MATH207 Vector Calculus
MATH207 Vector Calculus
Syllabus | International University of Sarajevo - Last Update on Feb 02, 2026
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Faculty of Engineering and Natural Sciences
Seyednima Rabiei
Course Lecturer
Course Objectives
This course is intended to cover mulit-variable and vector calculus which are useful Mathematical methods and tools to engineering students that are related to solving practical problems . Topics include vector, multi-variable functions, partial derivatives, double and triple integral, polar, cylindrical and spherical coordinates, integration on line and surfaces. After completing this course, students should be able to: 1. Understand the concepts of Multi variable functions, vector valued functions, vector field and their limits, continuity, partial derivatives and directional derivatives. 2. Calculate the gradients, curl, divergence and volume of solids. 3. Apply change of Variables for Multiple Integrals (double and triple integrals). 4. Solve problems involving line integrals and surface integrals. 5. Use the Stokes’ theory and Divergence’s theory to simplify calculation of integral.
Learning Outcomes
After successful completion of the course, the student will be able to:
Course Materials
Required Textbook
1. Calculus, Ron Larson, Bruce Edwards. 2. Vector Calculus, Marsden.
Additional Literature
Vector Calculus, Susan Jane Colley.Teaching Methods
Class lectures with lots of examples
Active tutorial sessions for engaged learning and continuous feedback on progress
Homework with more challenging or theoretical assignments
Weekly Topics
| Week | Topic | Readings / References |
|---|---|---|
| 1 | The inner products, length, distances, matrices, determinants and the cross products. | |
| 2 | The geometry of real-valued functions. Limits and continuity. | |
| 3 | Differentiation. Introduction to path and curves. | |
| 4 | Properties of the derivatives. Gradients and directional derivatives. | |
| 5 | Maxima and minima in several variables. | |
| 6 | Vector valued functions. Arc length. Vector fields. Divergence and Curl. | |
| 7 | Double integrals over a rectangles. The double integrals over more general region. | |
| 8 | Changing the order of integration. Change of variables ( polar coordinates) | |
| 9 | Triple integrals. Change of variables(cylindrical coordinates)(Midterm Exam) | |
| 10 | Change of variables (spherical coordinate). | |
| 11 | Line Integrals. | |
| 12 | Conservative Vector Fields and Independence of Path. | |
| 13 | surface integrals. | |
| 14 | Stokes theorem and Gauss' theorem. | |
| 15 | Review |
Course Schedule (All Sections)
| Section | Type | Day 1 | Venue 1 | Day 2 | Venue 2 |
|---|---|---|---|---|---|
| MATH207.1 | Course | Monday 12:00 - 14:50 | A F1.17 | - | - |
| MATH207.1 | Tutorial | Tuesday 09:00 - 11:50 | B F2.1 | - | - |
Office Hours & Room
Assessment Methods and Criteria
Assessment Components
Final Exam
AI: Not AllowedAlignment with Learning Outcomes : 3 4 5
Midterm Exam
AI: Not AllowedAlignment with Learning Outcomes : 1 2 3
Quizzes
AI: Not AllowedAlignment with Learning Outcomes : 1 2 3
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
42 hours ⏳ (14 week × 3 h)
Active Tutorials
28 hours ⏳ (14 week × 2 h)
Midterm Exam Study
12 hours ⏳ (1 week × 12 h)
Quizzes
9 hours ⏳ (3 week × 3 h)
Assignments
1 hours ⏳ (1 week × 1 h)
Home Study
42 hours ⏳ (14 week × 3 h)
Final Exam Study
16 hours ⏳ (1 week × 16 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 [MATH207] 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 Feb 02, 2026 | International University of Sarajevo
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Referencing Curricula Print this page
| Course Code | Course Title | Weekly Hours* | ECTS | Weekly Class Schedule | ||||||
| T | P | |||||||||
| MATH207 | Vector Calculus | 3 | 3 | 6 | ||||||
| Prerequisite | MATH101 | It is a prerequisite to | - | |||||||
| 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 |
|||||||
| nrabiei@ius.edu.ba | ||||||||||
| Assistant | Nima Rabiei | Assistant E-mail | nrabiei@ius.edu.ba | |||||||
| Course Objectives | This course is intended to cover mulit-variable and vector calculus which are useful Mathematical methods and tools to engineering students that are related to solving practical problems . Topics include vector, multi-variable functions, partial derivatives, double and triple integral, polar, cylindrical and spherical coordinates, integration on line and surfaces. After completing this course, students should be able to: 1. Understand the concepts of Multi variable functions, vector valued functions, vector field and their limits, continuity, partial derivatives and directional derivatives. 2. Calculate the gradients, curl, divergence and volume of solids. 3. Apply change of Variables for Multiple Integrals (double and triple integrals). 4. Solve problems involving line integrals and surface integrals. 5. Use the Stokes’ theory and Divergence’s theory to simplify calculation of integral. |
|||||||||
| Textbook | 1. Calculus, Ron Larson, Bruce Edwards. 2. Vector Calculus, Marsden. | |||||||||
| Additional Literature |
|
|||||||||
| Learning Outcomes | After successful completion of the course, the student will be able to: | |||||||||
| Teaching Methods | Class lectures with lots of examples. Active tutorial sessions for engaged learning and continuous feedback on progress. Homework with more challenging or theoretical assignments. | |||||||||
| Teaching Method Delivery | Face-to-face | Teaching Method Delivery Notes | ||||||||
| WEEK | TOPIC | REFERENCE | ||||||||
| Week 1 | The inner products, length, distances, matrices, determinants and the cross products. | |||||||||
| Week 2 | The geometry of real-valued functions. Limits and continuity. | |||||||||
| Week 3 | Differentiation. Introduction to path and curves. | |||||||||
| Week 4 | Properties of the derivatives. Gradients and directional derivatives. | |||||||||
| Week 5 | Maxima and minima in several variables. | |||||||||
| Week 6 | Vector valued functions. Arc length. Vector fields. Divergence and Curl. | |||||||||
| Week 7 | Double integrals over a rectangles. The double integrals over more general region. | |||||||||
| Week 8 | Changing the order of integration. Change of variables ( polar coordinates) | |||||||||
| Week 9 | Triple integrals. Change of variables(cylindrical coordinates)(Midterm Exam) | |||||||||
| Week 10 | Change of variables (spherical coordinate). | |||||||||
| Week 11 | Line Integrals. | |||||||||
| Week 12 | Conservative Vector Fields and Independence of Path. | |||||||||
| Week 13 | surface integrals. | |||||||||
| Week 14 | Stokes theorem and Gauss' theorem. | |||||||||
| Week 15 | Review | |||||||||
| Assessment Methods and Criteria | Evaluation Tool | Quantity | Weight | Alignment with LOs | AI Usage |
| Final Exam | 1 | 40 | 3,4,5 | Not Allowed | |
| Semester Evaluation Components | |||||
| Midterm Exam | 1 | 40 | 1,2,3 | Not Allowed | |
| Quizzes | 2 | 20 | 1,2,3 | Not Allowed | |
| *** ECTS Credit Calculation *** | |||||
| Activity | Hours | Weeks | Student Workload Hours | Activity | Hours | Weeks | Student Workload Hours | |||
| Lecture Hours | 3 | 14 | 42 | Active Tutorials | 2 | 14 | 28 | |||
| Midterm Exam Study | 12 | 1 | 12 | Quizzes | 3 | 3 | 9 | |||
| Assignments | 1 | 1 | 1 | Home Study | 3 | 14 | 42 | |||
| Final Exam Study | 16 | 1 | 16 | |||||||
| Total Workload Hours = | 150 | |||||||||
| *T= Teaching, P= Practice | ECTS Credit = | 6 | ||||||||
| Course Academic Quality Assurance: Semester Student Survey | Last Update Date: 21/02/2026 | |||||||||