Mathematics II(SOC162)
| Course Code | Course Name | Semester | Theory | Practice | Lab | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| SOC162 | Mathematics II | 2 | 2 | 0 | 0 | 2 | 4 |
| Prerequisites | SOC161 |
| Admission Requirements | SOC161 |
| Language of Instruction | French |
| Course Type | Compulsory |
| Course Level | Bachelor Degree |
| Course Instructor(s) | İpek KASPİ ŞOEF ipekkaspi@gmail.com (Email) |
| Assistant | |
| Objective | The course comprises two basic parts; linear algebra and differential calculus with multi variables functions. The objective of the first part is to recall to the student elementary linear algebra necessary for the comrehension of the second part as well as to follow other similar courses. The objective of the second part is to transmit to the student fundamental on differential calculus, topology of real functions of several real variables and their optimization. |
| Content |
Week 1 : 1) Factorial, permutation, combinaison (Reminder) 2) Concept of determinant, properties and computation of a determinant. Week 2 : 1) Definition of a matrix, properties, basic operations. 2) Basic matrix operations. Week 3 : 1) Linear equations, solving methods and interpretations of the solutions. 2) Linear and homogen equations, solving methods and interpretations of the solutions. Week 4 : 1) Eigenvalues and eigenvectors of a square matrix. 2) Diagonalization of a square matrix and quadratic forms Week 5 : 1) Quadratic forms. 2) Several real variables functions – Introduction, domain, limits and continuity. Week 6 : 1) Partial derivatives of a functions of several real varibles. 2) Partial derivatives and differantial of a functions of multiple real varibles. Week 7 : 1) Exam 1. 2) Partial derivatives of parametric and implicite functions. Week 8 : 1) Homogenous functions and Euler formula. 2) Directional derlvative, gradient and contour lines. Week 9 : 1) Contour lines. 2) Second order partial derivative, Schwarz theorem Week 10 : 1) Second order partial derivative of parametric and implicite functions. 2) n.th order partial derivative Taylor and Mc-Laurin formulas. Week 11 : 1) Free extrema of two variables functions. 2) Free extrema of two variables functions. Week 12 : 1) Exam 2. 2) Extrema sub consraints of two variables functions. Week 13 : 1) Extrema sub consraints of two variables functions. 2) Free extrema of multivariate functions. Week 14 : 1) Free extrema of multivariate functions. 2) Extrema sub consraints of multivariate functions. |
| Course Learning Outcomes |
At the end of the course, the studient will be able to, 1) Execute basic operations with determinants and matrices. 2) Solve linear equations by use of determinants and matrices. 3) Calculate the limits and partial derivatives of real functions of several real variables. 4) Represent the topology of real functions of several real variables. 5) Define and solve elementary optimization problems modelled by real functions of several real variables related to management problems. |
| Teaching and Learning Methods | |
| References |
Archinard, Gabriel ve Guerrien, Bernard. Principes Mathématiques pour Economistes. Paris : Economica, 1992 Flory, G. Exercices de Topologie et d’Analyse : Topologie. Paris : Vuibert, 1990 Hirsch, Gérard ve Eguether, Gérard. Fonctions de Plusieurs Variables : 364 exercices corrigés. Paris : Masson, 1994 Oudot, Xavier ve Delye-Chevalier, Marie. Analyse: 1re année MPSI. Paris : Hachette Supérieur, 1998 Pichon, Jacques. Topologie dans R Fonctions de Plusieurs Variables. Paris : Ellipses, 1991 Rudin, Walter. Trad. de l'américain par Jean Dhombres. Analyse réelle et complexe : cours et exercices. 3. édition. Paris : Dunod, 1998 Saada, Maurice. Mathématiques Financiéres. Paris : Presses Universitaires de France, 1991. Oudot, Xavier ve Delye-Chevalier, Marie. Analyse: 1re année MPSI. Paris : Hachette Supérieur, 1998 |
Theory Topics
| Week | Weekly Contents |
|---|---|
| 1 | Factorial, permutation, combinaison. Concept of determinant, properties and computation of a determinant. |
| 2 | Definition of a matrix, properties, basic operations with matrix. |
| 3 | Linear equations, solving methods and interpretations of the solutions. |
| 4 | Eigenvalues and eigenvectors of a square matrix. Diagonalization of a square matrix and quadratic forms. |
| 5 | Several real variables functions – Introduction, domain, limits and continuity. |
| 6 | Partial derivatives and differantial of a functions of multiple real variables. |
| 7 | Exam 1. Partial derivatives of parametric and implicite functions. |
| 8 | Homogenous functions and Euler formula. Directional derlvative, gradient and contour lines. |
| 9 | Second order partial derivative, Schwarz theorem. |
| 10 | n.th order partial derivative Taylor and Mc-Laurin formulas. |
| 11 | Free extrema of two variables functions. |
| 12 | Exam 2. Extrema sub consraints of two variables functions. |
| 13 | Extrema sub consraints of two variables functions. Free extrema of multivariate functions. |
| 14 | Free extrema of multivariate functions. Extrema sub consraints of multivariate functions. |
Practice Topics
| Week | Weekly Contents |
|---|
Contribution to Overall Grade
| Number | Contribution | |
|---|---|---|
| Contribution of in-term studies to overall grade | 3 | 60 |
| Contribution of final exam to overall grade | 1 | 40 |
| Toplam | 4 | 100 |
In-Term Studies
| Number | Contribution | |
|---|---|---|
| Assignments | 1 | 10 |
| Presentation | 1 | 20 |
| Midterm Examinations (including preparation) | 1 | 30 |
| 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 |
| Make-up | 0 | 0 |
| Toplam | 3 | 60 |
| No | Program Learning Outcomes | Contribution | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| 1 | The student will be able to recognize and assess the essential theoretical perspectives both in sociology and its related domains. | X | ||||
| 2 | The student will be able to make use of the major theoretical analyses and sociological concepts in his/her own research topics. | X | ||||
| 3 | The student will be able to articulate sociological perspective and reasoning with social and historical facts, and to interpret social and historical issues with a sociological eye. | X | ||||
| 4 | The student will be able to assess the current state of research and knowledge on the classical and contemporary domains of sociological inquiry as well as its relevant fields. | X | ||||
| 5 | The student will be able to design and conduct a sociological research with appropriate theoretical construction and empirical methods. | X | ||||
| 6 | The student will be able to produce a written research report that relates research questions to empirical findings. | X | ||||
| 7 | The student will be able to appropriately use both quantitative and qualitative methodologies. | X | ||||
| 8 | The student will be able to make appropriate use of statistical software programs for data processing and analysis. | X | ||||
| 9 | The student will be able to make appropriate use of statistical software programs for data processing and analysis. | X | ||||
| 10 | Graduates will be able to follow the scientific production both in English and French as well as Turkish. | X | ||||
| 11 | Graduates will be able to develop a comparative and interdisciplinary approach which will integrate sociology within a broader social science perspective. | X | ||||
| 12 | Graduates will be able to interpret the history and modernization of Turkey through its sociological consequences. | X | ||||
| Activities | Number | Period | Total Workload |
|---|---|---|---|
| Class Hours | 28 | 2 | 56 |
| Working Hours out of Class | 16 | 2 | 32 |
| Assignments | 0 | 0 | 0 |
| Presentation | 0 | 0 | 0 |
| Midterm Examinations (including preparation) | 2 | 10 | 20 |
| Project | 0 | 0 | 0 |
| Laboratory | 0 | 0 | 0 |
| Other Applications | 0 | 0 | 0 |
| Final Examinations (including preparation) | 1 | 33 | 33 |
| Quiz | 0 | 0 | 0 |
| 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 |
| Make-up | 0 | 0 | 0 |
| Total Workload | 141 | ||
| Total Workload / 25 | 5.64 | ||
| Credits ECTS | 6 | ||