| MATHEMATICS | |||||
| Bachelor | TR-NQF-HE: Level 6 | QF-EHEA: First Cycle | EQF-LLL: Level 6 | ||
| Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
| MAT4070 | Computational Mathematics | Fall | 3 | 0 | 3 | 6 |
| The course opens with the approval of the Department at the beginning of each semester |
| Language of instruction: | En |
| Type of course: | Departmental Elective |
| Course Level: | Bachelor |
| Mode of Delivery: | Hybrid |
| Course Coordinator : | Dr. Öğr. Üyesi GÜLSEMAY YİĞİT |
| Course Objectives: | This course aims to understand and apply the methods and techniques such as fixed-point theorem and its applications, difference schemes generated by an exact difference scheme and by Taylor’s decomposition function on two or three points for obtaining approximate solutions to differential and integral equations that are not solvable exactly. |
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The students who have succeeded in this course; 1. Can solve nonlinear equations and systems of equations 2. Can solve first and second order ordinary differential equations 3. Can solve integral equations 4. Can solve partial differential equations 5. Have a comprension and discussion of difference schemes generated by an exact difference scheme and their applications 6. Have a comprensive and discussion of difference schemes generated by Taylor's decomposition function on two points and their applications 7. Have a comprehension and discussion of difference schemes generated by Taylor's decomposition function on three points and their applications |
| In this course the methods and techiques for obtaining approximate solutions of differential and integral equations will be covered. The fixed-point theorem and its applications will be given. Difference schemes generated by an exact difference scheme will be studied. Finally, difference schemes generated by Taylor’s decomposition function on two or three points will be taught. |
| Week | Subject | Related Preparation | |
| 1) | A Fixed-Point Theorem in R. Iteration method for nonlinear equations. | ||
| 2) | A Fixed-Point Theorem in Rn. Iteration method for to system of equations. | ||
| 3) | A Fixed-Point Theorem in C[a,b]. Iteration method for the first and second order ordinary differential equations. | ||
| 4) | A Fixed-Point Theorem in C[a,b]. Iteration method for the first and second order ordinary differential equations. | ||
| 5) | Iteration method for integral equations. | ||
| 6) | Iteration method for parabolic and hyperbolic differential equations. | ||
| 7) | Iteration method for parabolic and hyperbolic differential equations. | ||
| 8) | Difference schemes generated by an exact difference scheme. - Midterm | ||
| 9) | Difference schemes generated by Taylor’s decomposition function on two points. | ||
| 10) | Difference schemes generated by an exact difference scheme for the second order ODE. | ||
| 11) | Difference schemes generated by an exact difference scheme for the second order ODE. | ||
| 12) | Taylor’s decomposition function on three points. | ||
| 13) | Difference schemes generated by Taylor’s decomposition function on three points. | ||
| 14) | Difference schemes generated by Taylor’s decomposition function on three points. | ||
| Course Notes: | Ashyralyev A., Computational Mathematics, Textbook, The South Kazakhstan State University named after M. Auezovuku Printing House, Chimkent, 2014, 145 sayfa. "1. Ashyralyev A. and Sobolevskii P.E., New Difference Schemes for Partial Differential Equations. Birkhauser Verlag: Basel. Boston. Berlin, vol. 148, 2004, 443 p. 2. Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, New York, 1993." |
| References: | Ashyralyev A., Computational Mathematics, Textbook, The South Kazakhstan State University named after M. Auezovuku Printing House, Chimkent, 2014, 145 pages. "1. Ashyralyev A. and Sobolevskii P.E., New Difference Schemes for Partial Differential Equations. Birkhauser Verlag: Basel. Boston. Berlin, vol. 148, 2004, 443 p. 2. Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, New York, 1993." |
| Semester Requirements | Number of Activities | Level of Contribution |
| Attendance | % 0 | |
| Laboratory | % 0 | |
| Application | % 0 | |
| Field Work | % 0 | |
| Special Course Internship (Work Placement) | % 0 | |
| Quizzes | % 0 | |
| Homework Assignments | % 0 | |
| Presentation | % 0 | |
| Project | % 0 | |
| Seminar | % 0 | |
| Midterms | 1 | % 40 |
| Preliminary Jury | % 0 | |
| Final | 1 | % 60 |
| Paper Submission | % 0 | |
| Jury | % 0 | |
| Bütünleme | % 0 | |
| Total | % 100 | |
| PERCENTAGE OF SEMESTER WORK | % 40 | |
| PERCENTAGE OF FINAL WORK | % 60 | |
| Total | % 100 | |
| Activities | Number of Activities | Duration (Hours) | Workload |
| Course Hours | 14 | 3 | 42 |
| Laboratory | 0 | 0 | 0 |
| Application | 0 | 0 | 0 |
| Special Course Internship (Work Placement) | 0 | 0 | 0 |
| Field Work | 0 | 0 | 0 |
| Study Hours Out of Class | 14 | 8 | 112 |
| Presentations / Seminar | 0 | 0 | 0 |
| Project | 0 | 0 | 0 |
| Homework Assignments | 0 | 0 | 0 |
| Quizzes | 0 | 0 | 0 |
| Preliminary Jury | 0 | 0 | 0 |
| Midterms | 1 | 2 | 2 |
| Paper Submission | 0 | 0 | 0 |
| Jury | 0 | 0 | 0 |
| Final | 1 | 2 | 2 |
| Total Workload | 158 | ||
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution |