Course Code : | 1001WETMRD |

Study domain: | Mathematics |

Academic year: | 2019-2020 |

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) | Sonja Hohloch Jaume Alonso Fernandez |

At the start of this course the student should have acquired the following competences:

an active knowledge of

- competences corresponding the final attainment level of secondary school

an active knowledge of

- Dutch

a passive knowledge ofThe courses (hoorcolleges) are taught in Dutch.

- English

specific prerequisites for this courseThe course is taught in Dutch, but the exercise sessions are probably taught in English.

The content of the Course Calcuus I should be well known.

- Sequences, Series and their convergence properties.
- Continuity in metric and normed spaces.
- Differential calculus in several variables.
- Tangent space of R^n and of submanifolds.
- Optimization and Lagrange multipliers.
- Integration over several variables.
- Theorem of Fubini; Change of variables.
- Path and surface integrals.

Chapter 1: Metric and normed spaces; sequences and series and their convergence.

Chapter 2: Continuity on metric and normed spaces.

Chapter 3: Differential calculus in several variables (derivative, partial derivative, higher derivatieves etc.); tangen spaces; important theorems (invers functions, implicit functions); Optimization and Lagrange multipliers.

Chapter 4: Integration (Riemann integral) in several variables; important theorems (Fubini, change of coordinates); path and surface integrals.

Class contact teachingLectures Practice sessions

Personal workExercises Assignments Individually Assignments In group

Personal work

homeworks

Examination

Continuous assessment

There exist lecture notes from 2015 which get revised this year (cf. my webpage). Some chapters of Bob Lowen's old lecture notes (cf. blackboard) may also be helpful.

There exist many books on `multivariable calculus'. Pick your favourite one.

Lectures: Sonja Hohloch, email sonja.hohloch AT uantwerpen.be

Exercise sessions: Jaume Alonso, email jaume.alonsofernandez AT uantwerpen.be