| Biomedical Engineering (English) | |||||
| Bachelor | TR-NQF-HE: Level 6 | QF-EHEA: First Cycle | EQF-LLL: Level 6 | ||
| Course Code: | MATH205 | ||||
| Course Name: | Differential Equations | ||||
| Semester: | Fall | ||||
| 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 make the students know mainly the concepts ordinary differential equations, their solution methods, and their applications in modeling and simulating engineering systems. |
| Course Content: | The content of the course consists of introduction to ordinary differential equations, first order differential equations, second order linear equations, higher order linear equations; series solutions of second order linear equations; the Laplace transform, systems of first order linear equations. |
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The students who have succeeded in this course;
1) Solve first-order separable and linear differential equations. 2) Find the fundamental solution and the general solution of certain second order linear differential equations. 3) Use the Laplace transform method to solve linear ordinary differential equations. 4) Find the particular solution to a nonhomogeneous linear system of ordinary differential equations. 5) Solve higher-order certain linear differential equations and systems of differential equations. 6) Apply mathematical modelling in areas such as physics, engineering, biology or economics. |
| Week | Subject | Related Preparation |
| 1) | Introduction, classification of differential equations | |
| 2) | First order differential equations: linear equations, method of integrating factors, separable equations, difference between linear and nonlinear equations | |
| 3) | Exact equations and integrating factors, existence and uniqueness theorem | |
| 4) | Second order linear equations: homogeneous equations with constant coefficients, fundamental solutions of linear homogeneous equations, linear independence, Wronskian. | |
| 5) | Complex roots, repeated roots; reduction of order | |
| 6) | Nonhomogeneous equations: method of undetermined coefficients, variation of parameters | |
| 7) | Higher order linear equations: general theory, homogeneous equations with constant coefficients, method of undetermined coefficients, variation of parameters. | |
| 8) | Midterm Exam | |
| 9) | The Laplace transform: definitions, solution of initial value problems | |
| 10) | Step functions, solution of differential equations with discontinuous forcing functions | |
| 11) | Impulse functions, the convolution integral | |
| 12) | Systems of first order linear equations: introduction, linear independence, eigenvalues, eigenvectors | |
| 13) | Complex eigenvalues, fundamental matrices, repeated eigenvalues, nonhomogeneous linear systems | |
| 14) | Series Solutions: power series, series solutions near an ordinary point |
| Course Notes / Textbooks: | Boyce, William E.; DiPrima, Richard C., Meade, Douglas B., Elementary Differential Equations and Boundary Value Problems, 12th Edition, Wiley-Blackwell, 2021. |
| References: | Lecture notes |
| 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 | 3 | 39 | |||
| Study Hours Out of Class | 13 | 0 | 4 | 52 | |||
| Midterms | 1 | 18 | 2 | 20 | |||
| Final | 1 | 25 | 2 | 27 | |||
| Total Workload | 138 | ||||||