CIVIL ENGINEERING | |||||

Bachelor | TR-NQF-HE: Level 6 | QF-EHEA: First Cycle | EQF-LLL: Level 6 |

Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |

MAT3012 | Numerical Analysis | Fall | 2 | 2 | 3 | 6 |

Language of instruction: | English |

Type of course: | Must Course |

Course Level: | Bachelor’s Degree (First Cycle) |

Mode of Delivery: | Hybrid |

Course Coordinator : | Dr. Öğr. Üyesi LAVDİE RADA ÜLGEN |

Course Lecturer(s): |
Dr. UTKU GÜLEN Dr. Öğr. Üyesi ERKUT ARICAN RA ÇİĞDEM ERİŞ Dr. Öğr. Üyesi LAVDİE RADA ÜLGEN |

Recommended Optional Program Components: | None |

Course Objectives: | Numerical Analysis is concerned with the mathematical derivation, description and analysis of obtaining numerical solutions of mathematical problems. We have several objectives for the students. Students should obtain an intuitive and working understanding of some numerical methods for the basic problems of numerical analysis. They should gain some appreciation of the concept of error and of the need to analyze and predict it. Topics cover linear and nonlinear system of equations, interpolation, curve fitting using least-squares method integration, eigenvalue, and singular value decomposition. And also they should develop some experience in the implementation of numerical methods by using MATLAB. |

The students who have succeeded in this course; 1. Define errors, big O notation, use Taylor’s theorem 2. Solve nonlinear algebraic equations 3. Solve linear systems and to use iterative methods for linear systems 4. Solve systems of nonlinear algebraic equations 5. Use interpolation methods and polynomial approximation for a given data, piecewise linear interpolation and spline function interpolation; 6. Use least-squares method for curve fitting 7. Calculate maximum eigenvalues and corresponding eigenvectors and to calculate singular value decomposition of a matrix and apply it on image processing 8. Implement numerical methods on MATLAB and test their programs behavior through expected results in accordance with the Numerical Analysis theory. |

The course studies algorithms and computer techniques for solving mathematical problems. They do all computations using MATLAB. |

Week | Subject | Related Preparation |

1) | Introduction to Numerical Analysis: kinds of problems we solve. Error analysis, round-off and truncation errors. Taylor Theorem and Taylor series. | |

2) | Loss of Significance Big O notation | |

3) | Solution of Nonlinear Equations, i.e. f(x)=0. Bracketing Methods for Locating a Root. Bisection (Method of Bolzano). False-position (Regula-Falsi) Method. | |

4) | Newton-Raphson Method (Applications from thermodynamics, fluid mechanics, and electronics) | |

5) | Solution of Linear Systems of Equations. Properties of Vectors and Matrices. Upper-Triangular Linear Systems. Gaussian Elimination and Pivoting. | |

6) | Triangular Factorization (LU Decomposition) | |

7) | Iterative Methods for Linear Systems. Jacobi Method. Gauss-Sedidel Method. | |

8) | Iterative Methods for Linear Systems Gauss-Sedidel Method. Diagonally dominant matrix. Errors is solving linear systems. | |

9) | System of Nonlinear Equations (Newton’s Method) | |

10) | Interpolation and Polynomial Approximation. Introduction to Interpolation. Lagrange Approximation. | |

11) | Newton Interpolation Polynomials. Piecewise Linear Interpolation, Cubic Spline Functions | |

12) | Curve Fitting (Applications from heat transfer and electrical engineering). Least-Squares Approximation. Linearization of Nonlinear Relationships. | |

13) | Eigenvalues and Eigenvectors. The power method | |

14) | Singular Value decomposition. Applications from Image Processing |

Course Notes / Textbooks: | Stephen C. Chapra, Applied Numerical Methods W/MATLAB: for Engineers & Scientists, 3rd Edition, McGrawHill |

References: | • J. Douglas Faires and Richard L. Burden, Numerical Methods, Brooks/Cole Publishing Co., 4th Edition, 2013. • Applied Numerical Methods Using MATLAB, Won Young Yang, Wenwu Cao, Tae-Sang Chung, John Morris. • John H. Mathews and Kurtis D. Fink Numerical Methods Using MATLAB, Pearson, 2004. ISBN 0-13-191178-3 • Mustafa Bayram, Nümerik Analiz, Sürat Üniversite Yayınları, 3. Baskı, 2013. • İrfan Karagöz, Sayısal Analiz ve Mühendislik Uygulamaları, Nobel Yayın Dağıtım, ISBN: 978-605-395-077-6. • Ömer Akın, Nümerik Analiz, Ankara Üniversitesi Basımevi, 1998, ISBN: 975-482-448-7 |

Semester Requirements | Number of Activities | Level of Contribution |

Quizzes | 3 | % 10 |

Homework Assignments | 1 | % 10 |

Midterms | 1 | % 35 |

Final | 1 | % 45 |

Total | % 100 | |

PERCENTAGE OF SEMESTER WORK | % 55 | |

PERCENTAGE OF FINAL WORK | % 45 | |

Total | % 100 |

Activities | Number of Activities | Duration (Hours) | Workload |

Course Hours | 14 | 2 | 28 |

Laboratory | 14 | 2 | 28 |

Study Hours Out of Class | 14 | 2 | 28 |

Homework Assignments | 1 | 4 | 4 |

Quizzes | 3 | 1 | 3 |

Midterms | 1 | 2 | 2 |

Final | 1 | 2 | 2 |

Total Workload | 95 |

No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |

Program Outcomes | Level of Contribution | |

1) | Adequate knowledge in mathematics, science and civil engineering; the ability to use theoretical and practical knowledge in these areas in complex engineering problems. | |

2) | Ability to identify, formulate, and solve complex engineering problems; ability to select and apply proper analysis and modeling methods for this purpose. | |

3) | Ability to design a complex system, process, structural and/or structural members to meet specific requirements under realistic constraints and conditions; ability to apply modern design methods for this purpose. | |

4) | Ability to develop, select and use modern techniques and tools necessary for the analysis and solution of complex problems encountered in civil engineering applications; ability to use civil engineering technologies effectively. | |

5) | Ability to design, conduct experiments, collect data, analyze and interpret results for the study of complex engineering problems or civil engineering research topics. | |

6) | Ability to work effectively within and multi-disciplinary teams; individual study skills. | |

7) | Ability to communicate effectively in English and Turkish (if he/she is a Turkish citizen), both orally and in writing. | |

8) | Awareness of the necessity of lifelong learning; ability to access information to follow developments in civil engineering technology. | |

9) | To act in accordance with ethical principles, professional and ethical responsibility; having awareness of the importance of employee workplace health and safety. | |

10) | Information about business life practices such as project management, risk management, and change management; awareness of entrepreneurship, innovation, and sustainable development. | |

11) | Knowledge about contemporary issues and the global and societal effects of engineering practices on health, environment, and safety; awareness of the legal consequences of civil engineering solutions. |