Industrial Engineering | |||||
Bachelor | TR-NQF-HE: Level 6 | QF-EHEA: First Cycle | EQF-LLL: Level 6 |
Course Code: | MAT202 | ||||
Course Name: | Numerical Analysis | ||||
Course Semester: | Spring | ||||
Course Credits: |
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Language of instruction: | TR | ||||
Course Requirement: | |||||
Does the Course Require Work Experience?: | No | ||||
Type of course: | Necessary | ||||
Course Level: |
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Mode of Delivery: | Face to face | ||||
Course Coordinator : | Assoc. Prof. HATİCE ESRA ÖZKAN UÇAR | ||||
Course Lecturer(s): | Dr. Öğr. Üyesi M. Fatih UÇAR | ||||
Course Assistants: |
Course Objectives: | Basic numerical methods, algorithms and programming techniques used to find solutions to mathematical problems are explained. At the end of this course, the student learns how to approach a given problem numerically with numerical methods developed using basic analysis techniques. |
Course Content: | Approaching methods to problems with basic numerical algorithms. |
The students who have succeeded in this course;
1) It understands standard IEEE binary floating point arithmetic, machine precision, and calculates its error. 2) It approximates functions using Taylor polynomials and calculates an upper limit for the resulting error. 3) It solves the equation f(x)=0 using the bisection algorithm and calculates the number of steps required for a given precision. 4) Calculates the fixed points of the f(x) function using an iterative method. 5) For a given ratio range, it finds the solutions of the equation f(x)=0 using Newton, Newton-Raphson and secant methods. 6) Performs polynomial interpolation for curve fitting using Lagrange polynomials, learns and applies the Neville method, and uses the Newton divided difference algorithm. 7) It deduces the difference formulas used to approximate the derivative of a function and calculates the error in the approximation using Lagrange polynomials. 8) Performs numerical definite integration calculations using open-closed Newton-Cotes formulas, trapezoidal and Simpson rules, and obtains and uses compound integration formulas. 9) Calculates generalized integrals using numerical methods. |
Week | Subject | Related Preparation |
1) | Preliminary Information: Limits and Continuity, Differentiability, Integration, Taylor Polynomials and Series | J. Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University, 2013. Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3. |
2) | Rounding Errors, Decimal Machine Numbers, and Convergence Speed | J. Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University, 2013. Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3. |
3) | Bisection Method; Fixed Point Iteration | J. Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University, 2013. Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3. |
4) | Newton and Secant Methods | J. Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University, 2013. Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3. |
5) | Regula False Method, Interpolation | J. Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University, 2013. Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3. |
6) | Lagrange Interpolation Polynomials, Neville Method | J. Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University, 2013. Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3. |
7) | Inverse Interpolation, Split Differences | J. Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University, 2013. Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3. |
7) | Inverse Interpolation, Split Differences | J. Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University, 2013. Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3. |
8) | Forward, Reverse Differences | J. Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University, 2013. Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3. |
9) | Central Differences | J. Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University, 2013. Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3. |
10) | Numerical Differential: Richardson Extrapolation | J. Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University, 2013. Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3. |
11) | Numerical Integration: Explicit and Implicit Newton-Cotes Formulas | J. Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University, 2013. Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3. |
12) | Rounding Errors Occurring in Compound Numerical Integration and Compound Integral Calculation | J. Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University, 2013. Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3. |
13) | Romberg Integration, Numerical Solutions of Initial Value Problems: Euler, Mid-Point Method | J. Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University, 2013. Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3. |
14) | Modified Euler, Heun and Runge-Kutta Methods | J. Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University, 2013. Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3. |
15) | final exam | |
16) | final exam |
Course Notes / Textbooks: | -J. Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University, 2013. -Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3. -K. Atkinson and W. Han, Elementary Numerical Analysis, John Wiley, 3rd edition. -Cheney,W.,-Kincaid,D., Numerical Mathematics and Computing,Brooks,1985 |
References: | -J. Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University, 2013. -Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3. -K. Atkinson and W. Han, Elementary Numerical Analysis, John Wiley, 3rd edition. -Cheney,W.,-Kincaid,D., Numerical Mathematics and Computing,Brooks,1985 |
No Effect | 1 Lowest | 2 Medium | 3 Highest |
Program Outcomes | Level of Contribution | |
1) | Adequate knowledge in mathematics, science, and related engineering discipline; ability to use theoretical and practical knowledge in these areas in complex engineering problems. | 2 |
2) | An ability to detect, identify, formulate, and solve complex engineering problems; the ability to select and apply appropriate analysis and modelling methods for this purpose. | 3 |
3) | An ability to design a complex system, process, device, or product to meet specific requirements under realistic constraints and conditions; the ability to apply modern design methods for this purpose. | 1 |
4) | An ability to develop, select and use modern techniques and tools necessary for the analysis and solution of complex problems in engineering applications. | 2 |
5) | An ability to use information technologies effectively. | 2 |
6) | Ability to design, conduct experiments, collect data, analyse, and interpret results to investigate complex engineering problems or discipline-specific research topics. | 1 |
7) | Ability to work effectively in disciplinary and multidisciplinary teams; ability to work individually. | 1 |
8) | Ability to communicate effectively in oral and written Turkish. | 1 |
9) | Knowledge of at least one foreign language. | 1 |
10) | Ability to write effective reports and understand written reports, to prepare design and production reports, to make effective presentations, to give clear and understandable instructions. | 2 |
11) | Awareness of the necessity of lifelong learning; ability to access information, follow developments in science and technology and ability to renew themselves. | 2 |
Course | |
Homework | |
Problem Çözme |
Yazılı Sınav (Açık uçlu sorular, çoktan seçmeli, doğru yanlış, eşleştirme, boşluk doldurma, sıralama) | |
Homework |
Semester Requirements | Number of Activities | Level of Contribution |
Homework Assignments | 1 | % 20 |
Midterms | 1 | % 30 |
Final | 1 | % 40 |
Kanaat Notu | 1 | % 10 |
total | % 100 | |
PERCENTAGE OF SEMESTER WORK | % 60 | |
PERCENTAGE OF FINAL WORK | % 40 | |
total | % 100 |
Activities | Number of Activities | Aktiviteye Hazırlık | Aktivitede Harçanan Süre | Aktivite Gereksinimi İçin Süre | Workload | ||
Course Hours | 17 | 2 | 34 | ||||
Study Hours Out of Class | 1 | 6 | 6 | ||||
Midterms | 1 | 48 | 48 | ||||
Final | 1 | 48 | 48 | ||||
Total Workload | 136 |