# Calculus

Course Code : | 1001WETCAL |

Study domain: | Mathematics |

Academic year: | 2017-2018 |

Semester: | 2nd semester |

Contact hours: | 90 |

Credits: | 9 |

Study load (hours): | 252 |

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

specific prerequisites for this courseThe professor's lecture notes for this class are written in Dutch. The material of this class is covered in standard calculus text books, i.e., for additional reading, passive knowledge of English is useful.

For most of the topics in this course, no explicit prerequisites are required, in view of the fact that they will be built up from scratch. However, it is desired that the student has a certain familiarity with the notions and concepts that were taught at secondary school. In particular, students are required to exhibit specific skills related to the following mathematical methods that were considered at secondary level:

- Logic and the systematics of a mathematical proof.

- Being able to calculate with real numbers, and to deal with polynomials in a finite number of variables.

- Factoring polynomials.

- Solving elementary equations and inequalities.

- Being able to handle functions of first and second degree.

- Newton's binomial formula.

- Solving linear systems of equations (in 2 and 3 variables).

- Trigonometry.

### 2. Learning outcomes *

- At the end of this course, the Bachelor in Computer Science is familiar with elementary calculus (differential- and integral) in one and several real variables, both from the theoretical and the practical point of view. To be more precise: - the student is familiar with the notions and definitions that will be seen in the course of the year (see also contents for an overview). This must result in the acquirement of a mathematical and scientific basis. - the student is able to reproduce certain arguments (it will be made clear for which results this will be a requirement), and in this way is able to prove that he has understood how certain formal results are obtained (developing the ability to formalize). - the student is able to reduce a given problem to a formal mathematical question expressed in a correct mathematical framework, using a sound logical deduction, and he is able to use properties that were seen in the course to answer this question. In other words, the student is required to learn to handle abstract mathematics as a formal language to recognize a problem (and possibly categorize it), and as a tool to obtain the answer.

### 3. Course contents *

This course deals with : sequences of real numbers (convergence tests), functions and their properties (boundedness, injection/surjection/bijection, continuity), limits of functions, one-dimensional differential calculus (with an introduction to differential calculus in several variables) and applications (practical rules for calculating derivatives, mean value theorems, extremal problems, graph sketching), integral calculus in one variable and applications (volume, arc length), series (including power series and Fourier series).

In short, this means that we will treat classical calculus as developed by Newton and Leibniz, together with all possible applications which are crucial in more or less all scientific courses in which 'functions of a continuous variable' play a dominant role. In a nice application we will treat the Fourier series, important in signal analysis.

### 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

Calculus (6th Edition) James Stewart

ISBN10: 0495011606

ISBN13: 9780495011606

One can find this book seemingly legally as PDF somewhere on the internet.

**7.2 Optional reading**

The following study material can be studied voluntarily :This class covers standard calculus material which one can find in almost any book on calculus. Parts are covered for example by

**Calculus (6th Edition)** van James Stewart

which one can find somewhere on the internet.

### 8. Contact information *

sonja.hohloch AT uantwerpen.be