Multivariable Analysis I (MAT201) | GSÜ

Content

Objective

Master the notion of convergence of sequences and series (both for those of numbers and functions).

Course Content

Convergence of sequences and series (both for those of numbers and functions).

Course Learning Outcomes

1.Treatment of convergence of sequences of numbers.

2.Treatment of convergence of series of numbers.

3.Right treatment of integration and differentiation of series of functions.

4. Preparation for the study of differential equations, complex analysis and functional analysis.

Teaching and Learning Methods

Lectures, exercises, discussions and working groups.

References

Analyse, François Cottet-Emard, de Boeck.

Principes d’Analyse Mathématique, W. Rudin, Ediscience.

Weekly Contents

Theory Topics
Week	Weekly Contents
1	Series of numbers. Criterion by Cauchy on the convergence. Absolute convergence.
2	Series with positive terms. Comparison theorems. Riemann series.
3	Criteria for convergence: by Cauchy and d`Alembert.
4	Criteria for convergence: by Abel
5	Alternative series.
6	Mid-term examination.
7	Series of functions. Point-wise convergence
8	Uniform convergence of a series of functions.
9	Theorem on the double limit, Theorems on continuity, differentiability and integration.
10	Uniform convergence of series of functions.
11	Stone-Weierstrass theorem.
12	Power series.
13	Power series and their applications to some differential equations.
14	Fourier series. Trigonometric polynomials. Fourier coefficients.

Assessment System

Contribution to Overall Grade
Activities	Number	Contribution
Contribution of in-term studies to overall grade	2	50
Contribution of final exam to overall grade	1	50
Total	3	100

In-Term Studies
Activities	Number	Contribution
Assignments	1	20
Presentation	0	0
Midterm Examinations (including preparation)	1	20
Project	0	0
Laboratory	0	0
Other Applications	0	0
Quiz	0	0
Term Paper/ Project	0	0
Portfolio Study	0	0
Reports	0	0
Learning Diary	0	0
Thesis/ Project	0	0
Seminar	0	0
Other	1	10
Total	3	50

Relation of Proficiency

No	Program Learning Outcomes	Contribution
No	Program Learning Outcomes	1	2	3	4	5
1	understands principles of deductive reasoning; has experience to verify well-foundedness and exactness of mathematical statements in systematic ways;				X
2	can properly state and use concepts and results of major mathematical interest;		X
3	masters current computational techniques and algorithms; has a good ability in their use; can identify relevant tools, among those one has learned, suitable to solve a problem and is able to judge whether or not one is in possession of these tools;			X
4	is able to express one’s mathematical ideas in an organised way both in written and oral forms;			X
5	understands relations connecting substantial concepts and results; can switch from one viewpoint to another on mathematical objects (pictures, formulae, precise statements, heuristic trials, list of examples,...);				X
6	has followed individually a guided learning strategy; has pursued steps toward the resolution of unfamiliar problems;		X
7	has a theoretical and practical knowledge in computer science well adapted for learning a programming language;	X
8	has investigated the relevance of modeling and using mathematical tools in natural sciences and in the professional life; is conscious about historical development of mathematical notions;	X
9	has followed introduction to some mathematical or non-mathematical disciplines after one’s proper choice; had experience to learn selected subjects according to one’s proper arrangement;			X
10	masters French language as well as other foreign languages, to a level sufficient to study or work abroad.	X

ECTS

Activities	Number	Period	Total Workload
Class Hours	14	6	84
Working Hours out of Class	14	3	42
Assignments	1	1	1
Presentation	1	8	8
Midterm Examinations (including preparation)	1	8	8
Project	1	8	8
Final Examinations (including preparation)	1	3	3
Total Workload			154
Total Workload / 25			6.16
Credits ECTS			6