# Multivariate Calculus

Course Code : | 1001WETMRD |

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) | Sonja Hohloch |

### 1. Prerequisites *

- competences corresponding the final attainment level of secondary school

an active knowledge of

- Dutch

a passive knowledge ofThe course (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 we well known.

### 2. Learning outcomes *

- 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.

### 3. Course contents *

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.

### 4 International dimension*

### 5. Teaching method and planned learning activities

Personal work

### 6. Assessment method and criteria

homeworks

Examination

Continuous assessment

### 7. Study material *

#### 7.1 Required reading

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.

**7.2 Optional reading**

The following study material can be studied voluntarily :There exist many books on `multivariable calculus'. Pick your favourite one.

### 8. Contact information *

Sonja.Hohloch@uantwerpen