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| EEE3007 | Numerical Analysis | 3+0+0 | ECTS:4 | | Year / Semester | Fall Semester | | Level of Course | First Cycle | | Status | Elective | | Department | DEPARTMENT of ELECTRICAL and ELECTRONICS ENGINEERING | | Prerequisites and co-requisites | None | | Mode of Delivery | | | Contact Hours | 14 weeks - 3 hours of lectures per week | | Lecturer | Dr. Öğr. Üyesi Mehmet ÖZTÜRK | | Co-Lecturer | | | Language of instruction | | | Professional practise ( internship ) | None | | | | The aim of the course: | | Introduction of the Numerical Solutions and constructing a basis for the other numerical lectures. |
| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | Know the differences between Numerical Analysis and Analytical Analysis. | 2,3,4,12 | 1, | | LO - 2 : | Calculate the roots of functions / polynomials. | 2,3,4,12 | 1, | | LO - 3 : | Numerically solve differential and integral calculation problems. | 2,3,4,12 | 1, | | LO - 4 : | Solve linear equation sets. | 2,3,4,12 | 1, | | LO - 5 : | Numerically solve solutions of ordinary differential equations. | 2,3,4,12 | 1, | | CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), LO : Learning Outcome | | |
| Chapt. -1: Introduction; Basic concepts and definitions
Chapt. -2: Errors in Numerical Analysis
Chapt. -3: Matrixes
Chapt. -4: Solutions of the Equations in One Variable and the Equation Systems
Chapt. -5: Taylor Series and Finite Differences
Chapt. -6: Interpolations, Extrapolations
Chapt. -7: Numerical Differentiation
Chapt. -8: Numerical Integration
Chapt. -9: Numerical Solutions of the Ordinary Differential Equations
Chapt. -10: Least Square Method and Curve Fitting |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Approximation and Round-off Errors, Significant Figures, Accuracy and Precision, Error Definitions, Round-Off Errors, The Taylor Series
| | | Week 2 | The Bisection Method, Simple Fixed-Point Iteration, The Newton-Raphson Method, The Secant Method, Multiple Roots
| | | Week 3 | Roots of Polynomials, Conventional Methods, Müllers Method, Bairstows Method
| | | Week 4 | Cramer's rule, Naive Gauss Elimination, Gauss-Jordan, The Matrix Inverse
| | | Week 5 | LU Decomposition, Gauss-Seidel, Cholesky decomposition
| | | Week 6 | Linear Regression, Polynomial Regression, General Linear Least Squares
| | | Week 7 | Newtons Divided-Difference Interpolating Polynomials, Lagrange Interpolating Polynomials, Coefficients of an Interpolating Polynomial, Inverse Interpolation
| | | Week 8 | High-Accuracy Differentiation Formulas, Richardson Extrapolation, Derivatives of Unequally Spaced Data
| | | Week 9 | Mid-term exam
| | | Week 10 | The Trapezoidal Rule, Simpsons Rules, Integration with Unequal Segments, Open Integration Formulas
| | | Week 11 | Multiple Integrals, Newton-Cotes Algorithms for Equations, Improper Integrals
| | | Week 12 | Ordinary Differential Equations, Eulers Method, Improvements of Eulers Method
| | | Week 13 | Runge-Kutta Methods, Adaptive Runge-Kutta Methods
| | | Week 14 | Partial Differential Equations
| | | Week 15 | The Laplace Equation, Solution Technique, Boundary Conditions
| | | Week 16 | End-of-term exam
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| 1 | Chapra, Steven,Canale Raymond,1985,Numerical Methods For Engineers,McGrawHill,İSBN 0 07 010664-9 | | | |
| 1 | Akpınar, A.Sefa,2008,Sayısal Çözümleme,KTÜ Mühendislik Fakültesi Fakülte Ders Notları Serisi No::2,Trabzon | | | 2 | Akpınar, A.Sefa,Kürüm, Hasan,2005,Sayısal Çözümleme,Nobel Basımevi,Kitap,Yayın No:26 | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | | 1,5 | 50 | | End-of-term exam | 16 | | 1,5 | 50 | | |
| Student Work Load and its Distribution | | Type of work | Duration (hours pw) | No of weeks / Number of activity | Hours in total per term | | Yüz yüze eğitim | 3 | 14 | 42 | | Sınıf dışı çalışma | 2 | 14 | 28 | | Arasınav için hazırlık | 2 | 7 | 14 | | Arasınav | 1.5 | 1 | 1.5 | | Dönem sonu sınavı için hazırlık | 2 | 7 | 14 | | Dönem sonu sınavı | 1.5 | 1 | 1.5 | | Diğer 1 | 2 | 7 | 14 | | Total work load | | | 115 |
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