381 Numerical Analysis 1
Catalog description:
Solutions of nonlinear equations. Bisection, Newton`s,
secant and fixed point iteration methods. Convergence, stability, error analysis
and conditioning. Solving systems of linear equations: The LU and Cholesky
factorization, pivoting, error analysis in Gaussian elimination.
Matrix eigenvalue problem, power method, orthogonal factorizations and least
squares problems
Course Objectives:
The objective of this course is to provide students
mathematical foundations of numerical methods to analyze their stability,
accuracy and mathematical complexity and demonstrate their performance
in examples.
Text and Reference Books:
1. W. Cheney, D. Kincaid, Numerical mathematics and and computations
2. M. Tezer, C. Bozkaya, Numerical Analysis
3. R. Burden and J. Faires, Numerical Analysis
4. Johnson and Riesz, 1982, Numerical Analysis
Exams and Grading:
There will be five midterm exams (each of which is out of 14 %) and one final exam (out of 30 %).
Exam 1: 10 November 2020
Exam 2: 24 November 2020
Exam 3: 15 December 2020
Exam 4: 29 December 2020
Exam 5: 12 January 2020
Lecture Hours: Tuesday 13:40-15:30,
Thursday 12:40-13:30
NA Policy:
If you miss at least three exams, you will receive a grade
of NA for the course. 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. A student cannot get make-up examinations
for two or more missed exams. The make-up examination for all exams will be after
the all exams and will include all topics.
Important Dates:
October 12: Classes start
October 19-23: Add-drop
October 29: Holiday (Thursday)
December 14-20: Withdrawal deadline
January 1: Holiday (New year's day)
January 15: Classes end
January 19-30: Final Exams
February 8: Grades announced
Course Schedule
1-2 weeks: Mathematical preliminaries. Review of basic concepts.
Error analysis. Error propagation. Stability.
2-3 weeks: Solutions of nonlinear equations. Bisection method.
Newton's method. Secant method. Fixed point iteration. Convergence.
Roots of Polynomials
4-6 weeks Solving systems of linear equations Matrix Algebra.
LU factorizations. Gaussian elimination method. Pivoting. Norms and error analysis.
Iterative methods for solving linear systems.
3-4 weeks Eigenvalue problems. Localization of eigenvalues. Iterative techniques
to compute eigenvalues. Power method.
Inverse Power method. Orthogonal matrices and factorizations
Syllabus