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)
None
Corequisite(s)
None
Special Requisite(s)
Read, understand, formulate, explain, and apply mathematical statements, and state and apply important results in key mathematical areas.
Instructor(s)
Assist. Prof. Dr. M. Fatih UÇAR
Course Assistant(s)
Schedule
Monday - 09:00~11:00, Thursday - 13:00~15:00
Office Hour(s)
Wednesday - 13:00~14:00 cats
Teaching Methods and Techniques
Lectures and recitation.
Principle Sources
-J. Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University, 2013.
Other Sources
-Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3.
-K. Atkinson and W. Han, Elementary Numerical Analysis, John Wiley, 3rd edition.
-W. Cheney, D. Kincaid, Numerical Mathematics and Computing.
-S. Chapra, R. Canale, Numerical Methods for Engineers.
Course Schedules
Week
Contents
Learning Methods
1. Week
Review of Calculus: Limits and Continuity, Differentiability, Integral, Taylor Polynomial and Series
Lectures and recitation
2. Week
Round-off Errors and Computer Arithmetic: Binary Machine Numbers, Decimal Machine Numbers, Rate of Convergence
Lectures and recitation
3. Week
The Bisection Method; Fixed-Point Iteration
Lectures and recitation
4. Week
The Newton's Method; The Secant Method
Lectures and recitation
5. Week
The Method of False Position; Error Analysis for Iterative Methods; Accelerating Convergence
Lectures and recitation
6. Week
Interpolation and the Lagrange Polynomial
Lectures and recitation
7. Week
Data Approximation and Neville's Method
Lectures and recitation
8. Week
Fist Midterm
Exam
9. Week
Divided Differences: Forward, Backward and Centered Differences
Lectures and recitation
10. Week
Numerical Differentiation: Three and Five Point Formulas
Numerical Integration
Lectures and recitation
11. Week
Numerical Differentiation: Second Derivative Midpoint Formula; Round-Off Error Instability
Lectures and recitation
12. Week
Numerical Integration: the Trapezoidal and Simpson's Rule
Lectures and recitation, Second Midterm Exam
13. Week
Numerical Integration: Open and Closed Newton-Cotes Formulas
Lectures and recitation
14. Week
Numerical Integration: Composite Numerical Integration and Round-Off Error Stability
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 fixed point iteration 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, Newton-Raphson'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.
LO-9
Derive the composite numerical integration using the open or closed Newton-Cotes formula.
