAVT_WS0203/docs/intro.pdf Matlab Primer: http://www.math.ethz.ch/~grsam/Numerik_MAVT_WS0203/docs/primer.pdf | |||||

Literature | - Gilbert Strang: Introduction to linear algebra. Wellesley-Cambridge Press - A Practical Introduction to MATLAB: http://www.math.ethz.ch/~grsam/Numerik_MAVT_WS0203/docs/intro.pdf - Matlab Primer: http://www.math.ethz.ch/~grsam/Numerik_MAVT_WS0203/docs/primer.pdf | |||||

406-0353-AAL | Analysis IIIEnrolment 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. | E- | 4 credits | 9R | F. Da Lio | |

Abstract | Introduction to partial differential equations. Differential equations which are important in applications are classified and solved. Elliptic, parabolic and hyperbolic differential equations are treated. The following mathematical tools are introduced: Laplace transforms, Fourier series, separation of variables, methods of characteristics. | |||||

Objective | Mathematical treatment of problems in science and engineering. To understand the properties of the different types of partlial differentail equations. | |||||

Content | Laplace Transforms: - Laplace Transform, Inverse Laplace Transform, Linearity, s-Shifting - Transforms of Derivatives and Integrals, ODEs - Unit Step Function, t-Shifting - Short Impulses, Dirac's Delta Function, Partial Fractions - Convolution, Integral Equations - Differentiation and Integration of Transforms Fourier Series, Integrals and Transforms: - Fourier Series - Functions of Any Period p=2L - Even and Odd Functions, Half-Range Expansions - Forced Oscillations - Approximation by Trigonometric Polynomials - Fourier Integral - Fourier Cosine and Sine Transform Partial Differential Equations: - Basic Concepts - Modeling: Vibrating String, Wave Equation - Solution by separation of variables; use of Fourier series - D'Alembert Solution of Wave Equation, Characteristics - Heat Equation: Solution by Fourier Series - Heat Equation: Solutions by Fourier Integrals and Transforms - Modeling Membrane: Two Dimensional Wave Equation - Laplacian in Polar Coordinates: Circular Membrane, Fourier-Bessel Series - Solution of PDEs by Laplace Transform | |||||

Literature | E. Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, 10. Auflage, 2011 C. R. Wylie & L. Barrett, Advanced Engineering Mathematics, McGraw-Hill, 6th ed. Stanley J. Farlow, Partial Differential Equations for Scientists and Engineers, (Dover Books on Mathematics). G. Felder, Partielle Differenzialgleichungen für Ingenieurinnen und Ingenieure, hypertextuelle Notizen zur Vorlesung Analysis III im WS 2002/2003. Y. Pinchover, J. Rubinstein, An Introduction to Partial Differential Equations, Cambridge University Press, 2005 For reference/complement of the Analysis I/II courses: Christian Blatter: Ingenieur-Analysis (Download PDF) | |||||

Prerequisites / Notice | Up-to-date information about this course can be found at: http://www.math.ethz.ch/education/bachelor/lectures/hs2013/other/analysis3_itet |

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