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
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-1
Adequate knowledge in mathematics, science and engineering subjects pertaining to the relevant discipline; ability to use theoretical and applied information in these areas to model and solve engineering problems.
PO-2
Ability to identify, formulate, and solve complex engineering problems; ability to select and apply proper analysis and modeling methods for this purpose.
PO-3
Ability to design a complex system, process, device or product under realistic constraints and conditions, in such a way so as to meet the desired result; ability to apply modern design methods for this purpose. (Realistic constraints and conditions may include factors such as economic and environmental issues, sustainability, manufacturability, ethics, health, safety issues, and social and political issues according to the nature of the design.)
PO-4
Ability to devise, select, and use modern techniques and tools needed for engineering practice; ability to employ information technologies effectively.
PO-5
Ability to design and conduct experiments, gather data, analyze and interpret results for investigating engineering problems.
PO-6
Ability to work efficiently in intra-disciplinary and multi-disciplinary teams; ability to work individually.
PO-7
Ability to communicate effectively, both orally and in writing; knowledge of a minimum of one foreign language.
PO-8
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.
PO-9
Awareness of professional and ethical responsibility.
PO-10
Information about business life practices such as project management, risk management, and change management; awareness of entrepreneurship, innovation, and sustainable development.
PO-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 engineering solutions.
Learning Outcomes
LO-1
Understand IEEE standard binary floating point format, machine precision and computer errors. (KNOWLEDGE)
LO-2
Develop understanding of the Talyor series to set up approximate polynomials. (KNOWLEDGE)
LO-3
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)
LO-4
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)
LO-5
Use Newton's method or the Secant method to solve the equation f(x)=0 within the given tolerance. (KNOWLEDGE)
LO-6
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)
LO-7
Derive difference formulas to approximate derivatives of functions and use the Lagrange polynomial to estimate the errors of the approximations. (KNOWLEDGE)
LO-8
Use 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-9
Calculate improper integrals in numerical ways. (KNOWLEDGE)
