# 406-0353-AAL  Analysis III

 Semester Autumn Semester 2017 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

NumberTitleHoursLecturers
406-0353-AA RAnalysis III
Self-study course. No presence required.
120s hrsF. 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. 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 TransformsFourier 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 TransformPartial 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, 2011C. 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, 2005For 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 (210 mm x 297 mm) self-authored summary (handwritten or typed in LaTeX). Dictionary for non-native English speakers. No other aids are allowed (in particular no calculators). This information can be updated until the beginning of the semester; information on the examination timetable is binding.

### Learning materials

 Main link Angela Iozzi's Lecture notes Literature Angela Iozzi's Lecture notes Errata Only public learning materials are listed.

### Groups

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### Restrictions

 There are no additional restrictions for the registration.

### Offered in

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