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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS MAT 3008 NUMERICAL ANALYSIS II ELECTIVE 4 0 0 7

Offered By

Mathematics (English)

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

PROFESSOR DOCTOR HALIL ORUÇ

Offered to

Mathematics (Evening) Mathematics (English)

Course Objective

This course aims to introduce students to the theory underlying numerical methods for approximation of functions and numerical differentiation and integration.

Learning Outcomes of the Course Unit

1   will be able write a polynomial for a function given with some of its data. 2   will be able to find a nearest curve to a function that lies on a different space. 3   will be able to choose points that minimize error of interpolation problem. 4   will be able to solve Numerical Differentiation. 5   will be able to solve Numerical Integration. 6   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 Polynomial Interpolation, Vandermonde Matrix, Lagrange Interpolation, Divided Difference Sec. 6.1, 6.2 Numerical Analysis, D. Kincaid, W Cheney 2 Equally spaced points, Forward difference, Backward difference, Central difference, Accuracy of interpolation Sec. 6.1 Numerical Analysis, D. Kincaid, W Cheney 3 Hermite interpolation, Divided difference method, Lagrange form of the Hermite interpolation Sec. 6.2, 6.3 Numerical Analysis, D. Kincaid, W Cheney 4 The choice of interpolating points (Optimal interpolation). Chebyshev polynomials, Sec. 6.1 Numerical Analysis, D. Kincaid, W Cheney 5 Weierstrass Approximation Theorem, Bohman-Korovkin Theorem, Bernstein Polynomials 6 Spline functions and interpolation, Cubic spline function, B-spline, Marsden s Identity Sec. 6.4 Numerical Analysis, D. Kincaid, W Cheney 7 Best Approximation-Least Square Theory, Sec. 6.8 Numerical Analysis, D. Kincaid, W Cheney 8 Problems and Solutions 9 Inner product spaces, Orthonormal systems Sec. 6.8, 6.9 Numerical Analysis, D. Kincaid, W Cheney 10 Legendre polynomials, Chebyshev polynomials, Gram Matrix Sec. 6.8, 6.9 Numerical Analysis, D. Kincaid, W Cheney 11 Numerical Differentiation and Integration, Differentiation via polynomial interpolation, Richardson Extrapolation Sec. 7.1 Numerical Analysis, D. Kincaid, W Cheney 12 Numerical integration, Trapezoid rule, Simpson s rule, Error analysis of Trapezoid and Simpson rules Sec. 7.2 Numerical Analysis, D. Kincaid, W Cheney 13 The method of undetermined coefficients, Change of intervals Sec. 7.3 Numerical Analysis, D. Kincaid, W Cheney 14 Gauss Quadrature, Error Formula Sec. 7.3 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 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

To be announced.

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 85 87

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 12 3 36 Preparation for midterm exam 1 30 30 Preparation for final exam 1 40 40 Final 1 2 2 Midterm 1 2 2 TOTAL WORKLOAD (hours) 166

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 5 5 5 5 2 2 2 LO.2 5 5 5 5 2 2 3 LO.3 5 5 2 4 LO.4 5 5 2 2 LO.5 5 5 2 2 LO.6 5 5 5 5 2 4