Erciyes University - Info Package

Dersin Adı	Dersin Seviyesi	Dersin Kodu	Dersin Tipi	Dersin Dönemi	Yerel Kredi	AKTS Kredisi	Ders Bilgileri
NUMERICAL ANALYSIS & SCIENTIFIC PROGRAMMING	Birinci Düzey	YZ 209	Zorunlu	3	5.00	5.00	Yazdır

Dersin Tanımı

Ön Koşul Dersleri
Eğitimin Dili	English
Koordinatör	DR. ÖĞR. ÜYESİ RUKİYE NUR KAÇMAZ
Dersi Veren Öğretim Eleman(lar)ı
Yardımcı Öğretim Eleman(lar)ı
Dersin Veriliş Şekli
Dersin Amacı	The primary objective of this course is to provide students with the numerical techniques and mathematical foundations required to solve complex engineering problems that cannot be solved analytically. It aims to develop proficiency in implementing numerical algorithms for root-finding, interpolation, and numerical calculus while emphasizing error analysis and approximation theory.
Dersin Tanımı	This course covers a wide range of numerical methods used in engineering, starting with error types and Taylor series approximations. Students will explore numerical integration techniques and the solution of ordinary differential equations (ODEs) through Euler and Runge-Kutta methods. The course emphasizes the practical application of these methods using scientific programming environments to solve real-world engineering challenges while recognizing the limitations of computational approximations.

Dersin İçeriği

1	Introduction To Numeric.
2	Taylor Series, Maclaurin Series, Error Types, Truncation- Relative- Absolute-Rounding- Stopping Condition.
3	Intermediate Value Theorem - Non-Linear Equation in One Variable Solution Situation. Bisection - Linear Interpolation - Newton Raphson.
4	Secant Method.
5	The fixed point iteration and stopping condition - Least Square Methods.
6	Interpolation Types (Linear- Quadratic-Lagrange).
7	Solution of Linear Equation Systems.
8	Numerical Integration (Trapezoidal Rule-Simpson’s).
9	Ordinary Differential Equations.
10	Taylor Series-Eular Series.
11	Picard - Midpoint.
12	Runge Kutta (1.-2.-3. degree).
13	Heun Method.
14	Gauss Elimination.
15	Low Triangle.
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Dersin Öğrenme Çıktıları

1	Analyzes error types and applies series expansions (Taylor/Maclaurin) to approximate mathematical functions in engineering problems.
2	Solves non-linear equations in one variable using iterative methods like Bisection and Newton-Raphson.
3	Implements interpolation and regression techniques (Least Squares) to model data and approximate values.
4	Solves systems of linear equations using direct (Gauss) and iterative numerical methods.
5	Applies numerical integration techniques such as Trapezoidal and Simpson’s rules to calculate definite integrals.
6	Solves ordinary differential equations (ODEs) using Euler, Runge-Kutta, and Heun methods.
7	Utilizes modern scientific programming tools (e.g., Python, MATLAB) to implement and automate numerical algorithms.
8	Recognizes the limitations and truncation errors of numerical methods when generating engineering solutions.
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*Dersin Program Yeterliliklerine Katkı Seviyesi

1	Applies engineering knowledge related to mathematics, science, basic engineering, and computer-based calculations to solve engineering problems.
2	Gains the ability to develop engineering solutions using discipline-specific knowledge and methods.
3	Defines complex engineering problems and formulates them using fundamental science and engineering knowledge.
4	Defines and analyzes solutions to problems, taking into account the UN Sustainable Development Goals.
5	Designs creative solutions to complex engineering problems.
6	Gains the ability to design complex systems, processes, devices, or products by considering realistic constraints in the engineering problem-solving process.
7	For the analysis and solution of complex engineering problems, selects and effectively applies appropriate methods, techniques, resources, and modern engineering and computing tools, including estimation and modeling.
8	Aware of the limitations of the methods, techniques, and IT tools used, it produces and implements appropriate solutions.
9	Conducts literature research to examine complex engineering problems and collects data within the scope of these studies.
10	Using research methods, the student designs and conducts experimental or applied studies, analyze and evaluate the results.
11	Within the scope of the UN Sustainable Development Goals, the student is knowledgeable about the impacts of engineering solutions on society, health and safety, the economy, sustainability, and the environment, and analyze these impacts.
12	Gains awareness of the legal consequences of engineering solutions.
13	The student acts in accordance with professional principles and legal regulations in engineering practice and acquires knowledge about ethical responsibilities.
14	Gains awareness about non-discrimination, impartiality, and inclusiveness of diversity.
15	Gains the ability to work effectively as an individual, team member, or team leader in intra-disciplinary or multi-disciplinary team projects.
16	Gains the ability to communicate effectively in technical matters, both verbally and in writing by taking into account the differences in the target audience''s education, language, and profession.
17	Gains the ability to apply project management principles, perform time and resource planning, and conduct economic feasibility analysis.
18	Gains awareness about entrepreneurship and innovation.
19	Gains the ability to adapt to new and emerging technologies and to evaluate technological changes with a questioning and critical perspective.
20	Gains the ability to independently and continuously learn new knowledge and skills.
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Yıldızların sayısı 1’den (en az) 5’e (en fazla) kadar katkı seviyesini ifade eder

Planlanan Öğretim Faaliyetleri, Öğretme Metodları ve AKTS İş Yükü

	Sayısı	Süresi (saat)	Sayı*Süre (saat)
Yüz yüze eğitim	0	0	0
Sınıf dışı ders çalışma süresi (ön çalışma, pekiştirme)	0	0	0
Ödevler	0	0	0
Sunum / Seminer hazırlama	0	0	0
Kısa sınavlar	0	0	0
Ara sınavlara hazırlık	0	0	0
Ara sınavlar	0	0	0
Proje (Yarıyıl ödevi)	0	0	0
Laboratuvar	0	0	0
Arazi çalışması	0	0	0
Yarıyıl sonu sınavına hazırlık	0	0	0
Yarıyıl sonu sınavı	0	0	0
Araştırma	0	0	0
Toplam iş yükü			0
AKTS			0.00

Değerlendirme yöntemleri ve kriterler

Yarıyıl içi değerlendirme	Sayısı	Katkı Yüzdesi
Ara sınav	1	100
Kısa sınav	0	0
Ödev	0	0
Yarıyıl içi toplam		100
Yarıyıl içi değerlendirmelerin başarıya katkı oranı		40
Yarıyıl sonu sınavının başarıya katkı oranı		60
Genel toplam		100

Önerilen Veya Zorunlu Okuma Materyalleri

Ders kitabı	NUMERICAL METHODS IN ENGINEERING WITH PYTHON-JAAN KIUSALAAS, SAYISAL YÖNTEMLER VE MATLAB UYGULAMALARI-Prof.NURHAN KARABOĞA
Yardımcı Kaynaklar

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