| Biomedical Engineering (English) | |||||
| Bachelor | TR-NQF-HE: Level 6 | QF-EHEA: First Cycle | EQF-LLL: Level 6 | ||
| Course Code: | MATH112 | ||||
| Course Name: | Linear Algebra with Applications | ||||
| Semester: | Spring | ||||
| Course Credits: |
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| Language of instruction: | English | ||||
| Course Condition: | |||||
| Does the Course Require Work Experience?: | No | ||||
| Type of course: | Compulsory Courses | ||||
| Course Level: |
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| Mode of Delivery: | Face to face | ||||
| Course Coordinator: | Dr. Öğr. Üy. FUNDA ÖZDEMİR | ||||
| Course Lecturer(s): | Assist. Prof. Dr. FUNDA ÖZDEMIR | ||||
| Course Assistants: |
| Course Objectives: | The course aims to improve abstract thinking skills by equipping students with the fundamental concepts of linear algebra and to gain the ability to use these concepts in solving engineering problems. |
| Course Content: | The content of the course consists of systems of linear equations and their solution sets, linear transformations, matrices and matrix operations, determinants, vector spaces, subspaces, linear independence, dimension, bases, change of basis, eigenvalues and eigenvectors, inner product, orthogonality, singular value decomposition. |
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The students who have succeeded in this course;
1) Solve a system of linear equations using matrix reduction (elimination). 2) Represent linear transformations as matrices and, conversely, interpret matrices as linear maps; do basic arithmetical operations with matrices and find the inverse of an invertible matrix. 3) Compute determinant of a matrix and comprehends the properties of determinants. 4) Find the dimension and basis of a vector space and its subspaces,analyze some fundamental subspaces. 5) Compute eigenvalues and eigenvectors of a matrix via characteristic equation, identify whether a matrix is diagonalizable or not, learn how to diagonalize the symmetric matrices and to learn singular value decomposition. 6) Knows the concepts of length, distance and orthogonality in inner product spaces, and produce an orthogonal basis for any of its subspaces. |
| Week | Subject | Related Preparation |
| 1) | Systems of linear equations, row reduction and echelon forms | |
| 2) | Vector equations, the matrix equation Ax=b, solution sets of linear systems, linear independence | |
| 3) | Introduction to linear transformations;, the matrix of a linear transformation | |
| 4) | Matrix operations, the inverse of a matrix, characterization of invertible matrices | |
| 5) | Partitioned (block) matrices, LU decomposition | |
| 6) | Determinants, properties of determinants, Cramer’s rule, volume | |
| 7) | Vector spaces, subspaces, null spaces and column spaces, kernel and range of a linear transformation | |
| 8) | Midterm Exam | |
| 9) | Linearly independent sets, span, bases, coordinates | |
| 10) | Dimension, rank, change of basis | |
| 11) | Eigenvalues and eigenvectors, characteristic equation, diagonalization | |
| 12) | Inner product spaces, length, distance and orthogonality, orthogonal sets | |
| 13) | Orthogonal projections, Gram-Schmidt process and QR decomposition | |
| 14) | Diagonalization of symmetric matrices, singular value decomposition |
| Course Notes / Textbooks: | Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson. |
| References: | Elementary Linear Algebra, Howard Anton, Chris Rorres, Wiley, 11th Edition. |
| Course Learning Outcomes | 1 |
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| Program Outcomes | |||||||||||
| 1) Adequate knowledge of mathematics, science and biomedical engineering disciplines; Ability to use theoretical and applied knowledge in these fields in solving complex engineering problems. | |||||||||||
| 2) Ability to identify, formulate and solve complex biomedical engineering problems; ability to select and apply appropriate analysis and modeling methods for this purpose. | |||||||||||
| 3) Ability to design a complex system, process, device or product to meet specific requirements under realistic constraints and conditions; ability to apply modern design methods for this purpose. | |||||||||||
| 4) Ability to select and use modern techniques and tools necessary for the analysis and solution of complex problems encountered in biomedical engineering practices; Ability to use information technologies effectively. | |||||||||||
| 5) Ability to design, conduct experiments, collect data, analyze and interpret results for the investigation of complex biomedical engineering problems or discipline-specific research topics. | |||||||||||
| 6) Ability to work effectively in disciplinary and multi-disciplinary teams; individual working skills. | |||||||||||
| 7) Ability to communicate effectively orally and in writing; knowledge of at least one foreign language, ability to write effective reports and understand written reports, to prepare design and production reports, to make effective presentations, to give and receive clear and understandable instructions. | |||||||||||
| 8) Awareness of the necessity of lifelong learning; the ability to access information, follow developments in science and technology, and constantly renew oneself. | |||||||||||
| 9) Knowledge of ethical principles, professional and ethical responsibility, and standards used in engineering practices. | |||||||||||
| 10) Knowledge of business practices such as project management, risk management and change management; awareness of entrepreneurship, innovation; information about sustainable development. | |||||||||||
| 11) Information about the effects of biomedical engineering practices on health, environment and safety in universal and social dimensions and the problems of the age reflected in the field of engineering; Awareness of the legal consequences of biomedical engineering solutions. | |||||||||||
| No Effect | 1 Lowest | 2 Average | 3 Highest |
| Program Outcomes | Level of Contribution | |
| 1) | Adequate knowledge of mathematics, science and biomedical engineering disciplines; Ability to use theoretical and applied knowledge in these fields in solving complex engineering problems. | |
| 2) | Ability to identify, formulate and solve complex biomedical engineering problems; ability to select and apply appropriate analysis and modeling methods for this purpose. | |
| 3) | Ability to design a complex system, process, device or product to meet specific requirements under realistic constraints and conditions; ability to apply modern design methods for this purpose. | |
| 4) | Ability to select and use modern techniques and tools necessary for the analysis and solution of complex problems encountered in biomedical engineering practices; Ability to use information technologies effectively. | |
| 5) | Ability to design, conduct experiments, collect data, analyze and interpret results for the investigation of complex biomedical engineering problems or discipline-specific research topics. | |
| 6) | Ability to work effectively in disciplinary and multi-disciplinary teams; individual working skills. | |
| 7) | Ability to communicate effectively orally and in writing; knowledge of at least one foreign language, ability to write effective reports and understand written reports, to prepare design and production reports, to make effective presentations, to give and receive clear and understandable instructions. | |
| 8) | Awareness of the necessity of lifelong learning; the ability to access information, follow developments in science and technology, and constantly renew oneself. | |
| 9) | Knowledge of ethical principles, professional and ethical responsibility, and standards used in engineering practices. | |
| 10) | Knowledge of business practices such as project management, risk management and change management; awareness of entrepreneurship, innovation; information about sustainable development. | |
| 11) | Information about the effects of biomedical engineering practices on health, environment and safety in universal and social dimensions and the problems of the age reflected in the field of engineering; Awareness of the legal consequences of biomedical engineering solutions. |
| Semester Requirements | Number of Activities | Level of Contribution |
| Midterms | 1 | % 40 |
| Final | 1 | % 60 |
| total | % 100 | |
| PERCENTAGE OF SEMESTER WORK | % 40 | |
| PERCENTAGE OF FINAL WORK | % 60 | |
| total | % 100 | |
| Activities | Number of Activities | Preparation for the Activity | Spent for the Activity Itself | Completing the Activity Requirements | Workload | ||
| Course Hours | 13 | 0 | 2 | 26 | |||
| Application | 13 | 0 | 2 | 26 | |||
| Study Hours Out of Class | 13 | 0 | 2 | 26 | |||
| Midterms | 1 | 13 | 2 | 15 | |||
| Final | 1 | 23 | 2 | 25 | |||
| Total Workload | 118 | ||||||