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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

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

PROFESSOR HALIL ORUÇ

Offered to

Mathematics (Evening) Mathematics

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 Sec. 1.1, 1.2 Numerical Analysis, D. Kincaid, W Cheney 2 Floating-Point Numbers and Roundoff Errors Absolute and relative error Stable and unstable computations: conditioning Sec. 2.2, 2.3 Numerical Analysis, D. Kincaid, W Cheney 3 Bisection method and its analysis, Newton s method, Quiz I Sec. 3.1, 3.2 Numerical Analysis, D. Kincaid, W Cheney 4 Error analysis of Newton Method, Secant Method and its Analysis. Sec. 3.2, 3.3 Numerical Analysis, D. Kincaid, W 5 -Fixed point and functional iteration, Contractive mapping and contractive mapping theorem Sec. 3.4 Numerical Analysis, D. Kincaid, W Cheney 6 Solving linear system of equations: LU factorization Doolittle factorizaiton, Crout s factorization, Cholesky factorization, Block Matrices Sec. 4.2, 4.3 Numerical Analysis, D. Kincaid, W Cheney 7 Gauss Elimination, Partial Pivoting Sec. 4.2, 4.3 Numerical Analysis, D. Kincaid, W Cheney 8 Mid-term exam 9 Solutions of mid-term examination 10 Nonlinear system of equations Sec. 3.6 Numerical Analysis, D. Kincaid, W Cheney 11 Norms of Matrices, Neumann Series, Condition number of matrices, Sec. 4.4, 4.5 Numerical Analysis, D. Kincaid, W Cheney 12 Iterative Methods: Jacobi Method, Gauss-Siedel Method Sec. 4.6 Numerical Analysis, D. Kincaid, W Cheney 13 Eigenvalue problems: Gerchgorin s Theorem Power Method Sec. 5.1, 5.2 Numerical Analysis, D. Kincaid, W Cheney 14 Least-squares problems, Sec. 5.3 Numerical Analysis, D. Kincaid, W Cheney

Recomended or Required Reading

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

Planned Learning Activities and Teaching Methods

Presentation Question-Answer Solving Problems

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA 1 MTE MIDTERM EXAM 2 QUZ QUIZ 3 FIN FINAL EXAM 4 FCG FINAL COURSE GRADE MTE * 0.25 + QUZ * 0.25 + FIN * 0.50 5 RST RESIT 6 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.25 + QUZ * 0.25 + RST * 0.50

Further Notes About Assessment Methods

None

Assessment Criteria

To be announced.

Language of Instruction

English

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

e-mail: meltem.evrenosoglu@deu.edu.tr Office: (232) 301 86 42

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours) Lectures 13 4 52 Preparations before/after weekly lectures 12 3 36 Preparation for midterm exam 1 20 20 Preparation for final exam 1 30 30 Preparation for quiz etc. 4 3 12 Preparing assignments 1 15 15 Final 1 2 2 Midterm 1 2 2 Quiz etc. 4 1 4 TOTAL WORKLOAD (hours) 173

Contribution of Learning Outcomes to Programme Outcomes

PO/LO PO.1 PO.2 PO.3 PO.4 PO.5 PO.6 PO.7 PO.8 PO.9 PO.10 PO.11 PO.12 PO.13 LO.1 3 5 5 2 2 LO.2 5 5 5 5 3 2 2 LO.3 5 3 2 2 LO.4 5 5 5 5 3 2 3 LO.5 5 5 5 5 5 2 2 5 3