MATH202 Differential Equations
MATH202 Differential Equations
Syllabus | International University of Sarajevo - Last Update on Oct 10, 2025
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Faculty of Engineering and Natural Sciences
Seyednima Rabiei
Course Lecturer
Course Objectives
Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations deal with functions of one variable, which can often be thought of as time. The goal of the course is to give students an understanding of the fundamental principles of ordinary differential equations and their applications to everyday life and technology and to develop an appreciation of ordinary differential equations topics as a human Endeavor, thereby enriching the students' experience of life. The course will provide a reasonably broad perspective of modeling using first order ordinary differential equations, and model solving, using them in the professional life, as well as further graduate studies in computer engineering, and other fields of engineering and after taking this course, students will be able to deal with the problems of engineering and science by the use of higher order ordinary differential equations and to develop an appreciation of ordinary differential equations modeling as a creative activity, using informed intuition and imagination to create an understanding of the beauty, simplicity and symmetry in the calculated nature. Course Policies The following are the policies for this course: 1. Attendance: It is mandatory to attend every lecture equipped with a writing instrument and either a notebook or papers. 2. Mobile Phone Usage: Mobile phones, including text messaging or checking messages, are strictly prohibited during lectures. Please ensure your mobile phone is turned off or set to silent mode. 3. Use of Electronic Devices: Laptops and other electronic devices are not permitted in the classroom unless you have obtained permission from the instructor to use them solely for note-taking purposes. 4. Language: English is the designated language for all classroom interactions and discussions. 5. Electronic Communication: All course-related electronic communication will be conducted through the university email or Teams platform. I will make every effort to respond to your emails within 24-48 hours. If you do not receive a reply within this timeframe, please feel free to resend your message. 6. Deadlines: It is crucial to adhere to all assignment and quiz deadlines. Late submissions will not be accepted unless accompanied by a serious and compelling reason, subject to instructor approval. Make-up assignments or quizzes will not be provided. By following these policies, we can ensure a productive and engaging learning environment for everyone in the course. Attendance Policy 1. It is mandatory for students to attend a minimum of 70 percent of lectures and 80 percent of other course components, such as tutorials, workshops, lab hours, and application classes, regardless of the reason for absence (medical or otherwise). This requirement is outlined in Article 16, item 1. 2. Failure to meet the attendance requirements may result in students being prohibited from taking the midterm and final examinations. This policy is stated in Article 16, item 2. 3. Exchange students are also expected to maintain a minimum attendance of 50 percent in all course activities, regardless of the reason for their absence (medical or otherwise). This is specified in Article 16, item 3. 4. If a student is unable to take an examination due to excessive absenteeism, they will receive a mark of "N/A" for that particular course. This is outlined in Article 16, item 4. 5. It is important to note that if a student is absent for one third or more of a class session, they will be considered absent. Additionally, three instances of tardiness will be counted as one absence. Leaving the class early will also be considered as being tardy. 6. In the event that a student misses a class, it is their responsibility to make up the material that was missed. By adhering to these attendance policies, students can ensure their academic success and maintain a positive learning environment.
Learning Outcomes
After successful completion of the course, the student will be able to:
Course Materials
Required Textbook
Dennis G. Zill. A First Course in Differential Equations with Modeling applications.
Additional Literature
C. Henry Edwards, David E. Penney. Elementary Differential Equations with Boundary Value Problems. Shepley l. Ross. Differential Equations. M. Can, E.Tacgin, R.Koker, c. Sarioglu. Differential Equations. R. Kent Nagle, Arthur David Snider, Edward B. Saff. Fundamentals of Differential EquationsTeaching Methods
Class discussions with examples
Active tutorial sessions for engaged learning and continuous feedback on progress
Weekly Topics
| Week | Topic | Readings / References |
|---|---|---|
| 1 | Introduction to Differential Equations. | |
| 2 | The General Solution of a Differential Equation. | |
| 3 | First Order Differential Equations. Separable Equations. Linear Equations.Exact Equations. | |
| 4 | Solutions by Substitutions. Modeling with First Order Differential Equations. | |
| 5 | Higher Order Differential Equations. Preliminary Theory-linear Equations. | |
| 6 | Initial Value and Boundary Value Problems. Homogeneous Equations. | |
| 7 | Non-Homogeneous Equations. Reduction of Order. Homogeneous linear Equations with Constant Coefficients | |
| 8 | Power Series Methods. Review of Power Series. Series solution Near Ordinary Points. | |
| 9 | Solutions about Singulars Points. Special Functions. | |
| 10 | Laplace Transform Methods. | |
| 11 | Linear systems of linear first order Differential Equations. Homogeneous linear systems | |
| 12 | Distinct Real Eigenvalues. Repeated Eigenvalues. complex Eigenvalues. | |
| 13 | Non-Homogeneous Linear system. | |
| 14 | Partial Differential Equations. | |
| 15 | Review |
Course Schedule (All Sections)
| Section | Type | Day 1 | Venue 1 | Day 2 | Venue 2 |
|---|---|---|---|---|---|
| MATH202.1 | Course | Wednesday 10:00 - 11:50 | B F2.15 - Amphitheater II | Tuesday 10:00 - 10:50 | B F2.16 |
| MATH202.2 | Course | Monday 09:00 - 10:50 | B F2.16 | Tuesday 13:00 - 13:50 | A F1.24 - Amphitheater I |
| MATH202.1 | Tutorial | Wednesday 09:00 - 10:50 | B F2.8 | - | - |
| MATH202.2 | Tutorial | Friday 14:00 - 15:50 | A F1.25 | - | - |
| MATH202.3 | Tutorial | Wednesday 12:00 - 13:50 | A F1.17 | - | - |
| MATH202.4 | Tutorial | Thursday 15:00 - 16:50 | A F2.13 | - | - |
Office Hours & Room
| Day | Time | Office | Notes |
|---|---|---|---|
| Monday | 10:00 - 11:30 | A F2.4 | |
| Tuesday | 13:00 - 15:00 | A F2.4 | |
| Wednesday | 13:00 - 15:00 | A F2.4 | |
| Thursday | 10:00 - 13:00 | A F2.4 | |
| Friday | 10:00 - 12:00 | A F2.4 |
Assessment Methods and Criteria
Assessment Components
Final Exam
AI: Not AllowedAlignment with Learning Outcomes : 1 2 3
Midterm Exam
AI: Not AllowedAlignment with Learning Outcomes : 1 2
Quizes
AI: Not AllowedAlignment with Learning Outcomes : 1 2
IUS Grading System
| Grading Scale | IUS Grading System | IUS Coeff. | Letter (B&H) | Numerical (B&H) |
|---|---|---|---|---|
| 0 - 44 | F | 0 | F | 5 |
| 45 - 54 | E | 1 | ||
| 55 - 64 | C | 2 | E | 6 |
| 65 - 69 | C+ | 2.3 | D | 7 |
| 70 -74 | B- | 2.7 | ||
| 75 - 79 | B | 3 | C | 8 |
| 80 - 84 | B+ | 3.3 | ||
| 85 - 94 | A- | 3.7 | B | 9 |
| 95 - 100 | A | 4 | A | 10 |
Late Work Policy
Information about late submission policies will be shared during class and posted in this section. Please check back for official guidelines.
ECTS Credit Calculation
📚 Student Workload
This 6 ECTS credit course corresponds to 150 hours of total student workload, distributed as follows:
Lecture Hours
45 hours ⏳ (15 week × 3 h)
Active tutorials
26 hours ⏳ (13 week × 2 h)
Home study
52 hours ⏳ (13 week × 4 h)
Midterm and quiz study
5 hours ⏳ (1 week × 5 h)
Final Exam study
12 hours ⏳ (1 week × 12 h)
Quiz Study
10 hours ⏳ (2 week × 5 h)
150 Total Workload Hours
6 ECTS Credits
Course Policies
Academic Integrity
All work submitted must be your own. Plagiarism, cheating, or any form of academic dishonesty will result in disciplinary action according to university policies. When in doubt about citation practices, consult the instructor.
Attendance Policy
Students are expected to adhere to the attendance requirements as outlined in the International University of Sarajevo Study Rules and Regulations. Excessive absences, whether excused or unexcused, may impact academic performance and eligibility for assessment. Mandatory sessions (e.g., labs, workshops) require attendance unless formally exempted. For detailed policies on absences, documentation, and penalties, please refer to the official university regulations.
Technology & AI Policy
Laptops/tablets may be used for note-taking only during lectures. Phones should be silenced and put away during all class sessions. Audio/video recording requires prior permission from the instructor.
Artificial Intelligence (AI) Usage: The use of AI tools (e.g., ChatGPT, Copilot, Gemini) varies by assessment component. Please refer to the AI usage indicator next to each assessment item in the Assessment Methods and Criteria section above. Submitting AI-generated content as your own work, where AI is not explicitly allowed, constitutes an academic integrity violation.
Communication Policy
All course-related communication should occur through official university channels (institutional email or SIS). Emails should include [MATH202] in the subject line.
Academic Quality Assurance Policy
Course Academic Quality Assurance is achieved through Semester Student Survey. At the end of each academic year, the institution of higher education is obliged to evaluate work of the academic staff, or the success of realization of the curricula.
Learning Tips
Be prepared to contribute thoughtfully during class discussions, labs, or collaborative work. Active participation deepens understanding and encourages critical thinking.
Complete assigned readings or prep materials before class. Take notes, highlight key ideas, and jot down questions. Aim to grasp core concepts and their applications—not just facts.
Use course frameworks or methodologies to analyze problems, case studies, or projects. Begin early to allow time for reflection and refinement. Seek feedback to improve your work.
Don’t hesitate to reach out when something is unclear. Use office hours, discussion boards, or peer networks to clarify concepts and stay on track.
Syllabus Last Updated on Oct 10, 2025 | International University of Sarajevo
Print Syllabus
Referencing Curricula Print this page
| Course Code | Course Title | Weekly Hours* | ECTS | Weekly Class Schedule | ||||||
| T | P | |||||||||
| MATH202 | Differential Equations | 3 | 2 | 6 | ||||||
| Prerequisite | MATH102 | It is a prerequisite to | EE309, ENS206, MATH205, ME208-6, ME304, ME306 | |||||||
| Lecturer | Seyednima Rabiei | Office Hours / Room / Phone | Monday: 10:00-11:30 Tuesday: 13:00-15:00 Wednesday: 13:00-15:00 Thursday: 10:00-13:00 Friday: 10:00-12:00 |
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| nrabiei@ius.edu.ba | ||||||||||
| Assistant | Nima Rabiei | Assistant E-mail | nrabiei@ius.edu.ba | |||||||
| Course Objectives | Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations deal with functions of one variable, which can often be thought of as time. The goal of the course is to give students an understanding of the fundamental principles of ordinary differential equations and their applications to everyday life and technology and to develop an appreciation of ordinary differential equations topics as a human Endeavor, thereby enriching the students' experience of life. The course will provide a reasonably broad perspective of modeling using first order ordinary differential equations, and model solving, using them in the professional life, as well as further graduate studies in computer engineering, and other fields of engineering and after taking this course, students will be able to deal with the problems of engineering and science by the use of higher order ordinary differential equations and to develop an appreciation of ordinary differential equations modeling as a creative activity, using informed intuition and imagination to create an understanding of the beauty, simplicity and symmetry in the calculated nature. Course Policies The following are the policies for this course: 1. Attendance: It is mandatory to attend every lecture equipped with a writing instrument and either a notebook or papers. 2. Mobile Phone Usage: Mobile phones, including text messaging or checking messages, are strictly prohibited during lectures. Please ensure your mobile phone is turned off or set to silent mode. 3. Use of Electronic Devices: Laptops and other electronic devices are not permitted in the classroom unless you have obtained permission from the instructor to use them solely for note-taking purposes. 4. Language: English is the designated language for all classroom interactions and discussions. 5. Electronic Communication: All course-related electronic communication will be conducted through the university email or Teams platform. I will make every effort to respond to your emails within 24-48 hours. If you do not receive a reply within this timeframe, please feel free to resend your message. 6. Deadlines: It is crucial to adhere to all assignment and quiz deadlines. Late submissions will not be accepted unless accompanied by a serious and compelling reason, subject to instructor approval. Make-up assignments or quizzes will not be provided. By following these policies, we can ensure a productive and engaging learning environment for everyone in the course. Attendance Policy 1. It is mandatory for students to attend a minimum of 70 percent of lectures and 80 percent of other course components, such as tutorials, workshops, lab hours, and application classes, regardless of the reason for absence (medical or otherwise). This requirement is outlined in Article 16, item 1. 2. Failure to meet the attendance requirements may result in students being prohibited from taking the midterm and final examinations. This policy is stated in Article 16, item 2. 3. Exchange students are also expected to maintain a minimum attendance of 50 percent in all course activities, regardless of the reason for their absence (medical or otherwise). This is specified in Article 16, item 3. 4. If a student is unable to take an examination due to excessive absenteeism, they will receive a mark of "N/A" for that particular course. This is outlined in Article 16, item 4. 5. It is important to note that if a student is absent for one third or more of a class session, they will be considered absent. Additionally, three instances of tardiness will be counted as one absence. Leaving the class early will also be considered as being tardy. 6. In the event that a student misses a class, it is their responsibility to make up the material that was missed. By adhering to these attendance policies, students can ensure their academic success and maintain a positive learning environment. |
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| Textbook | Dennis G. Zill. A First Course in Differential Equations with Modeling applications. | |||||||||
| Additional Literature |
|
|||||||||
| Learning Outcomes | After successful completion of the course, the student will be able to: | |||||||||
|
||||||||||
| Teaching Methods | Class discussions with examples. Active tutorial sessions for engaged learning and continuous feedback on progress. | |||||||||
| Teaching Method Delivery | Face-to-face | Teaching Method Delivery Notes | ||||||||
| WEEK | TOPIC | REFERENCE | ||||||||
| Week 1 | Introduction to Differential Equations. | |||||||||
| Week 2 | The General Solution of a Differential Equation. | |||||||||
| Week 3 | First Order Differential Equations. Separable Equations. Linear Equations.Exact Equations. | |||||||||
| Week 4 | Solutions by Substitutions. Modeling with First Order Differential Equations. | |||||||||
| Week 5 | Higher Order Differential Equations. Preliminary Theory-linear Equations. | |||||||||
| Week 6 | Initial Value and Boundary Value Problems. Homogeneous Equations. | |||||||||
| Week 7 | Non-Homogeneous Equations. Reduction of Order. Homogeneous linear Equations with Constant Coefficients | |||||||||
| Week 8 | Power Series Methods. Review of Power Series. Series solution Near Ordinary Points. | |||||||||
| Week 9 | Solutions about Singulars Points. Special Functions. | |||||||||
| Week 10 | Laplace Transform Methods. | |||||||||
| Week 11 | Linear systems of linear first order Differential Equations. Homogeneous linear systems | |||||||||
| Week 12 | Distinct Real Eigenvalues. Repeated Eigenvalues. complex Eigenvalues. | |||||||||
| Week 13 | Non-Homogeneous Linear system. | |||||||||
| Week 14 | Partial Differential Equations. | |||||||||
| Week 15 | Review | |||||||||
| Assessment Methods and Criteria | Evaluation Tool | Quantity | Weight | Alignment with LOs | AI Usage |
| Final Exam | 1 | 40 | 1,2 ,3 | Not Allowed | |
| Semester Evaluation Components | |||||
| Midterm Exam | 1 | 40 | 1,2 | Not Allowed | |
| Quizes | 2 | 20 | 1, 2 | Not Allowed | |
| *** ECTS Credit Calculation *** | |||||
| Activity | Hours | Weeks | Student Workload Hours | Activity | Hours | Weeks | Student Workload Hours | |||
| Lecture Hours | 3 | 15 | 45 | Active tutorials | 2 | 13 | 26 | |||
| Home study | 4 | 13 | 52 | Midterm and quiz study | 5 | 1 | 5 | |||
| Final Exam study | 12 | 1 | 12 | Quiz Study | 5 | 2 | 10 | |||
| Total Workload Hours = | 150 | |||||||||
| *T= Teaching, P= Practice | ECTS Credit = | 6 | ||||||||
| Course Academic Quality Assurance: Semester Student Survey | Last Update Date: 15/10/2025 | |||||||||