Partial Differential Equations (MAT328) | GSÜ

Content

Objective

Introduction to Fourier analysis, to theory of linear PDE.

Course Content

Fourier series, Separation of variables, Heat equation, Wave equation. Laplace equation, harmonic functions.

Course Learning Outcomes

1. Learn fundamental theorems on the Fourier series e.g. Parseval formula.
2. Make acquaintance with several applications of Fourier analysis to PDE.
3. Understand the fundamental properties of heat, wave, elliptic equations.
4. Get ideas on three types of PDE =hyperbolic, parabolic, elliptic.

Teaching and Learning Methods

Lectures and exercises.

References

Equations aux dérivées partielles, Introduction. H.Reinhard, Dunod, 1991.

Analyse 2, Calcul différentiel, intégrales multiples, séries de Fourier. F.Cottet-Emard, De Boeck, 2006

Weekly Contents

Theory Topics
Week	Weekly Contents
1	Fourier series
2	Fourier series
3	Dirichlet's theorem
4	Bessel inequality, Parseval formula.
5	Heat equation
6	Mid term examination.
7	Separation of variables
8	Wave equation
9	Wave equation
10	Initial value problem for the heat equation.
11	Laplace equation
12	Harmonic functions
13	Boundary value problems
14	Green's function

Assessment System

Contribution to Overall Grade
Activities	Number	Contribution
Contribution of in-term studies to overall grade	7	61
Contribution of final exam to overall grade	-1	40
Total	6	101

In-Term Studies
Activities	Number	Contribution
Assignments	0	0
Presentation	0	0
Midterm Examinations (including preparation)	2	60
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	0	0
Total	2	60

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	4	56
Working Hours out of Class	14	4	56
Presentation	2	1	2
Midterm Examinations (including preparation)	2	30	60
Final Examinations (including preparation)	1	20	20
Total Workload			194
Total Workload / 25			7.76
Credits ECTS			8