# 406-0251-AAL Mathematics I

Semester | Spring Semester 2020 |

Lecturers | A. Cannas da Silva |

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 | |
---|---|---|---|---|

406-0251-AA R | Mathematics I Self-study course. No presence required. | 180s hrs | A. Cannas da Silva |

### Catalogue data

Abstract | This course covers mathematical concepts and techniques necessary to model, solve and discuss scientific problems - notably through ordinary differential equations. |

Objective | Mathematics is of ever increasing importance to the Natural Sciences and Engineering. The key is the so-called mathematical modelling cycle, i.e. the translation of problems from outside of mathematics into mathematics, the study of the mathematical problems (often with the help of high level mathematical software packages) and the interpretation of the results in the original environment. The goal of Mathematics I and II is to provide the mathematical foundations relevant for this paradigm. Differential equations are by far the most important tool for modelling and are therefore a main focus of both of these courses. |

Content | 1. Linear Algebra and Complex Numbers: systems of linear equations, Gauss-Jordan elimination, matrices, determinants, eigenvalues and eigenvectors, cartesian and polar forms for complex numbers, complex powers, complex roots, fundamental theorem of algebra. 2. Single-Variable Calculus: review of differentiation, linearisation, Taylor polynomials, maxima and minima, fundamental theorem of calculus, antiderivative, integration methods, improper integrals. 3. Ordinary Differential Equations: variation of parameters, separable equations, integration by substitution, systems of linear equations with constant coefficients, 1st and higher order equations, introduction to dynamical systems. |

Literature | - Bretscher, O.: Linear Algebra with Applications, Pearson Prentice Hall. - Thomas, G. B.: Thomas' Calculus, Part 1, Pearson Addison-Wesley. |

### Performance assessment

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

Performance assessment as a semester course | |

ECTS credits | 6 credits |

Examiners | A. Cannas da Silva |

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 90 minutes |

Written aids | Summary with up to 20 A4 pages (= 10 double-sided sheets of paper). 1 English dictionary. No calculators, no laptops, no cellular phones. |

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

### Learning materials

Main link | Link to course syllabus and suggested work plan in English |

Additional links | Link to course syllabus and suggested work plan in English |

Only public learning materials are listed. |

### Groups

No information on groups available. |

### Restrictions

There are no additional restrictions for the registration. |