## Multivariable Analysis II(MAT202)

Course Code Course Name Semester Theory Practice Lab Credit ECTS
MAT202 Multivariable Analysis II 4 5 0 0 5 7
 Language of Instruction French Course Type Compulsory Course Level Bachelor Degree Course Instructor(s) Serap GÜRER serapgurer@gmail.com (Email) Assistant Objective The aim of this course is to generalize the notion of derivation and integration for single variable functions to the functions of multivariable functions, and to understand and to be able to apply the Stoke's theorem. Content Differentiable functions, Local inverse function theorem, Implicite function theorem, Higher order partial derivatives, Derivatives of integrals, Multiple integral, Change of variables, Differential forms, Stokes' theorem, Closed forms and Exact forms, Vector analysis, Green's theorem. Course Learning Outcomes To be able to calculate partial derivatives of multivariable functionsTo be able to use the local inverse function and the implicit function theorems To be able to calculate multiple integralsTo be able to calculate the integral of differential formsTo be able to use the Stokes' and Green's theorems Teaching and Learning Methods Lecture, discussion, problem solving References Principes d’Analyse Mathématique, Walter Rudin.Analyse Concepts et Contextes : Volume 2, Fonctions de Plusieurs Variables, James Stewart.
###### Theory Topics
Week Weekly Contents
1 Recall (Elementary topology + Linear applications)
2 Limit and continuity of multivariable functions
3 Differentiable functions
4 Fixed point theorem, Local İnverse function theorem
5 Implicit Function theorem
6 Rank theoremi, Determinant
7 Higher order partial derivatives, Derivatives of integrals
8 Multiple integration, primitive functions
9 Change of variables
10 Differential forms, Simlexes and chains
11 Stokes' theorem
12 Closed forms and exact forms
13 Vectorial analysis
14 Vektorial analysis, Green's theorem
###### Practice Topics
Week Weekly Contents
Number Contribution
Contribution of in-term studies to overall grade 7 60
Contribution of final exam to overall grade 1 40
Toplam 8 100
###### In-Term Studies
Number Contribution
Assignments 4 10
Presentation 0 0
Midterm Examinations (including preparation) 1 30
Project 0 0
Laboratory 0 0
Other Applications 0 0
Quiz 2 20
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
Toplam 7 60
No Program Learning Outcomes Contribution
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;
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;
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.
Class Hours 14 5 70
Working Hours out of Class 14 4 56
Assignments 4 2 8
Presentation 0 0 0
Midterm Examinations (including preparation) 1 10 10
Project 0 0 0
Laboratory 0 0 0
Other Applications 0 0 0
Final Examinations (including preparation) 1 20 20
Quiz 2 5 10
Term Paper/ Project 0 0 0
Portfolio Study 0 0 0
Reports 0 0 0
Learning Diary 0 0 0
Thesis/ Project 0 0 0
Seminar 0 0 0
Other 0 0 0