# 401-0243-00L Analysis III

Semester | Autumn Semester 2021 |

Lecturers | M. Akka Ginosar |

Periodicity | yearly recurring course |

Language of instruction | German |

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. |

Learning 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 through Separation of variables as an introduction to Fourier Series. Systematic treatment of the complex and real Fourier Series Study of the wave equation and general hyperbolic problems using Fourier Series, D'Alembert solution and the method of characteristics. Laplace transform and it's uses to differential equations 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. Time permitting, we will introduce the Fourier transform. |

Lecture notes | Lecture notes will be provided |

Literature | large part of the material follow certain chapters of the following first two books quite closely. S.J. Farlow: Partial Differential Equations for Scientists and Engineers, (Dover Books on Mathematics), 1993 E. Kreyszig: Advanced Engineering Mathematics, John Wiley & Sons, 10. Auflage, 2001 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/ Y. Pinchover and J. Rubinstein: An Introduction to Partial Differential Equations, Cambridge University Press, 2005 C.R. Wylie and L. Barrett: Advanced Engineering Mathematics, McGraw-Hill, 6th ed, 1995 |

Prerequisites / Notice | Analysis I and II, insbesondere, gewöhnliche Differentialgleichungen. |