| BIOMEDICAL ENGINEERING | |||||
| Bachelor | TR-NQF-HE: Level 6 | QF-EHEA: First Cycle | EQF-LLL: Level 6 | ||
| Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
| MAT2043 | Linear Algebra with Applications | Fall | 3 | 2 | 4 | 6 |
| Language of instruction: | English |
| Type of course: | Must Course |
| Course Level: | Bachelor’s Degree (First Cycle) |
| Mode of Delivery: | Face to face |
| Course Coordinator : | Prof. Dr. SÜREYYA AKYÜZ |
| Course Lecturer(s): |
Prof. Dr. SÜREYYA AKYÜZ 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. |
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The students who have succeeded in this course; The students who succeeded in this course; The students who have succeeded in this course; Students will be able to: 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. 7)Apply linear algebra problems using MATLAB tools |
| 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) | Bir Matrisin Tersi | |
| 4) | The Determinant of a Matrix - Evaluation of a Determinant Using Elementary Operations | |
| 5) | Properties of Determinants | |
| 6) | Vectors in n-dimensionVector spaces, vector spaces, | |
| 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 | |
| 13) | Eigenvalues and Eigenvectors - Diagonalization | |
| 14) | Symmetric Matrices and Orthogonal Diagonalization |
| Course Notes / Textbooks: | Elementary Linear Algebra with Supplemental Applications, 10th Edition, Howard Anton and Chris Rorres, John Wiley, 2010. |
| References: | . |
| Semester Requirements | Number of Activities | Level of Contribution |
| Attendance | 14 | % 0 |
| Application | 14 | % 0 |
| Quizzes | 10 | % 20 |
| Homework Assignments | 5 | % 10 |
| Midterms | 1 | % 30 |
| 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 |
| Application | 14 | 2 | 28 |
| Study Hours Out of Class | 14 | 2 | 28 |
| Quizzes | 4 | 1 | 4 |
| Midterms | 1 | 10 | 10 |
| Final | 1 | 27 | 27 |
| Total Workload | 139 | ||
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution | |
| 1) | Adequate knowledge of subjects specific to mathematics (analysis, linear, algebra, differential equations, statistics), science (physics, chemistry, biology) and related engineering discipline, and the ability to use theoretical and applied knowledge in these fields in complex engineering problems. | 4 |
| 2) | Identify, formulate, and solve complex Biomedical Engineering problems; select and apply proper modeling and analysis methods for this purpose | 4 |
| 3) | Design complex Biomedical systems, processes, devices or products under realistic constraints and conditions, in such a way as to meet the desired result; apply modern design methods for this purpose. | 2 |
| 4) | Devise, select, and use modern techniques and tools needed for solving complex problems in Biomedical Engineering practice; employ information technologies effectively. | 4 |
| 5) | Design and conduct numerical or physical experiments, collect data, analyze and interpret results for investigating the complex problems specific to Biomedical Engineering. | 5 |
| 6) | Cooperate efficiently in intra-disciplinary and multi-disciplinary teams; and show self-reliance when working on Biomedical Engineering-related problems. | 2 |
| 7) | Ability to communicate effectively in Turkish, oral and written, to have gained the level of English language knowledge (European Language Portfolio B1 general level) to follow the innovations in the field of Biomedical Engineering; gain the ability to write and understand written reports effectively, to prepare design and production reports, to make effective presentations, to give and receive clear and understandable instructions. | 2 |
| 8) | Recognize the need for life-long learning; show ability to access information, to follow developments in science and technology, and to continuously educate oneself. | 2 |
| 9) | Having knowledge for the importance of acting in accordance with the ethical principles of biomedical engineering and the awareness of professional responsibility and ethical responsibility and the standards used in biomedical engineering applications | |
| 10) | Learn about business life practices such as project management, risk management, and change management; develop an awareness of entrepreneurship, innovation, and sustainable development. | |
| 11) | Acquire knowledge about the effects of practices of Biomedical Engineering on health, environment, security in universal and social scope, and the contemporary problems of Biomedical Engineering; is aware of the legal consequences of Mechatronics engineering solutions. |