NUMERICAL ANALYSIS

Course Description

The aim of this course is to give fundamental methods to solve numerical problems in mathematics, computer science, physical sciences and engineering. Topics included are as follow: Definitions: Error types, Taylor series and truncation error and rounding numbers. Numerical solution of nonlinear equations; Bracketing methods, Bisection and False position, Iterative methods: Fixed point and Newton method. Numerical methods for solution of linear systems, Iterative methods and LU decomposition methods. Interpolation and polynomial approximation, Lagrange polynomials, Least square lines, curve fitting and spline functions (linear and quadratic). Evaluate derivatives by numerical analysis, numerical differentiation, finite difference formulas. Evaluate integrals by numerical analysis, numerical integration, Simpson's rules and Trapezoidal rules.

NUMERICAL ANALYSIS

Evaluation Tools (Active Term)

Course outcomes

1. 01 Able to identify numerical analysis methods
2. 02 Able to solve nonlinear equations
3. 03 Able to solve linear/nonlinear systems
4. 04 Able to use numerical methods to find interpolation
5. 05 Able to evaluate derivatives and integrals by using numerical analysis
6. 06 Able to use numerical methods to solve engineering problems

Course Syllabus

Reference Books & Course Materials

1. 01 Numerical Analysis, Richard L. Burden, J. Dougles Faires, 9th Edition. ISBN-13: 978-0-538-73351-9
2. 02 Elementary Numerical Analysis , An Algorithm Approach, Third Edition, Samuel D. Conte,Carle de Boor, McGRAW HILL. ISBN-13: 978-0070124479 ISBN-10: 0070124477
3. 03 Numerical Methods Using Matlab, John H. Mathews, Kurtis D. Fink . ISBN 978–0–07–305194–9—ISBN 0–07–305194–2

Learning Outcomes

1. L01 Able to identify numerical analysis methods
2. L02 Able to solve nonlinear equations
3. L03 Able to solve linear/nonlinear systems
4. L04 Able to use numerical methods to find interpolation
5. L05 Able to evaluate derivatives and integrals by using numerical analysis
6. L06 Able to use numerical methods to solve engineering problems

Program Outcomes

1. P01 Adequate knowledge in mathematics, science and engineering subjects pertaining to the relevant discipline; ability to use theoretical and applied knowledge in these areas in complex engineering problems.
2. P02 Ability to identify, formulate, and solve complex engineering problems; ability to select and apply proper analysis and modelling methods for this purpose.
3. P03 Ability to design a complex system, process, device or product under realistic constraints and conditions, in such a way as to meet the desired result; ability to apply modern design methods for this purpose.
4. P04 Ability to devise, select, and use modern techniques and tools needed for analysing and solving complex problems encountered in engineering practice; ability to employ information technologies effectively
5. P05 Ability to design and conduct experiments, gather data, analyse and interpret results for investigating complex engineering problems or discipline specific research questions.
6. P06 Ability to work efficiently in intra-disciplinary and multi-disciplinary teams; ability to work individually.
7. P07 Ability to communicate effectively in Turkish, both orally and in writing; knowledge of a minimum of one foreign language; ability to write effective reports and comprehend written reports, prepare design and production reports, make effective presentations, and give and receive clear and intelligible instructions.
8. P08 Recognition of the need for lifelong learning ; ability to access information, to follow developments in science and technology, and to continue to educate him/herself.
9. P09 Consciousness to behave according to ethical principles and professional and ethical responsibility; knowledge on standards used in engineering practice.
10. P10 Knowledge about business life practices such as project management, risk management, and change management; awareness in entrepreneurship, innovation; knowledge about sustainable development.
11. P11 Knowledge about the global and social effects of engineering practices on health, environment, and safety, and contemporary issues of the century reflected into the field of engineering; awareness of the legal consequences of engineering solutions.

Po-Lo Matrix