### General Information

Course Code | X_400641 |
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Credits | 6 EC |

Period | P1+2 |

Course Level | 100 |

Language of Tuition | English |

Faculty | Faculty of Science |

Course Coordinator | dr. F. Pasquotto |

Examiner | dr. F. Pasquotto |

Teaching Staff |
dr. M.A. Estevez Fernandez L.G.A.J. van Montfort C.H. Schutte dr. F. Pasquotto |

### 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 studenta) is able prove a theorem with mathematical induction.

b) knows the definition of limit of a sequence and a function and is

able to calculate limits, using various calculus techniques (e.g.

squeeze law and l'Hospitals rule).

c) knows the definition of continuity and is able to prove or disprove

the continuity of a function.

d) knows the definition of derivative of a single variable function and

is able to calculate (higher) derivatives and a Taylor polynomial of a

function.

e) knows the definition of a Riemann integral and is able to prove if a

function is Riemann integrable.

f) is able to calculate an integral, using various calculus techniques

(e.g. substitution method, integration by parts, partial fraction

decomposition).

g) is able to determine if an improper integral is convergent, and

calculate its value.

h) is able to work with complex numbers.

### Course Content

In this course we present a thorough introduction of the theory of realanalysis for single variable functions. Theorems and their proofs form

an important part of this course. In addition sufficient attention is

paid to various calculus techniques. We will treat the following topics:

a) Natural numbers and mathematical induction.

b) Rational and real numbers and the completeness of the real numbers.

c) Sequences of real numbers (convergence, subsequences, Cauchy

sequences).

d) Continuity and limits of real functions. Uniform continuity.

e) Differentiation (derivative of a function, mean value theorems,

L'Hospital's rule, Taylor's theorem).

f) Integration (Riemann integral, improper integral, integration

techniques)

g) Complex numbers

### Teaching Methods

Lectures (2x2 hours per week) and tutorials (1x2 hours per week).### Method of Assessment

There will be a midterm exam at the end of period 1 and a final exam atthe end of period 2. Details about the topics treated in each exam and

the calculation of the final grade will be published in Canvas. If your

grade is not sufficient, it is possible to make the resit about all

topics in the spring semester.

### Literature

1) A Friendly Introduction to Analysis; Single and Multivariable, secondedition, Witold A. J. Kosmala, Pearson. ISBN 0130457965/978-0130457967.

2) Lecture notes, available via Canvas.

### Target Audience

1 EOR### Additional Information

We expect that you attend the tutorials well prepared! That means thatyou have already tried to make the exercises at home! Some exercises

will be treated on the blackboard. You can ask questions about other

exercises to the teaching assistant. An attendance list will be used.