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 15:0016:30, Wednesday 11:0012:30
Office Hour(s)
Wednesday 13:0014:00 IKUCATS
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, ISBN13:9780538735643.
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
Roundoff Errors, Computer Arithmetic and Rate of Convergence
Romberg Integration, Elementary Theory of InitialValue Problems Euler’s Method
Lectures and recitation
14. Week
Modified Euler, Heun and RungeKutta 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
PO1
Adequate 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.
PO2
Ability to formulate, and solve complex engineering problems; ability to select and apply proper analysis and modeling methods for this purpose.
PO3
Ability 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.
PO4
Ability 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.
PO5
Ability to design and conduct experiments, gather data, analyze and interpret results for investing complex engineering problems or discipline specific research questions.
PO6
Ability to work efficiently in intradisciplinary and multidisciplinary teams; ability to work individually.
PO7
Ability 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.
PO8
Awareness of the need for lifelong learning; ability to access information, to follow developments in science and technology, and to continue to educate him/herself.
PO9
Knowledge on behavior according ethical principles, professional and ethical responsibility and standards used in engineering practices.
PO10
Knowledge about business life practices such as project management, risk management, and change management; awareness in entrepreneurship, innovation; knowledge about sustainable development.
PO11
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.
Learning Outcomes
LO1
Understand IEEE standard binary floating point format, machine precision and computer errors. (KNOWLEDGE)
LO2
Develop understanding of the Talyor series to set up approximate polynomials. (KNOWLEDGE)
LO3
Use 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)
LO4
Use the iterative method to find the fixed point of the function f(x), and analyze the error of the algorithm after n steps. (KNOWLEDGE)
LO5
Use Newton's method or the Secant method to solve the equation f(x)=0 within the given tolerance. (KNOWLEDGE)
LO6
Use 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)
LO7
Derive difference formulas to approximate derivatives of functions and use the Lagrange polynomial to estimate the errors of the approximations. (KNOWLEDGE)
LO8
Use the open or closed NewtonCotes 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 NewtonCotes formula. (KNOWLEDGE)
LO9
Calculate improper integrals in numerical ways. (KNOWLEDGE)