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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS MAT 4072 COMPUTATIONAL MATHEMATICS II ELECTIVE 4 0 0 7

Offered By

Mathematics

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

DOCTOR CEM ÇELIK

Offered to

Mathematics

Course Objective

The aim of this course is to combine basic mathematical expressions and methods with current programming languages and to learn how to solve mathematical problems using this programming languages when necessary.

Learning Outcomes of the Course Unit

1   Will be able to make symbolic solutions of differential equations and their types using computer. 2   Will be able to learn about floating-point numbers and types. 3   Will be able to learn real and complex intervals in computers and their arithmetic. 4   Will be able to use matrix decomposition methods. 5   Will be able to apply methods related to nonlinear equations. 6   Will be able to use numerical integration techniques.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description 1 First- and second-order differential equations. 2 The Laplace transform, and systems of linear differential equations. 3 Linear and non-homogeneous recurrence relations. 4 Floating-point numbers, rounding. 5 Complex floating-point numbers, real intervals. 6 Complex intervals, interval arithmetic. 7 Non-linear equations. 8 Midterm. 9 The fundamental theorem of algebra. 10 Iterative approximation methods. 11 Matrix norms and condition number. 12 Dense matrices, decomposition methods. 13 The method of least squares, curve fitting. 14 Numerical integration, multiple integrals.

Recomended or Required Reading

Textbook(s): Zimmermann P., Casamayou A., Cohen N., Connan G., Dumont T., Fousse L., Maltey F., Meulien M., Mezzarobba M., Pernet C., Thiéry N. M., Bray E., Cremona J., Forets M., Ghitza A., Thomas H., Computational Mathematics with SageMath, Philadelphia: Society for Industrial and Applied Mathematics, 2018. Supplementary Book(s): References: Materials: Instructor s notes and presentations.

Planned Learning Activities and Teaching Methods

Lecture Notes, Presentation, Problem Solving.

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA 1 MTE MIDTERM EXAM 2 FIN FINAL EXAM 3 FCG FINAL COURSE GRADE MTE * 0.40 + FIN * 0.60 4 RST RESIT 5 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.40 + FIN * 0.60 *** Resit Exam is Not Administered in Institutions Where Resit is not Applicable.

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)

To be announced.

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 4 48 Preparation for midterm exam 1 30 30 Preparation for final exam 1 30 30 Midterm 1 3 3 Final 1 3 3 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 5 4 LO.2 5 5 5 5 5 4 LO.3 5 5 5 5 5 4 LO.4 5 5 5 5 5 4 LO.5 5 5 5 5 5 4 LO.6 5 5 5 5 5 4