382 Numerical Analysis II
Catalog description:
Approximating functions: polynomial interpolation, divided differences,
Hermite interpolation, spline interpolation, the B-splines, Taylor Series,
least square app-roximation. Numerical differentiation and integration based on interpolation.
Richardson extrapolation, Gaussian quadrature, Romberg integration,
adaptive quadrature, Bernoulli polynomials and Euler-Maclaurin formula
Course Objectives:
At the end of this course, the student will gain :
-an ability to apply knowledge of different numerical interpolation techniques for approximating functions
-an ability to apply knowledge of numerical differentiation via interpolation
-an ability to apply knowledge of numerical integration approaches via interpolation.
Text and Reference Books:
1. Numerical Analysis. Mathematics of Scientific Computing, W. Cheney, D. Kincaid, Books/Cole Publishing, (1991)
2. Numerical Mathematics and Computing, 6th edition, D. Kincaid , W. Cheney. Thomson Brooks/Cole, (2008)
3. Numerical Analysis, M. Tezer, C. Bozkaya, METU(2018)
3. Numerical Analysis, R. Burden and J. Faires,
4. Introduction to Numerical Analysis, J. Stoer and R. Bulirsch, Springer (1976)
Grading:
60% (Midterm exam + possible quizzes/Hmws)
40% (Final exam + possible Oral exam)
Exam Date: 3 May, Monday 10:40 (via zoom)
Lecture Hours: Monday 10:40-12:30,
Thursday 15:40-16:30
Note :
All exams will be online (via zoom). All participants accept to have webcamera in order to take those exams
NA Policy:
If you miss more than three quizes or two quizes and one midterm exam, you will receive NA
Attendence of online lectures are strictly encouraged.
Make-up Policy:
In order to be eligible to enter a make-up examination for a missed examination, a
student should have a documented or verifiable, and officially acceptable excuse.
However, due to electricty cut during online-exam(s), infection, or special reason(s),
the instructor may provide make up exam. A student cannot get make-up examinations
for two missed exams. Only ONE make up exam is offered.
The make-up examination will be after the final exam and will include all topics.
Important Dates:
March 15: Classes start
March 22-26: Add-drop
April 23: Holiday (Friday)
May 1:Holiday (Saturday)
May 8-16: Spring break
May 13-15: Religious break
May 17-23: Course withdrawal applications
May 19: Holiday (Wednesday)
June 25: Last day of classes
June 28- July 10: Final Exams
Course Topics
1. Approximating Functions:
Polynomial interpolation
Divided differences
Hermite interpolation
Spline interpolation
Interpolation Error
2. Numerical differentiation:
Differentiating via polynomial interpolation
Richardson Extrapolation
3. Numerical Integration
Integration via polynomial interpolation
Trapezoid rule
Method of undetermined coefficients
Simpsons rule
Error analysis
Gaussian quadrature
Romberg integration
Syllabus