MATH205 Numerical Analysis
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| 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 | None |
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| Lecturer | Seyednima Rabiei | Office Hours / Room / Phone | Tuesday: 14:00-16:00 Thursday: 11:00-13:00 Friday: 12:00-14:00 |
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| nrabiei@ius.edu.ba | ||||||||||
| Assistant | Tarik | Assistant E-mail | tnamas@ius.edu.ba | |||||||
| Course Objectives | Main objectives of the course are to teach the fundamentals of numerical methods, with emphasis on the most essential methods. To provide students with opportunity to improve their programming skills using the MATLAB and Julia environments to implement algorithms. This course analyzed the basic techniques for the efficient numerical solution of problems in science and engineering. Topics spanned root finding, interpolation, approximation of functions, integration, differential equations and direct and iterative methods in linear algebra. |
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| Textbook | Richard L. Burden, J. Douglas Faires, Annette M. Burden. Numerical Analysis. | |||||||||
| Additional Literature |
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| Learning Outcomes | After successful completion of the course, the student will be able to: | |||||||||
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| Teaching Methods | Class discussions with examples, active tutorial sessions for engaged learning and continuous feedback on progress. Team projects that involve engineering problems, interpretation and reporting. | |||||||||
| Teaching Method Delivery | Face-to-face | Teaching Method Delivery Notes | ||||||||
| WEEK | TOPIC | REFERENCE | ||||||||
| Week 1 | Errors Analysis- Round-off Errors and Computer arithmetic - MATLAB and Julia introduction | |||||||||
| Week 2 | Solving Equations- The Bisection Method, Fixed-Point Iteration | |||||||||
| Week 3 | Newton's Methods, Root-Finding without Derivatives | |||||||||
| Week 4 | Interpolation and Polynomial Approximation- Interpolation and the Lagrange Polynomial, Divided Differences | |||||||||
| Week 5 | Hermit Interpolation, Chebyshev interpolation, Piece wise Interpolation | |||||||||
| Week 6 | Numerical Differentiation and Integration- Finite Difference Formulas, Rounding error | |||||||||
| Week 7 | Newton-cotes Formulas for Numerical Integration- Trapezoid Rule, Simpsons's Rule | |||||||||
| Week 8 | Composite Newton-Cotes Formulas, Open Newton-Cotes Methods | |||||||||
| Week 9 | Midterm Exam | |||||||||
| Week 10 | Ordinary Differential Equations- Initial Value Problems, Euler's Method | |||||||||
| Week 11 | Systems of Ordinary Differential Equations- Higher Order equations | |||||||||
| Week 12 | Runge-Kutta Methods and Applications | |||||||||
| Week 13 | Iterative Technique in Matrix Algebra- The Jacobi and Gauss-Siedel Iterative Techniques | |||||||||
| Week 14 | Least Squares, Fitting models to data | |||||||||
| Week 15 | Review | -- | ||||||||
| Assessment Methods and Criteria | Evaluation Tool | Quantity | Weight | Alignment with LOs |
| Final Exam | 1 | 30 | ||
| Semester Evaluation Components | ||||
| Quizzes-Homework | 4 | 40 | ||
| Midterm Exam | 1 | 31 | ||
| *** 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: 08/04/2024 | |||||||||