### General Information

Course Code | X_400635 |
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Credits | 6 EC |

Period | P1 |

Course Level | 100 |

Language of Tuition | English |

Faculty | Faculty of Science |

Course Coordinator | dr. O. Fabert |

Examiner | prof. dr. G.J.B. van den Berg |

Teaching Staff |
dr. O. Fabert |

### Practical Information

You need to register for this course yourself

Last-minute registration is available for this course.

Teaching Methods | Seminar, Lecture |
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Target audiences

This course is also available as:

### Course Objective

At the end of this course the student is able toa) calculate limits, using several methods like l'Hopitals rule or the

squeeze theorem

b) calculate derivatives and to find local extreme values

c) calculate integrals, using several methods like the substitution

method, integration by parts, partial fraction expansion

d) verify if a function is continuous, differentiable,

Riemann-integrable

e) calulate and apply a Taylor polynomial

f) formulate and apply several important theorems for continuous and/or

differentiable functions, like the Intermediate Value Theorem, the Mean

Value Theorem and the Fundamental Theorem of Calculus

### Course Content

Real functions of one variable. Topics that will be treated are:1) Preliminaries, Real functions, Trigonometric functions

2) Limits, Continuity, Intermediate Value Theorem

3) Transcendental Functions, Inverse Functions

4) Differentiation, Chain Rule, Mean Value Theorem

5) Applications of Differentiation, Extreme Values, l'Hôpital's Rule,

Taylor Polynomial

6) Integration, Fundamental Theorem of Calculus, Improper Integrals

### Teaching Methods

Lectures (3 x 2 hours per week) and seminars (2 x 2 hours per week).Attendance for at least 10 out of a total of 14 seminars is mandatory.

### Method of Assessment

There is a midterm exam and a final exam. The final grade (G) forCalculus 1 is a weighted average of the midterm exam (M) and final exam

(F): G=(2M+3F)/5. There is one retake which covers all topics for the

midterm exam and the final exam. Midterm exam or final exam cannot be

retaken separately! More details can be found in the manual on Canvas.

### Literature

Adams en Essex, Calculus: A Complete Course, 9th edition, Pearson 2018,ISBN-10: 0134154363 • ISBN-13: 9780134154367.