Multivariable Analysis II(MAT202)

Course Code Course Name Semester Theory Practice Lab Credit ECTS
MAT202 Multivariable Analysis II 4 5 0 0 5 7
Admission Requirements
Language of Instruction French
Course Type Compulsory
Course Level Bachelor Degree
Course Instructor(s) Serap GÜRER (Email)
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 functions
To be able to use the local inverse function and the implicit function theorems
To be able to calculate multiple integrals
To be able to calculate the integral of differential forms
To 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.
Print the course contents
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
Contribution to Overall Grade
  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.
Activities Number Period Total Workload
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
Total Workload 174
Total Workload / 25 6,96
Credits ECTS 7
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