Undergraduate
Faculty of Engineering and Architecture
Civil Engineering
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Numerical Methods

Course CodeSemester Course Name LE/RC/LA Course Type Language of Instruction ECTS
MCB1008 2 Numerical Methods 4/0/0 CC English 6
Course Goals
This course introduces basic methods, algorithms and programming techniques to solve mathematical problems. The course is designed for students to learn how to develop numerical methods and estimate numerical errors using basic calculus concepts and results.
Prerequisite(s) -
Corequisite(s) -
Special Requisite(s) -
Instructor(s) Assist. Prof. Dr. MEHMET FATİH UÇAR
Course Assistant(s) -
Schedule Monday 15:00-16:30, Wednesday 11:00-12:30
Office Hour(s) Wednesday 13:00-14:00 IKU-CATS
Teaching Methods and Techniques -Lectures and recitation
Principle Sources -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.
Other Sources -K. Atkinson and W. Han, Elementary Numerical Analysis, John Wiley, 3rd edition.

-Cheney,W.,-Kincaid,D., Numerical Mathematics and Computing,Brooks,1985
Course Schedules
Week Contents Learning Methods
1. Week Review of Calculus, Taylor Polynomial Lectures and recitation
2. Week Round-off Errors, Computer Arithmetic and Rate of Convergence Lectures and recitation
3. Week The Bisection Method, Fixed-Point Iteration Lectures and recitation
4. Week Newton’s Method, Secant Method Lectures and recitation
5. Week False Position Method, Interpolation Lectures and recitation
6. Week Lagrange Interpolating Polynomial, Neville’s Method Lectures and recitation
7. Week Inverse Interpolation, Divided Differences Lectures and recitation
8. Week Forward-Backward Differences Exams
9. Week Centered Differences Lectures and recitation
10. Week Numerical Differentiation, Richardson Extrapolation Lectures and recitation
11. Week Numerical Integration, Open-Closed Newton-Cotes Formulas Lectures and recitation
12. Week Composite Numerical Integration, Error Analysis Lectures and recitation
13. Week Romberg Integration, Elementary Theory of Initial-Value Problems Euler’s Method Lectures and recitation
14. Week Modified Euler, Heun and Runge-Kutta of Order 4 Methods Lectures and recitation
15. Week
16. Week
17. Week
Assessments
Evaluation tools Quantity Weight(%)
Midterm(s) 1 30
Final Exam 1 70


Program Outcomes
PO-1Adequate knowledge in mathematics, science and engineering subjects pertaining to the relevant discipline; ability to use theoretical and applied knowledge in these areas in the solution of complex engineering problems.
PO-2Ability to formulate, and solve complex engineering problems; ability to select and apply proper analysis and modeling methods for this purpose.
PO-3Ability to design a complex systemi process, device or product under realistic constraints and conditions, in such a way as to meet the desired results; ability to apply modern design methods for this purpose.
PO-4Ability to select and use modern techniques and tools needed for analyzing and Solving complex problems encountered in engineering practice; ability to employ information technologies effectively.
PO-5Ability to design and conduct experiments, gather data, analyze and interpret results for investing complex engineering problems or discipline specific research questions.
PO-6Ability to work efficiently in intra-disciplinary and multi-disciplinary teams; ability to work individually.
PO-7Ability to communicate effectivley, 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 instruction.
PO-8Awareness of the need for lifelong learning; ability to access information, to follow developments in science and technology, and to continue to educate him/herself.
PO-9Knowledge on behavior according ethical principles, professional and ethical responsibility and standards used in engineering practices.
PO-10Knowledge about business life practices such as project management, risk management, and change management; awareness in entrepreneurship, innovation; knowledge about sustainable development.
PO-11Knowledge 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.
Learning Outcomes
LO-1Understand IEEE standard binary floating point format, machine precision and computer errors. (KNOWLEDGE)
LO-2Develop understanding of the Talyor series to set up approximate polynomials. (KNOWLEDGE)
LO-3Use the bisection method to solve the equation f(x)=0 and estimate the number of iterations in the algorithm to achieve desired accuracy with the given tolerance. (KNOWLEDGE)
LO-4Use the iterative method to find the fixed point of the function f(x), and analyze the error of the algorithm after n steps. (KNOWLEDGE)
LO-5Use Newton's method or the Secant method to solve the equation f(x)=0 within the given tolerance. (KNOWLEDGE)
LO-6Use polynomial interpolations, including the Lagrange polynomial for curve fitting, or data analysis; use Neville's iterative algorithm, Newton's divided difference algorithms to evaluate the interpolations. (KNOWLEDGE)
LO-7Derive difference formulas to approximate derivatives of functions and use the Lagrange polynomial to estimate the errors of the approximations. (KNOWLEDGE)
LO-8Use the open or closed Newton-Cotes formula, including the Trapezoidal rule and Simpson's rule, to approximate definite integrals; use the Lagrange polynomial to estimate the degree of accuracy; derive the composite numerical integration using the open or closed Newton-Cotes formula. (KNOWLEDGE)
LO-9Calculate improper integrals in numerical ways. (KNOWLEDGE)
Course Assessment Matrix:
Program Outcomes - Learning Outcomes Matrix
 PO 1PO 2PO 3PO 4PO 5PO 6PO 7PO 8PO 9PO 10PO 11