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Bachelor	TR-NQF-HE: Level 6	QF-EHEA: First Cycle	EQF-LLL: Level 6

Course General Introduction Information

Course Code:

MAT202

Course Name:

Numerical Analysis

Course Semester:

Spring

Course Credits:

ECTS

Language of instruction:

Course Requirement:

Does the Course Require Work Experience?:

Type of course:

Necessary

Course Level:

Bachelor

TR-NQF-HE:6. Master`s Degree

QF-EHEA:First Cycle

EQF-LLL:6. Master`s Degree

Mode of Delivery:

Face to face

Course Coordinator :

Assoc. Prof. HATİCE ESRA ÖZKAN UÇAR

Course Lecturer(s):

Dr. Öğr. Üyesi M. Fatih UÇAR

Course Assistants:

Course Purpose and Content

Course Objectives:	Basic numerical methods, algorithms and programming techniques used to find solutions to mathematical problems are explained. At the end of this course, the student learns how to approach a given problem numerically with numerical methods developed using basic analysis techniques.
Course Content:	Approaching methods to problems with basic numerical algorithms.

Learning Outcomes

The students who have succeeded in this course;
1) It understands standard IEEE binary floating point arithmetic, machine precision, and calculates its error.
2) It approximates functions using Taylor polynomials and calculates an upper limit for the resulting error.
3) It solves the equation f(x)=0 using the bisection algorithm and calculates the number of steps required for a given precision.
4) Calculates the fixed points of the f(x) function using an iterative method.
5) For a given ratio range, it finds the solutions of the equation f(x)=0 using Newton, Newton-Raphson and secant methods.
6) Performs polynomial interpolation for curve fitting using Lagrange polynomials, learns and applies the Neville method, and uses the Newton divided difference algorithm.
7) It deduces the difference formulas used to approximate the derivative of a function and calculates the error in the approximation using Lagrange polynomials.
8) Performs numerical definite integration calculations using open-closed Newton-Cotes formulas, trapezoidal and Simpson rules, and obtains and uses compound integration formulas.
9) Calculates generalized integrals using numerical methods.

Course Flow Plan

Week	Subject	Related Preparation
1)	Preliminary Information: Limits and Continuity, Differentiability, Integration, Taylor Polynomials and Series	J. Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University, 2013. Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3.
2)	Rounding Errors, Decimal Machine Numbers, and Convergence Speed	J. Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University, 2013. Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3.
3)	Bisection Method; Fixed Point Iteration	J. Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University, 2013. Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3.
4)	Newton and Secant Methods	J. Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University, 2013. Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3.
5)	Regula False Method, Interpolation	J. Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University, 2013. Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3.
6)	Lagrange Interpolation Polynomials, Neville Method	J. Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University, 2013. Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3.
7)	Inverse Interpolation, Split Differences	J. Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University, 2013. Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3.
7)	Inverse Interpolation, Split Differences	J. Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University, 2013. Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3.
8)	Forward, Reverse Differences	J. Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University, 2013. Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3.
9)	Central Differences	J. Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University, 2013. Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3.
10)	Numerical Differential: Richardson Extrapolation	J. Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University, 2013. Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3.
11)	Numerical Integration: Explicit and Implicit Newton-Cotes Formulas	J. Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University, 2013. Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3.
12)	Rounding Errors Occurring in Compound Numerical Integration and Compound Integral Calculation	J. Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University, 2013. Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3.
13)	Romberg Integration, Numerical Solutions of Initial Value Problems: Euler, Mid-Point Method	J. Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University, 2013. Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3.
14)	Modified Euler, Heun and Runge-Kutta Methods	J. Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University, 2013. Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3.
15)	final exam
16)	final exam

Sources

Course Notes / Textbooks:	-J. Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University, 2013. -Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3. -K. Atkinson and W. Han, Elementary Numerical Analysis, John Wiley, 3rd edition. -Cheney,W.,-Kincaid,D., Numerical Mathematics and Computing,Brooks,1985
References:	-J. Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University, 2013. -Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3. -K. Atkinson and W. Han, Elementary Numerical Analysis, John Wiley, 3rd edition. -Cheney,W.,-Kincaid,D., Numerical Mathematics and Computing,Brooks,1985

Course - Learning Outcome Relationship

No Effect	1 Lowest	2 Medium	3 Highest

	Program Outcomes	Level of Contribution
1)	Ability to utilize advanced theoretical and applied knowledge in the field.	1
2)	Using the advanced knowledge and skills acquired in the field, being able to interpret and evaluate data, identify problems, analyze them, and develop solution proposals based on research and evidence.	2
3)	Being able to organize and implement projects and activities for the social environment in which one lives with a sense of social responsibility.	2
4)	Being able to follow information in one foreign language at least at the European Language Portfolio B1 General Level and communicate with colleagues in the field.	1
5)	Ability to use information and communication technologies together with at least European Computer Driving License Advanced Level computer software, as required by the field.	1
6)	Being able to evaluate advanced knowledge and skills in the field critically.
7)	Identifying learning needs and being able to direct learning.
8)	Developing a positive attitude towards lifelong learning.	3
9)	Acting in accordance with social, scientific, cultural, and ethical values in the stages of collecting, interpreting, applying, and announcing the results related to the field.	2
10)	Having sufficient awareness about the universality of social rights, social justice, quality culture, preservation of cultural values, as well as environmental protection, occupational health, and safety.	1
11)	Being able to conduct an advanced study independently in the field.	1
12)	To take responsibility individually and as a team member to solve complex problems encountered in the field of application, which are unforeseen.	3
13)	Being able to plan and manage activities for the development of those under their responsibility within the framework of a project.	1
14)	Possess advanced level theoretical and practical knowledge supported by textbooks with updated information, practice equipments and other resources.	2
15)	Being able to inform relevant individuals and institutions about the field; expressing their thoughts and solution proposals for problems both in written and verbal form.	3
16)	Being able to share your thoughts and solutions regarding subjects related to the field with both experts and non-experts, supported by quantitative and qualitative data.	2

Learning Activity and Teaching Methods

Course
Homework
Problem Çözme

Measurement and Evaluation Methods and Criteria

Yazılı Sınav (Açık uçlu sorular, çoktan seçmeli, doğru yanlış, eşleştirme, boşluk doldurma, sıralama)
Homework

Assessment & Grading

Semester Requirements	Number of Activities	Level of Contribution
Homework Assignments	1	% 20
Midterms	1	% 30
Final	1	% 40
Kanaat Notu	1	% 10
total		% 100
PERCENTAGE OF SEMESTER WORK		% 60
PERCENTAGE OF FINAL WORK		% 40
total		% 100

İş Yükü ve AKTS Kredisi Hesaplaması

Activities	Number of Activities	Aktiviteye Hazırlık	Aktivitede Harçanan Süre	Aktivite Gereksinimi İçin Süre	Workload
Course Hours	17	2			34
Study Hours Out of Class	1	6			6
Midterms	1	48			48
Final	1	48			48
Total Workload					136