MEDICINE | |||||
Bachelor | TR-NQF-HE: Level 6 | QF-EHEA: First Cycle | EQF-LLL: Level 6 |
Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
MAT1041 | Linear Algebra | Spring Fall |
3 | 0 | 3 | 6 |
This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester. |
Language of instruction: | English |
Type of course: | Non-Departmental Elective |
Course Level: | Bachelor’s Degree (First Cycle) |
Mode of Delivery: | Face to face |
Course Coordinator : | Instructor MAHMOUD JAFARI SHAH BELAGHI |
Course Lecturer(s): |
Prof. Dr. SÜREYYA AKYÜZ Assoc. Prof. HALE GONCE KÖÇKEN Dr. Öğr. Üyesi DİLRÜBA ÖZMEN ERTEKİN Prof. Dr. NAFİZ ARICA |
Recommended Optional Program Components: | None |
Course Objectives: | To define matrix operations such as addition, multiplication, inversion and to prove some of related properties; To teach to solve a system of linear equations by using matrices; To give the definitions of a vector space, subspace, base and dimension and to prove some of related theorems; To introduce the notion of a linear map and the types of linear maps (such as injective, surjective and bijective); To teach the matrix representation of linear mappings and proving some of related properties; To construct the space of linear mappings and to give its structural properties; To define the transpose of a linear functional and to prove related properties. |
The students who have succeeded in this course; 1. Solve systems of linear equations using multiple methods, including Gaussian elimination and matrix inversion. 2. Carry out matrix operations, including inverses and determinants. 3. Demonstrate understanding of the concepts of vector space and subspace. 4. Demonstrate understanding of linear independence, span, and basis. 5. Determine eigenvalues and eigenvectors and solve eigenvalue problems. 6. Apply principles of matrix algebra to linear transformations. |
Systems of linear equations, matrices; Vector spaces, subspaces, base and dimension, coordinate; Linear mappings, kernel and image subspaces; Matrix representations of linear mappings; Linear functional, transpose of a linear mapping. Eigenvalues and eigenvectors, diagonalization of matrices. |
Week | Subject | Related Preparation |
1) | - Introduction to Systems of Linear Equations - Gaussian Elimination and Gauss-Jordan Elimination | |
2) | - Operations with Matrices - Properties of Matrix Operations | |
3) | - The Inverse of a Matrix | |
4) | - The Determinant of a Matrix - Evaluation of a Determinant Using Elementary Operations | |
5) | - Properties of Determinants | |
6) | - Vectors in R^n - Vector Spaces \ review. | |
7) | - Subspaces of Vector Spaces - Spanning Sets and Linear Independence | |
8) | - Basis and Dimension | |
9) | - Rank of a Matrix and Systems of Linear Equations | |
10) | - Introduction to Linear Transformations | |
11) | - The Kernel and Range of a Linear Transformation | |
12) | - Matrices for Linear Transformations - Transition Matrices and Similarity \ review. | |
13) | - Eigenvalues and Eigenvectors - Diagonalization | |
14) | - Symmetric Matrices and Orthogonal Diagonalization |
Course Notes / Textbooks: | Elementary Linear Algebra, Howard Anton, Wiley Publishing Co. (2000) |
References: | 1.Lang, S., "Linear Algebra", Addison-Wesley Publishing Company, (1968). 2.Hoffman, K. M., Kunze R. A., "Linear Algebra", Printice Hall, 2. edition, (1971). 3.Koç, C., "Basic Linear Algebra", Matematik Vakfı, (1995). 4. Lipschutz, S., "Linear Algebra, Schaum’s Outline Series", McGraw-Hill, Inc., (1974). 5.Kolman, B., Hill, D. R., "Introductory Algebra with Applications", Prentice Hall |
Semester Requirements | Number of Activities | Level of Contribution |
Midterms | 2 | % 60 |
Final | 1 | % 40 |
Total | % 100 | |
PERCENTAGE OF SEMESTER WORK | % 60 | |
PERCENTAGE OF FINAL WORK | % 40 | |
Total | % 100 |
Activities | Number of Activities | Duration (Hours) | Workload |
Course Hours | 14 | 3 | 42 |
Study Hours Out of Class | 14 | 7 | 98 |
Midterms | 2 | 2 | 4 |
Final | 1 | 2 | 2 |
Total Workload | 146 |
No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
Program Outcomes | Level of Contribution | |
1) | Integrates the knowledge, skills and attitudes acquired from basic and clinical medical sciences, behavioral sciences and social sciences, and uses them in health service delivery. | |
2) | In patient management, shows a biopsychosocial approach that takes into account the socio-demographic and sociocultural background of the individual, regardless of language, religion, race and gender. | |
3) | In the provision of health services, prioritizes the protection and development of the health of individuals and society. | |
4) | Taking into account the individual, societal, social and environmental factors affecting health; does the necessary work to maintain and improve the state of health. | |
5) | By recognizing the characteristics, needs and expectations of the target audience, provides health education to healthy/sick individuals and their relatives and other healthcare professionals. | |
6) | Shows a safe, rational and effective approach in health service delivery, prevention, diagnosis, treatment, follow-up and rehabilitation processes. | |
7) | Performs invasive and/or non-invasive procedures in diagnosis, treatment, follow-up and rehabilitation processes in a safe and effective way for the patient. | |
8) | Provides health services by considering patient and employee health and safety. | |
9) | In the provision of health services, takes into account the changes in the physical and socioeconomic environment on a regional and global scale, as well as the changes in the individual characteristics and behaviors of the people who apply to it. | |
10) | Takes good medical practice into account while carrying out his/her profession. | |
11) | Fulfills its duties and obligations within the framework of ethical principles, rights and legal responsibilities required by its profession. | |
12) | Demonstrates decisive behavior in providing high-quality health care, taking into account the integrity of the patient. | |
13) | Evaluates his/her performance in his/her professional practice by considering his/her emotions and cognitive characteristics. | |
14) | Advocates improving the provision of health services by considering the concepts of social reliability and social responsibility for the protection and development of public health. | |
15) | Can plan and carry out service delivery, training and consultancy processes related to individual and community health in cooperation with all components for the protection and development of health. | |
16) | Evaluates the impact of health policies and practices on individual and community health indicators and advocates increasing the quality of health services. | |
17) | The physician attaches importance to the protection of his/her own physical, mental and social health, and does what is necessary for this | |
18) | Shows exemplary behavior and leads the healthcare team during service delivery. | |
19) | Uses resources cost-effectively, for the benefit of society and in accordance with the legislation, in the planning, implementation and evaluation processes of health services in the health institution he/she is the manager of. | |
20) | Establishes positive communication within the health team it serves and assumes different team roles when necessary. | |
21) | Is aware of the duties and responsibilities of the health workers in the health team and acts accordingly. | |
22) | In the professional practices, works in harmony and effectively with the colleagues and other professional groups. | |
23) | Communicates effectively with patients, their relatives, healthcare professionals, other professional groups, institutions and organizations. | |
24) | Communicates effectively with individuals and groups that require a special approach and have different socio-cultural characteristics. | |
25) | In the diagnosis, treatment, follow-up and rehabilitation processes, shows a patient-centered approach that associates the patient with the decision-making mechanisms. | |
26) | Plans and implements scientific research, when necessary, for the population it serves, and uses the results and/or the results of other research for the benefit of the society. | |
27) | Reaches and critically evaluates current literature knowledge about his/her profession. | |
28) | Applies the principles of evidence-based medicine in clinical decision making. | |
29) | Uses information technologies to increase the effectiveness of its work on health care, research and education. | |
30) | Effectively manages individual work processes and career development. | |
31) | Demonstrates skills in acquiring and evaluating new knowledge, integrating it with existing knowledge, applying it to professional situations and adapting to changing conditions throughout professional life. | |
32) | Selects the right learning resources to improve the quality of the health service it offers, organizes its own learning process |