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) | Meral TOSUN mtosun@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 | |
|---|---|---|
| Contribution of in-term studies to overall grade | 6 | 50 |
| Contribution of final exam to overall grade | 1 | 45 |
| Toplam | 7 | 95 |
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 | 1 | 5 |
| Quiz | 1 | 10 |
| 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 | 55 |
| 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 |
| Midterm Examinations (including preparation) | 1 | 10 | 10 |
| Final Examinations (including preparation) | 1 | 20 | 20 |
| Quiz | 2 | 5 | 10 |
| Total Workload | 174 | ||
| Total Workload / 25 | 6.96 | ||
| Credits ECTS | 7 | ||