# Mathematical Methods for Physics III

Course Code : | 1003WETWMF |

Study domain: | Mathematics |

Academic year: | 2017-2018 |

Semester: | 2nd semester |

Contact hours: | 60 |

Credits: | 6 |

Study load (hours): | 168 |

Contract restrictions: | No contract restriction |

Language of instruction: | Dutch |

Exam period: | exam in the 2nd semester |

Lecturer(s) | David Eelbode |

### 1. Prerequisites *

- competences corresponding the final attainment level of secondary school

an active knowledge of

- Dutch

### 2. Learning outcomes *

- By the end of this course, the student has acquired knowledge on the topics covered during the classes (see below) and will be able to illustrate these.
- The student is able to apply this knowledge to standard exercises and true/false questions in which several theorems or mathematical techniques must be connected in order to obtain an answer.
- The student is able to reformulate a scientific problem into formal mathematics, knows how to solve this problem and is able to interpret the solution in the original setting.
- The student understands in what sense some of the results from the course are generalisations of things that were studied in earlier courses (e.g. calculus in a real variable versus complex analysis).

### 3. Course contents *

This course in a sense continues developing the classical calculus framework (see part I of this course), hereby covering the following subjects:

* Frobenius' method for solving differential equations (both for regular and singular points), with special attention for some special functions often occurring in physics (Airy - Bessel - Hermite)

* systems of differential equations and diagonalisation techniques

* multivariate calculus, with special emphasis on extremal problems in several variables (including the theory of Lagrange multipliers) and integration in several variables (surface and volume integrals + short summary of the connections between these objects)

* a concise introduction to complex analysis, starting from conservative vector fields (including residu calculus)