Course Detail
Course Description
| Course | Code | Semester | T+P (Hour) | Credit | ECTS |
|---|---|---|---|---|---|
| LINEAR ALGEBRA and DIFFERENTIAL EQUATIONS | - | Fall Semester | 4+0 | 4 | 8 |
| Course Program |
| Prerequisites Courses | |
| Recommended Elective Courses |
| Language of Course | English |
| Course Level | First Cycle (Bachelor's Degree) |
| Course Type | Required |
| Course Coordinator | Assist.Prof. Cihan Bilge KAYASANDIK |
| Name of Lecturer(s) | Assist.Prof. Mehmed Rafet ÖZDEMİR |
| Assistant(s) | |
| Aim | 1. To provide the methods of solution of systems of linear equations and the applications of matrix and determinant. 2. To introduce the basic concepts required to understand, construct, solve and interpret differential equations and to teach methods to solve differential equations of various types. 3. To give an ability to apply knowledge of mathematics on engineering problems |
| Course Content | This course contains; Matrices and Systems of Linear Equations,Matrices and Systems of Linear Equations,Determinants,Vector Spaces,Vector Spaces,Eigenvalues and Eigenvectors,Eigenvalues and Eigenvectors,First order differential equations,First order differential equations,Higher order differential equations,Higher order differential equations,Higher order differential equations,Laplace Transform,Laplace Transform. |
| Dersin Öğrenme Kazanımları | Teaching Methods | Assessment Methods |
| 5. Solve higher order linear differential equations with constant coefficients and construct all solutions from the linearly independent solutions ; solve initial value problems using the Laplace transform | 12, 14, 9 | A, E |
| 4. Solve first order linear equations and nonlinear equations of certain types , interpret the solutions and understand the conditions for the existence and uniqueness of solutions for linear differential equations | 12, 14, 9 | A, E |
| 3. Classify differential equations according to certain features | 12, 14, 9 | A, E |
| 2. Learn the importance of the concepts of vector space, basis and dimension and evaluate the eigenvalues and the corresponding eigenvectors of the matrix. | 12, 14, 9 | A, E |
| 1. Solve the systems of linear equations, provide arithmetic operations with matrices, compute the inverse of matrix, determine the value of determinant of a matrix and use Cramer rule to solve the systems | 12, 14, 9 | A, E |
| Teaching Methods: | 12: Problem Solving Method, 14: Self Study Method, 9: Lecture Method |
| Assessment Methods: | A: Traditional Written Exam, E: Homework |
Course Outline
| Order | Subjects | Preliminary Work |
|---|---|---|
| 1 | Matrices and Systems of Linear Equations | |
| 2 | Matrices and Systems of Linear Equations | |
| 3 | Determinants | |
| 4 | Vector Spaces | |
| 5 | Vector Spaces | |
| 6 | Eigenvalues and Eigenvectors | |
| 7 | Eigenvalues and Eigenvectors | |
| 8 | First order differential equations | |
| 9 | First order differential equations | |
| 10 | Higher order differential equations | |
| 11 | Higher order differential equations | |
| 12 | Higher order differential equations | |
| 13 | Laplace Transform | |
| 14 | Laplace Transform |
| Resources |
| Differential Equations & Linear Algebra Third Edition Edition, C.Henry Edwards ; David E. Penney Pearson International Education International,2011. |
Course Contribution to Program Qualifications
| Course Contribution to Program Qualifications | |||||||
| No | Program Qualification | Contribution Level | |||||
| 1 | 2 | 3 | 4 | 5 | |||
| 1 | Adequate knowledge in mathematics, science and engineering subjects pertaining to the relevant discipline; ability to use theoretical and applied knowledge in these areas in the solution of complex engineering problems. | X | |||||
| 2 | Ability to formulate, and solve complex engineering problems; ability to select and apply proper analysis and modeling methods for this purpose. | X | |||||
| 3 | Ability to design a complex system, process, device or product under realistic constraints and conditions, in such a way as to meet the desired result; ability to apply modern design methods for this purpose. | X | |||||
| 4 | Ability to select and use modern techniques and tools needed for analyzing and solving complex problems encountered in engineering practice; ability to employ information technologies effectively. | ||||||
| 5 | Ability to design and conduct experiments, gather data, analyze and interpret results for investigating complex engineering problems or discipline specific research questions. | ||||||
| 6 | Ability to work efficiently in intra-disciplinary and multi-disciplinary teams; ability to work individually. | ||||||
| 7 | Ability to communicate effectively, both orally and in writing; knowledge of a minimum of one foreign language; ability to write effective reports and comprehend written reports, prepare design and production reports, make effective presentations, and give and receive clear and intelligible instructions. | ||||||
| 8 | Awareness of the need for lifelong learning; ability to access information, to follow developments in science and technology, and to continue to educate him/herself. | ||||||
| 9 | Knowledge on behavior according ethical principles, professional and ethical responsibility and standards used in engineering practices. | ||||||
| 10 | Knowledge about business life practices such as project management, risk management, and change management; awareness in entrepreneurship, innovation; knowledge about sustainable development. | ||||||
| 11 | Knowledge about the global and social effects of engineering practices on health, environment, and safety, and contemporary issues of the century reflected into the field of engineering; awareness of the legal consequences of engineering solutions. | ||||||
Assessment Methods
| Contribution Level | Absolute Evaluation | |
| Rate of Midterm Exam to Success | 30 | |
| Rate of Final Exam to Success | 70 | |
| Total | 100 | |
| ECTS / Workload Table | ||||||
| Activities | Number of | Duration(Hour) | Total Workload(Hour) | |||
| Course Hours | 14 | 4 | 56 | |||
| Guided Problem Solving | 0 | 0 | 0 | |||
| Resolution of Homework Problems and Submission as a Report | 14 | 10 | 140 | |||
| Term Project | 0 | 0 | 0 | |||
| Presentation of Project / Seminar | 0 | 0 | 0 | |||
| Quiz | 0 | 0 | 0 | |||
| Midterm Exam | 1 | 22 | 22 | |||
| General Exam | 1 | 22 | 22 | |||
| Performance Task, Maintenance Plan | 0 | 0 | 0 | |||
| Total Workload(Hour) | 240 | |||||
| Dersin AKTS Kredisi = Toplam İş Yükü (Saat)/30*=(240/30) | 8 | |||||
| ECTS of the course: 30 hours of work is counted as 1 ECTS credit. | ||||||
Detail Informations of the Course
Course Description
| Course | Code | Semester | T+P (Hour) | Credit | ECTS |
|---|---|---|---|---|---|
| LINEAR ALGEBRA and DIFFERENTIAL EQUATIONS | - | Fall Semester | 4+0 | 4 | 8 |
| Course Program |
| Prerequisites Courses | |
| Recommended Elective Courses |
| Language of Course | English |
| Course Level | First Cycle (Bachelor's Degree) |
| Course Type | Required |
| Course Coordinator | Assist.Prof. Cihan Bilge KAYASANDIK |
| Name of Lecturer(s) | Assist.Prof. Mehmed Rafet ÖZDEMİR |
| Assistant(s) | |
| Aim | 1. To provide the methods of solution of systems of linear equations and the applications of matrix and determinant. 2. To introduce the basic concepts required to understand, construct, solve and interpret differential equations and to teach methods to solve differential equations of various types. 3. To give an ability to apply knowledge of mathematics on engineering problems |
| Course Content | This course contains; Matrices and Systems of Linear Equations,Matrices and Systems of Linear Equations,Determinants,Vector Spaces,Vector Spaces,Eigenvalues and Eigenvectors,Eigenvalues and Eigenvectors,First order differential equations,First order differential equations,Higher order differential equations,Higher order differential equations,Higher order differential equations,Laplace Transform,Laplace Transform. |
| Dersin Öğrenme Kazanımları | Teaching Methods | Assessment Methods |
| 5. Solve higher order linear differential equations with constant coefficients and construct all solutions from the linearly independent solutions ; solve initial value problems using the Laplace transform | 12, 14, 9 | A, E |
| 4. Solve first order linear equations and nonlinear equations of certain types , interpret the solutions and understand the conditions for the existence and uniqueness of solutions for linear differential equations | 12, 14, 9 | A, E |
| 3. Classify differential equations according to certain features | 12, 14, 9 | A, E |
| 2. Learn the importance of the concepts of vector space, basis and dimension and evaluate the eigenvalues and the corresponding eigenvectors of the matrix. | 12, 14, 9 | A, E |
| 1. Solve the systems of linear equations, provide arithmetic operations with matrices, compute the inverse of matrix, determine the value of determinant of a matrix and use Cramer rule to solve the systems | 12, 14, 9 | A, E |
| Teaching Methods: | 12: Problem Solving Method, 14: Self Study Method, 9: Lecture Method |
| Assessment Methods: | A: Traditional Written Exam, E: Homework |
Course Outline
| Order | Subjects | Preliminary Work |
|---|---|---|
| 1 | Matrices and Systems of Linear Equations | |
| 2 | Matrices and Systems of Linear Equations | |
| 3 | Determinants | |
| 4 | Vector Spaces | |
| 5 | Vector Spaces | |
| 6 | Eigenvalues and Eigenvectors | |
| 7 | Eigenvalues and Eigenvectors | |
| 8 | First order differential equations | |
| 9 | First order differential equations | |
| 10 | Higher order differential equations | |
| 11 | Higher order differential equations | |
| 12 | Higher order differential equations | |
| 13 | Laplace Transform | |
| 14 | Laplace Transform |
| Resources |
| Differential Equations & Linear Algebra Third Edition Edition, C.Henry Edwards ; David E. Penney Pearson International Education International,2011. |
Course Contribution to Program Qualifications
| Course Contribution to Program Qualifications | |||||||
| No | Program Qualification | Contribution Level | |||||
| 1 | 2 | 3 | 4 | 5 | |||
| 1 | Adequate knowledge in mathematics, science and engineering subjects pertaining to the relevant discipline; ability to use theoretical and applied knowledge in these areas in the solution of complex engineering problems. | X | |||||
| 2 | Ability to formulate, and solve complex engineering problems; ability to select and apply proper analysis and modeling methods for this purpose. | X | |||||
| 3 | Ability to design a complex system, process, device or product under realistic constraints and conditions, in such a way as to meet the desired result; ability to apply modern design methods for this purpose. | X | |||||
| 4 | Ability to select and use modern techniques and tools needed for analyzing and solving complex problems encountered in engineering practice; ability to employ information technologies effectively. | ||||||
| 5 | Ability to design and conduct experiments, gather data, analyze and interpret results for investigating complex engineering problems or discipline specific research questions. | ||||||
| 6 | Ability to work efficiently in intra-disciplinary and multi-disciplinary teams; ability to work individually. | ||||||
| 7 | Ability to communicate effectively, both orally and in writing; knowledge of a minimum of one foreign language; ability to write effective reports and comprehend written reports, prepare design and production reports, make effective presentations, and give and receive clear and intelligible instructions. | ||||||
| 8 | Awareness of the need for lifelong learning; ability to access information, to follow developments in science and technology, and to continue to educate him/herself. | ||||||
| 9 | Knowledge on behavior according ethical principles, professional and ethical responsibility and standards used in engineering practices. | ||||||
| 10 | Knowledge about business life practices such as project management, risk management, and change management; awareness in entrepreneurship, innovation; knowledge about sustainable development. | ||||||
| 11 | Knowledge about the global and social effects of engineering practices on health, environment, and safety, and contemporary issues of the century reflected into the field of engineering; awareness of the legal consequences of engineering solutions. | ||||||
Assessment Methods
| Contribution Level | Absolute Evaluation | |
| Rate of Midterm Exam to Success | 30 | |
| Rate of Final Exam to Success | 70 | |
| Total | 100 | |