6 ECTS credits
180 h study time

Offer 1 with catalog number 1010218BNR for all students in the 1st semester at a (B) Bachelor - advanced level.

Semester
1st semester
Enrollment based on exam contract
Impossible
Grading method
Grading (scale from 0 to 20)
Can retake in second session
Yes
Enrollment Requirements
Students who want to enroll for this course, must have passed for "Analyse: afleiden, integreren, wiskundige software".
Taught in
Dutch
Faculty
Faculty of Sciences and Bioengineering Sciences
Department
Mathematics
Educational team
Mark Sioen (course titular)
Activities and contact hours

26 contact hours Lecture
26 contact hours Seminar, Exercises or Practicals
Course Content

 

Construction of the real numbers. Elementary notions and properties concerning metric spaces. Compactness and connectedness for metric spaces and particular results for the real line and the complex plane.
Pointwise and uniform convergence of sequences of functions. Spaces of functions endowed with supnorm. Study of completeness and applications to fix-point theorems.
Theorem of Dini. Derivation and integration of limitfunctions.
Series, convergence and absolute convergence, series with positive terms, series of real and complex numbers.
Series of functions, Taylorseries, powerseries.
Analytical functions. Analytic extension.

Course material
Course text (Required) : Analyse II, Colebunders, VUB, 2220170002286, 2015
Handbook (Recommended) : Principles of Mathematical Analysis, W.Rudin, 3de, Mc Graw Hill, 9780070856134, 1976
Additional info

Syllabus is available

 

Learning Outcomes

General competencies

-The student has basic knowledge of the construction of the real numbers and of basic concepts and properties of metric spaces

- The student  has basic knowledge of metric concepts applied to the context of spaces of bounded functions with uniform convergence and recognizes the essential differences with pointwise convergence.

 

- The student knows the role of compactness in the study of functions.

 

- The student is able to work with series of numbers, and more generally series of functions and series in normed spaces.

 

- The student has good understanding of the theory of complex power series and their role with respect to analytic functions.

 

 

 

 

 

Calculus skills

 

- The student masters the standard techniques and has the skills to bring calculations to a good end.

Insight and connections

- The student has an overall insight in the material, has a deep understanding of new concepts and results and is aware of the connection between de various concepts.

- The student is able to make the link between concepts on one hand and illustrating examples on the other hand.

 

- The student has insight in the relation to analogous concepts as they were introduced in previous courses.

 

 

 

 

 

 

 

 

Construction & formulation

 

- The student can analyse proofs and understands the logical reasoning behind them. For a given proposition the student is aware of the role the conditions play in the proof.

- The student can complete easy proofs that are left as an exercise or that are only partially explained in the syllabus or in class. The missing arguments can be filled in independently. 

 

- The student masters the mathematical language and is able to produce correct mathematical formulations and proofs.

Independent problemsolving

- The student can independently solve problems: he/she is able to recognize a problem, to choose an appropriate strategy, to select the most suitable method

Grading

The final grade is composed based on the following categories:
Oral Exam determines 60% of the final mark.
Written Exam determines 40% of the final mark.

Within the Oral Exam category, the following assignments need to be completed:

  • Mondeling theorie examen with a relative weight of 1 which comprises 60% of the final mark.

Within the Written Exam category, the following assignments need to be completed:

  • Schriftelijk oefeningen examen with a relative weight of 1 which comprises 40% of the final mark.

    Note: Een gedeelte van de punten voor de oefeningen worden verdiend op basis van taken gedurende de semester.

Additional info regarding evaluation

Written exam: solving problems 40%
Oral exam: theoretical evaluation 60%
Part of the marks for the written exam is based upon points gained for tasks during the semester.

Allowed unsatisfactory mark
The supplementary Teaching and Examination Regulations of your faculty stipulate whether an allowed unsatisfactory mark for this programme unit is permitted.

Academic context

This offer is part of the following study plans:
Bachelor of Physics and Astronomy: Default track (only offered in Dutch)
Bachelor of Mathematics and Data Science: Standaard traject (only offered in Dutch)