DEPARTMENT OF SOFTWARE ENGINEERING (ENGLISH)
Qualification Awarded	Program Süresi	Toplam Kredi (AKTS)	Öğretim Şekli	Yeterliliğin Düzeyi ve Öğrenme Alanı
Bachelor's (First Cycle) Degree	4	240	FULL TIME	TYÇ, TR-NQF-HE, EQF-LLL, ISCED (2011):Level 6 QF-EHEA:First Cycle TR-NQF-HE, ISCED (1997-2013): 48,52

Ders Genel Tanıtım Bilgileri

Course Code:

MTH204

Ders İsmi:

Numerical Analysis

Ders Yarıyılı:

Spring

Ders Kredileri:

Theoretical	Practical	Labs	Credit	ECTS
3	2	0	4	5

Language of instruction:

Ders Koşulu:

Ders İş Deneyimini Gerektiriyor mu?:

Other Recommended Topics for the Course:

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 :

Dr.Öğr.Üyesi Recep DURANAY

Course Lecturer(s):

Course Assistants:

Dersin Amaç ve İçeriği

Course Objectives:

To teach the solution of linear and nonlinear equations, interpolation polynomials, numerical derivation and integration, solutions of ordinary differential equations and solution of Laplace's equation

Course Content:

Lineer denklem sistemlerinin çözümü, Cramer kuralı, Jacobi iterasyonu, Gauss-Seidel yöntemi, Hata düzeltme metodu, Gauss-Jordan Metodu, Gauss Eliminasyonu, Non-lineer denklem sistemlerinin çözümü, Cramer kuralı, Secant yöntemi, Newton Raphson yöntemi, İnterpolasyon ve Extrapolasyon, Lineer İnterpolasyon, Taylor Polinomu ile Extrapolasyon, Bölünmüş fark serisi ile extrapolasyon, Lagrange polinomu ile extrapolasyon, Kuvvet serisi ile least-square extrapolasyonu, Quadratik bir polinomla least-square extrapolasyonu, Üstel fonksiyonlarda least-square extrapolasyonu, trigonometrik fonksiyonlarda least-square extrapolasyonu, Sayısal Türev, sayısal kısmi türev, Taylor serisinden türev formüllerinin belirlenmesi ve hata analizi, Bölünmüş fark serisinden türev formüllerinin belirlenmesi, Lagrange polinomu ile türev, Sayısal İntegrasyon, Dikdörtgenler kuralı, Trapez kuralı, Simpson 1/3 ve 3/8 kuralları, Çok katlı integraller, Romberg integrasyon kuralı, Fourier serileri, Fourier katsayıları, Tek ve çift fonksiyonların fourier açılımları, Adi Diferansiyel Denklemler, Başlangıç Değer Problemleri, Euler Yöntemi, Taylor Serisi Yöntemi, Runge-Kutta yöntemi, Sınır Değer Problemleri, Atma Değer yöntemi, Sonlu farklar yöntemi, Kısmı Diferansiyel Denklemler, Eliptik Denklemler

Learning Outcomes

The students who have succeeded in this course;

Learning Outcomes

1 - Knowledge
Theoretical - Conceptual
2 - Skills
Cognitive - Practical
1) Finding approximate values of functions
3 - Competences
Communication and Social Competence
1) Finding the roots of functions
Learning Competence
Field Specific Competence
Competence to Work Independently and Take Responsibility

Ders Akış Planı

Week	Subject	Related Preparation
1)	Solution of systems of linear equations	Lecture notes
2)	Cramer's rule, Jacobi iteration	lecture notes
3)	Gauss-Seidel method, Error correction method	Lecture notes
4)	Gauss-Jordan Method, Gaussian Elimination	Lecture notes
5)	Solution of non-linear systems of equations	Lecture notes
6)	Cramer's rule, Secant method	Lecture notes
7)	Newton Raphson method	lecture notes
8)	Midterm	lecture notes
9)	Linear Interpolation	Lecture notes
10)	Extrapolation with Taylor Polynomial	Lecture notes
11)	Extrapolation with a divided difference series, Extrapolation with a Lagrange polynomial, At least-square extrapolation with a power series, At least-square extrapolation with a quadratic polynomial	Lecture notes
12)	least-square extrapolation of exponential functions, least-square extrapolation of trigonometric functions	Lecture notes
13)	Numerical derivative, numerical partial derivative, determination of derivative formulas from Taylor series and error analysis, determination of derivative formulas from split difference series	Lecture notes
14)	Derivative with Lagrangian polynomial, Numerical Integration, Rectangles rule, Trapezoidal rule, Simpson's 1/3 and 3/8 rules	Lecture notes
15)	Multiple integrals, Romberg integration rule, Fourier series, Fourier coefficients, Fourier expansions of odd and even functions, Ordinary Differential Equations, Initial Value Problems, Euler's Method	Lecture notes
16)	Taylor Series Method, Runge-Kutta method, Boundary Value Problems, Attrition Value method, Finite difference method, Partial Differential Equations, Elliptic Equations	Lecture notes

Sources

Course Notes / Textbooks:

1. Gerald, C. F., Applied Numerical Analysis, Second Edition, Addison-Wesley Publishing Company, 1980. 2. Chapra, S.C., Canale, R.P., Numerical Methods for Engineers, McGraw Hill, 2008. 3. Hoffman, J.D., Numerical Methods for Engineers and Scientists, McGraw Hill, 1993. 4. Akai, T.J., Applied Numerical Methods for Engineers, John Wiley, 1994. 5. Karabulut, H., Çınar, C., Sayısal Analiz Ders Notları

References:

Ders - Program Öğrenme Kazanım İlişkisi

Ders Öğrenme Kazanımları	1	2
Program Outcomes
1) Knowledge of mathematics, science, basic engineering, computer computing, and engineering discipline-specific topics; ability to use this knowledge in solving complex engineering problems
2) Sufficient knowledge of issues related to software engineering; theoretical and To be able to use applied knowledge in solving algorithmic and software problems Skill.
3) Ability to define, formulate and analyze complex engineering problems using basic science, mathematics and engineering knowledge and taking into account the UN Sustainable Development Goals relevant to the problem under consideration.
4) Ability to design creative solutions to complex engineering problems; The ability to design complex systems, processes, devices or products to meet current and future requirements, taking into account realistic constraints and conditions.
5) Ability to choose and use appropriate techniques, resources, modern engineering computational tools for the analysis, solution, prediction and modelling of complex engineering problems.
6) Ability to use research methods to examine complex engineering problems, including researching literature, designing experiments, conducting experiments, collecting data, analyzing and interpreting results.
7) Information about the effects of engineering practices on society, health and safety, economy, sustainability and the environment within the scope of the UN Sustainable Development Goals; Awareness of the legal consequences of engineering solutions
8) Acting in accordance with engineering professional principles and knowledge about ethical responsibility; Awareness of acting impartially, without discrimination on any issue, and being inclusive of diversity.
9) Ability to work effectively as a team member or leader in intradisciplinary and multidisciplinary teams (face-to-face, remote or hybrid).
10) Individual working ability.
11) Ability to communicate effectively verbally and in writing on technical issues, taking into account the various differences of the target audience (such as education, language, profession).
12) Knowledge of business practices such as project management and economic feasibility analysis
13) Awareness about entrepreneurship and innovation.
14) A lifelong learning skill that includes being able to learn independently and continuously, adapting to new and developing technologies, and thinking inquisitively about technological changes.

Ders - Öğrenme Kazanımı İlişkisi

No Effect	1 Lowest	2 Low	3 Average	4 High	5 Highest

	Program Outcomes	Level of Contribution
1)	Knowledge of mathematics, science, basic engineering, computer computing, and engineering discipline-specific topics; ability to use this knowledge in solving complex engineering problems
2)	Sufficient knowledge of issues related to software engineering; theoretical and To be able to use applied knowledge in solving algorithmic and software problems Skill.
3)	Ability to define, formulate and analyze complex engineering problems using basic science, mathematics and engineering knowledge and taking into account the UN Sustainable Development Goals relevant to the problem under consideration.
4)	Ability to design creative solutions to complex engineering problems; The ability to design complex systems, processes, devices or products to meet current and future requirements, taking into account realistic constraints and conditions.
5)	Ability to choose and use appropriate techniques, resources, modern engineering computational tools for the analysis, solution, prediction and modelling of complex engineering problems.
6)	Ability to use research methods to examine complex engineering problems, including researching literature, designing experiments, conducting experiments, collecting data, analyzing and interpreting results.
7)	Information about the effects of engineering practices on society, health and safety, economy, sustainability and the environment within the scope of the UN Sustainable Development Goals; Awareness of the legal consequences of engineering solutions
8)	Acting in accordance with engineering professional principles and knowledge about ethical responsibility; Awareness of acting impartially, without discrimination on any issue, and being inclusive of diversity.
9)	Ability to work effectively as a team member or leader in intradisciplinary and multidisciplinary teams (face-to-face, remote or hybrid).
10)	Individual working ability.
11)	Ability to communicate effectively verbally and in writing on technical issues, taking into account the various differences of the target audience (such as education, language, profession).
12)	Knowledge of business practices such as project management and economic feasibility analysis
13)	Awareness about entrepreneurship and innovation.
14)	A lifelong learning skill that includes being able to learn independently and continuously, adapting to new and developing technologies, and thinking inquisitively about technological changes.

Öğrenme Etkinliği ve Öğretme Yöntemleri

Bireysel çalışma ve ödevi
Course

Ölçme ve Değerlendirme Yöntemleri ve Kriterleri

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	2	% 10
Midterms	1	% 40
Semester Final Exam	1	% 50
total		% 100
PERCENTAGE OF SEMESTER WORK		% 50
PERCENTAGE OF FINAL WORK		% 50
total		% 100

İş Yükü ve AKTS Kredisi Hesaplaması

Activities	Number of Activities	Duration (Hours)	Workload
Course Hours	14	3	42
Study Hours Out of Class	14	5	70
Homework Assignments	4	10	40
Midterms	1	2	2
Final	1	3	3
Total Workload			157