COURSE UNIT TITLE

: NUMERICAL ANALYSIS I

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MAT 3059 NUMERICAL ANALYSIS I COMPULSORY 4 0 0 7

Offered By

Mathematics (English)

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

ASSOCIATE PROFESSOR ÇETIN DIŞIBÜYÜK

Offered to

Mathematics (English)
Mathematics (Evening)

Course Objective

The concept of error, convergence and stability analysis is provided. The basic numerical methods and their analysis for solving linear and nonlinear equations, eigenvalue problems are given.

Learning Outcomes of the Course Unit

1   Will be able to adopt the concept error, convergence and stability.
2   Will be able to develop at least one solution to solve equations or system of equations or eigenvalue problem.
3   Will be able to write a matrix as product of upper and lower triangular matrices.
4   Will be able to find exact or approximate solution of equations or system of equations.
5   Will be able to identify sources and magnitude of error of approximation.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Basic Concepts and Taylor's Theorem Orders of convergence
2 Floating-Point Numbers and Roundoff Errors Absolute and relative error Stable and unstable computations: conditioning
3 Bisection method and its analysis, Newton s method, Quiz I
4 Error analysis of Newton Method, Secant Method and its Analysis.
5 -Fixed point and functional iteration, Contractive mapping and contractive mapping theorem
6 Solving linear system of equations: LU factorization Doolittle factorizaiton, Crout s factorization, Cholesky factorization, Block Matrices
7 Gauss Elimination, Partial Pivoting
8 Exercise and discussion
9 Nonlinear system of equations
10 Norms of Matrices, Neumann Series,
11 Condition number of matrices,
12 Iterative Methods: Jacobi Method, Gauss-Seidal method Gauss-Siedel Method
13 Eigenvalue problems: Gerchgorin s Theorem Power Method
14 Least-squares problems and SVD

Recomended or Required Reading

Textbook(s): :
Numerical Analysis 10th Edition, Richard L. Burden , J. Douglas Faires, Cengage Learning (December 17, 2014)
ISBN-13: 978-1305253667
ISBN-10: 1305253663
Numerical Analysis, 3rd editioni, Timothy Sauer, Pearson 2017.
SBN-13: 978-0134696454
ISBN-10: 9780134696454


Supplementary Book(s): Theory and Applications of Numerical Analysis, G. M. Phillips, P. J. Taylor 2nd ed. ISBN 9780125535601
Numerical Analysis, D. Kincaid, W Cheney 2nd ed. ISBN 0534338925

References:
Materials: Presentations

Planned Learning Activities and Teaching Methods

Presentation
Question-Answer
Solving Problems

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 VZ Vize
2 FN Final
3 BNS BNS VZ * 0.40 + FN * 0.60
4 BUT Bütünleme Notu
5 BBN Bütünleme Sonu Başarı Notu VZ * 0.40 + BUT * 0.60


Further Notes About Assessment Methods

None

Assessment Criteria

Mid Term + Final Exam

Language of Instruction

English

Course Policies and Rules

to be announced.

Contact Details for the Lecturer(s)

e-mail: cetin.disibuyuk@deu.edu.tr
Office: (232) 301 8581 , 2nd floor B251/2

Office Hours

to be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 14 4 56
Preparations before/after weekly lectures 14 5 70
Preparation for midterm exam 1 20 20
Preparation for final exam 1 25 25
Final 1 1,5 2
Midterm 1 1,5 2
TOTAL WORKLOAD (hours) 175

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12PO.13
LO.135522
LO.25555322
LO.35322
LO.45555323
LO.5555552253

CONTACT INFORMATION
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Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

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