Multivariable Analysis II(MAT202)
| Course Code | Course Name | Semester | Theory | Practice | Lab | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| MAT202 | Multivariable Analysis II | 4 | 5 | 0 | 0 | 5 | 7 |
| Prerequisites | |
| Admission Requirements |
| Language of Instruction | French |
| Course Type | Compulsory |
| Course Level | Bachelor Degree |
| Course Instructor(s) | Ayberk ZEYTİN azeytin@gsu.edu.tr (Email) Öznur TURHAN oturhan@gsu.edu.tr (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 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. |
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 | |
|---|---|---|
| Toplam | 0 | 0 |
In-Term Studies
| Number | Contribution | |
|---|---|---|
| Toplam | 0 | 0 |
| No | Program Learning Outcomes | Contribution | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| Activities | Number | Period | Total Workload |
|---|---|---|---|
| Total Workload | 0 | ||
| Total Workload / 25 | 0,00 | ||
| Credits ECTS | 0 | ||