MATH205 Numerical Analysis
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
Main objectives of the course are to teach the fundamentals of numerical methods, with emphasis on the most essential methods. Furthermore, this course aims to prepare students to be able to understand the uses and limitations of various numerical algorithms and to be able to identify appropriate application of said algorithms.
Learning Outcomes
After successful completion of the course, the student will be able to:
Course Materials
Required Textbook
Richard L. Burden, J. Douglas Faires, Annette M. Burden - Numerical Analysis. E.Suli, D.Mayers - An Introduction to Numerical Analysis
Additional Literature
Timothy Sauer - Numerical Analysis. Steven C. Chapra - Applied Numerical Methods with MATLAB for Engineers and Scientists. R.Bulirsch, J.Stoer - Introduction to Numerical AnalysisTeaching Methods
In this course, we combine theory with practical implementation
We use Julia or MATLAB programming languages to solve numerical problems and help students understand how the methods work in practice
Lectures include clear explanations, worked examples, and interactive class discussions
In addition, we have tutorial sessions where students solve exercises, discuss difficulties, and receive additional guidance
Students will also complete a small project in which they apply numerical techniques using Julia or MATLAB to solve a real problem
This approach helps strengthen both their theoretical understanding and computational skills
Weekly Topics
| Week | Topic | Readings / References |
|---|---|---|
| 1 | Error analysis, Overview of computer arithmetic and floating-point numbers | |
| 2 | Nonlinear Equations : Root-Finding Methods: Bisection method , Fixed-point iteration, Newton’s method , Secant method , Order of convergence | |
| 3 | Nonlinear Equations : Root-Finding Methods: Bisection method , Fixed-point iteration, Newton’s method , Secant method , Order of convergence | |
| 4 | Linear Systems: Gaussian elimination, Iterative Methods, Jacobi method Gauss–Seidel | |
| 5 | Linear Systems: Gaussian elimination, Iterative Methods, Jacobi method Gauss–Seidel | |
| 6 | Interpolation and Approximation | |
| 7 | Interpolation and Approximation | |
| 8 | Numerical Differentiation and Integration | |
| 9 | Midterm exam | |
| 10 | Numerical Differentiation and Integration | |
| 11 | Numerical Differentiation and Integration | |
| 12 | Ordinary Differential Equations: Initial Value Problems: (Euler method Improved Euler Runge–Kutta, ...) | |
| 13 | Ordinary Differential Equations: Initial Value Problems: (Euler method Improved Euler Runge–Kutta, ...) | |
| 14 | Ordinary Differential Equations: Boundary Value Problems: Finite Difference Method | |
| 15 | Ordinary Differential Equations: Boundary Value Problems: Shooting Method (Brief Introduction) |
Course Schedule (All Sections)
| Section | Type | Day 1 | Venue 1 | Day 2 | Venue 2 |
|---|---|---|---|---|---|
| MATH205.1 | Course | Tuesday 09:00 - 11:50 | A F1.24 - Amphitheater I | - | - |
| MATH205.1 | Tutorial | Thursday 15:00 - 16:50 | B F2.17 | - | - |
| MATH205.2 | Tutorial | Friday 10:00 - 11:50 | A F1.24 - Amphitheater I | - | - |
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 : 3 4
Midterm Exam
AI: Not AllowedAlignment with Learning Outcomes : 1 2 5 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
39 hours ⏳ (13 week × 3 h)
Assignments
30 hours ⏳ (3 week × 10 h)
Active Tutorials
18 hours ⏳ (9 week × 2 h)
Home Study
39 hours ⏳ (13 week × 3 h)
In-term Exam Study
8 hours ⏳ (1 week × 8 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 [MATH205] 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 | |||||||||
| MATH205 | Numerical Analysis | 3 | 2 | 6 | ||||||
| Prerequisite | MATH201, MATH202 | 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 | Assistant E-mail | |||||||||
| Course Objectives | Main objectives of the course are to teach the fundamentals of numerical methods, with emphasis on the most essential methods. Furthermore, this course aims to prepare students to be able to understand the uses and limitations of various numerical algorithms and to be able to identify appropriate application of said algorithms. |
|||||||||
| Textbook | Richard L. Burden, J. Douglas Faires, Annette M. Burden - Numerical Analysis. E.Suli, D.Mayers - An Introduction to Numerical Analysis | |||||||||
| Additional Literature |
|
|||||||||
| Learning Outcomes | After successful completion of the course, the student will be able to: | |||||||||
|
||||||||||
| Teaching Methods | In this course, we combine theory with practical implementation. We use Julia or MATLAB programming languages to solve numerical problems and help students understand how the methods work in practice. Lectures include clear explanations, worked examples, and interactive class discussions. In addition, we have tutorial sessions where students solve exercises, discuss difficulties, and receive additional guidance. Students will also complete a small project in which they apply numerical techniques using Julia or MATLAB to solve a real problem. This approach helps strengthen both their theoretical understanding and computational skills. | |||||||||
| Teaching Method Delivery | Face-to-face | Teaching Method Delivery Notes | ||||||||
| WEEK | TOPIC | REFERENCE | ||||||||
| Week 1 | Error analysis, Overview of computer arithmetic and floating-point numbers | |||||||||
| Week 2 | Nonlinear Equations : Root-Finding Methods: Bisection method , Fixed-point iteration, Newton’s method , Secant method , Order of convergence | |||||||||
| Week 3 | Nonlinear Equations : Root-Finding Methods: Bisection method , Fixed-point iteration, Newton’s method , Secant method , Order of convergence | |||||||||
| Week 4 | Linear Systems: Gaussian elimination, Iterative Methods, Jacobi method Gauss–Seidel | |||||||||
| Week 5 | Linear Systems: Gaussian elimination, Iterative Methods, Jacobi method Gauss–Seidel | |||||||||
| Week 6 | Interpolation and Approximation | |||||||||
| Week 7 | Interpolation and Approximation | |||||||||
| Week 8 | Numerical Differentiation and Integration | |||||||||
| Week 9 | Midterm exam | |||||||||
| Week 10 | Numerical Differentiation and Integration | |||||||||
| Week 11 | Numerical Differentiation and Integration | |||||||||
| Week 12 | Ordinary Differential Equations: Initial Value Problems: (Euler method Improved Euler Runge–Kutta, ...) | |||||||||
| Week 13 | Ordinary Differential Equations: Initial Value Problems: (Euler method Improved Euler Runge–Kutta, ...) | |||||||||
| Week 14 | Ordinary Differential Equations: Boundary Value Problems: Finite Difference Method | |||||||||
| Week 15 | Ordinary Differential Equations: Boundary Value Problems: Shooting Method (Brief Introduction) | |||||||||
| Assessment Methods and Criteria | Evaluation Tool | Quantity | Weight | Alignment with LOs | AI Usage |
| Final Exam | 1 | 40 | 3,4 | Not Allowed | |
| Semester Evaluation Components | |||||
| Midterm Exam | 1 | 60 | 1,2,5,3 | Not Allowed | |
| *** ECTS Credit Calculation *** | |||||
| Activity | Hours | Weeks | Student Workload Hours | Activity | Hours | Weeks | Student Workload Hours | |||
| Lecture Hours | 3 | 13 | 39 | Assignments | 10 | 3 | 30 | |||
| Active Tutorials | 2 | 9 | 18 | Home Study | 3 | 13 | 39 | |||
| In-term Exam Study | 8 | 1 | 8 | 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: 20/02/2026 | |||||||||