Mathematics II(G112)
| Course Code | Course Name | Semester | Theory | Practice | Lab | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| G112 | Mathematics II | 2 | 4 | 0 | 0 | 4 | 6 |
| Prerequisites | G111 |
| Admission Requirements | G111 |
| Language of Instruction | Turkish |
| Course Type | Compulsory |
| Course Level | Bachelor Degree |
| Course Instructor(s) | Aslı Gül ÖNCEL aoncel@gsu.edu.tr (Email) Deniz UZTÜRK BARAN (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 | 2 | 50 |
| Contribution of final exam to overall grade | 1 | 50 |
| Toplam | 3 | 100 |
In-Term Studies
| Number | Contribution | |
|---|---|---|
| Assignments | 0 | 0 |
| Presentation | 0 | 0 |
| Midterm Examinations (including preparation) | 2 | 50 |
| 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 |
| Toplam | 2 | 50 |
| No | Program Learning Outcomes | Contribution | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| 1 | The acquisition of high-level knowledge of the functions of production management and marketing, management, accounting and finance; the skill of using this knowledge. | X | ||||
| 2 | The acquisition of basic conceptual knowledge about scientific fields related to professional life, such as law, economics, sociology, psychology, social psychology and quantitative methods. | X | ||||
| 3 | The ability to work effectively in a team; the ability to pass on knowledge to other members of the team. | X | ||||
| 4 | The competence to use his/her knowledge on the field, to analyze and interpret the data obtained, to identify the problems encountered, to provide appropriate solutions and scientifically defend these solution suggestions when necessary. | X | ||||
| 5 | The competence to determine the aims and objectives of the company or institution in which he/she is employed by taking into account the needs, the competitive dynamics of the market and by calculating the risks incurred; the ability to engage in entrepreneurship and establish and manage a business. | X | ||||
| 6 | Awareness of constantly updating his/her professional knowledge and skills; the ability to adapt to change and innovation; the competence to evaluate critically the information he/she has acquired. | X | ||||
| 7 | Basic knowledge of information and communication technologies required for professional life; the ability to use core office programs at an advanced level; expertise in data processing and report writing in the IT environment. | X | ||||
| 8 | Ability to follow current information in his/her field in both English and French and to communicate in writing and verbally with stakeholders in both languages. | X | ||||
| 9 | The ability to conduct researches and studies taking into account the market, dynamics of competition, organizational and global factors and scientific methods; contribute to projects, take responsibility in projects, display competence to make innovative and effective decisions. | X | ||||
| 10 | Ability to develop strategies, find creative solutions to management problems by building relations with other areas of the social sciences and take the responsibility of these decisions. | X | ||||
| 11 | Consciousness of taking into account ethical values, when making decisions and being involved in business life. | X | ||||
| 12 | Awareness of the impact of practices related to his/her field on the global and social dimensions (universality of social rights, social justice, cultural values, environmental problems, sustainability, etc.) and their legal consequences. | X | ||||
| Activities | Number | Period | Total Workload |
|---|---|---|---|
| Class Hours | 28 | 2 | 56 |
| Working Hours out of Class | 16 | 2 | 32 |
| Midterm Examinations (including preparation) | 2 | 10 | 20 |
| Final Examinations (including preparation) | 1 | 33 | 33 |
| Total Workload | 141 | ||
| Total Workload / 25 | 5.64 | ||
| Credits ECTS | 6 | ||