# 406-0353-AAL Analysis III

Semester | Autumn Semester 2020 |

Lecturers | F. Da Lio |

Periodicity | every semester recurring course |

Language of instruction | English |

Comment | 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. |

### Courses

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

406-0353-AA R | Analysis III Self-study course. No presence required. | 120s hrs | F. Da Lio |

### Catalogue data

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. |

Learning 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 |

### Performance assessment

Performance assessment information (valid until the course unit is held again) | |

Performance assessment as a semester course | |

ECTS credits | 4 credits |

Examiners | F. Da Lio |

Type | session examination |

Language of examination | English |

Repetition | The performance assessment is offered every session. Repetition possible without re-enrolling for the course unit. |

Mode of examination | written 120 minutes |

Written aids | 20 pages (=10 sheets) DIN A4 handwritten or typed personal summary. English dictionary. No further aids (in particular, no pocket calculator). |

This information can be updated until the beginning of the semester; information on the examination timetable is binding. |

### Learning materials

No public learning materials available. | |

Only public learning materials are listed. |

### Groups

No information on groups available. |

### Restrictions

There are no additional restrictions for the registration. |

### Offered in

Programme | Section | Type | |
---|---|---|---|

Mechanical Engineering Master | Course Units for Additional Admission Requirements | E- | |

Computational Science and Engineering Master | Course Units for Additional Admission Requirements | E- |