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.
-Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3.
-J. Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University, 2013.
Other Sources
-K. Atkinson and W. Han, Elementary Numerical Analysis, John Wiley, 3rd edition.
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,False Position Method
Romberg Integration, Elementary Theory of Initial-Value Problems Euler’s Method
Lectures and recitation
13. Week
Modified Euler, Heun and Runge-Kutta of Order 4 Methods
Lectures and recitation
14. Week
Iterative Methods for the Solution of Systems of Linear Equations
Lectures and recitation
15. Week
Final week
Exams
16. Week
Final week
Exams
17. Week
Final week
Exams
Assessments
Evaluation tools
Quantity
Weight(%)
Midterm(s)
1
40
Final Exam
1
60
Program Outcomes
PO-1
Interpreting advanced theoretical and applied knowledge in Mathematics and Computer Science.
PO-2
Critiquing and evaluating data by implementing the acquired knowledge and skills in Mathematics and Computer Science.
PO-3
Recognizing, describing, and analyzing problems in Mathematics and Computer Science; producing solution proposals based on research and evidence.
PO-4
Understanding the operating logic of computer and recognizing computational-based thinking using mathematics as a discipline.
PO-5
Collaborating as a team-member, as well as individually, to produce solutions to problems in Mathematics and Computer Science.
PO-6
Communicating in a foreign language, and interpreting oral and written communicational abilities in Turkish.
PO-7
Using time effectively in inventing solutions by implementing analytical thinking.
PO-8
Understanding professional ethics and responsibilities.
PO-9
Having the ability to behave independently, to take initiative, and to be creative.
PO-10
Understanding the importance of lifelong learning and developing professional skills continuously.
PO-11
Using professional knowledge for the benefit of the society.
Learning Outcomes
LO-1
Understand IEEE standard binary floating point format, machine precision and computer errors
LO-2
Develop understanding of the Talyor series to set up approximate polynomials.
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
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.
LO-5
Use Newton's method or the Secant method to solve the equation f(x)=0 within the given tolerance.
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.
LO-7
Derive difference formulas to approximate derivatives of functions and use the Lagrange polynomial to estimate the errors of the approximations.
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.
