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Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
NUMERICAL ANALYSIS MAT 216 4 3 + 0 3 5
Ön Koşul Dersleri
Önerilen Seçmeli Dersler
Dersin Dili Türkçe
Dersin Seviyesi Lisans
Dersin Türü ZORUNLU
Dersin Koordinatörü Prof.Dr. EKREM BÜYÜKKAYA
Dersi Verenler
Dersin Yardımcıları
Dersin Kategorisi
Dersin Amacı

The aim of the course is to teach the fundamentals of numerical methods, their application and limitations.

Dersin İçeriği

Mathematical modeling of engineering problems, Roots of algebraic equations, Review of linear systems of equations, Basic principles of optimization, Curve-fitting, Numerical differentiation and integration, Numerical solutions of ordinary differential equations, Inıtial- and boundary-value problems, Introduction to solution of partial differential equations.

Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri
1 - Understand the theoretical and practical aspects of the use of numerical methods 1 - 2 - 4 - 15 - A - C -
2 - Implement numerical methods for a variety of multidisciplinary applications 1 - 2 - 3 - 4 - A - C -
3 - Establish the limitations, advantages, and disadvantages of numerical methods 1 - 2 - 3 - 4 - 15 - A - C -
Öğretim Yöntemleri: 1:Lecture 2:Question-Answer 4:Drilland Practice 15:Problem Solving 3:Discussion
Ölçme Yöntemleri: A:Testing C:Homework

Ders Akışı

Hafta Konular ÖnHazırlık
1 Introduction to numerical methods, why to study numerical analyses?,Mathematical modeling and engineering problem solving, Computer packages
2 Approximations and rounding errors, Truncation errors and Taylor series expansion
3 Roots of equations: Bracketing methods (graphical, bisection and false-position methods), Open methods (One-point iteration, Newton-Raphson, Secant, Multiple roots
4 Systems of nonlinear algebraic equations: Newton-Raphson method, Case studies for roots of equations
5 System of linear algebraic equations, Reviewing Gauss methods, LU decomposition, and Thomas algorithm, Computer methods for linear systems, Engineering applications of linear systems
6 Fundamentals of optimization: Unconstrained and constrained optimization, Newton method, Lagrange multipliers method, Computer aided engineering applications
7 Curve-fitting: Least-squares regression (linear regression, polynomial regression, multiple linear regression, nonlinear regression)
8 Interpolation (Newton´s divided-difference interpolating polynomials, Lagrange interpolating polynomials, Coefficients of an interpolating polynomial)
9 Computer methods for curve-fitting, Engineering applications of curve-fitting
10 Numerical differentiation and integration: Newton-Cotes integration formulas, Integration of equations, Numerical differentiation
11 Computer methods for numerical integration and differentiation, Engineering applications
12 Ordinary differential equations: One-step methods (Euler, modified and improved Euler and Runge-Kutta methods), System of equations
13 Ordinary differential equations: Multistep and Predictor-corrector methods, Initial- and boundary-value problems, Computer-aided engineering applications
14 Introduction to partial differential equations: Finite difference method, Engineering applications

Kaynaklar

Ders Notu

Chapra, S.C. ve Canale, R.P., Numerical Methods for Engineers with Application Software and Programming
Turkish translation:: Heperkan, H. ve Kesgin, U., Liteatür, Istanbul, 2006.

Ders Kaynakları

1. Karagoz, I.,Numerical Analysis and Engineering Applications, 3. publication, Nobel, 2011.

2. Gerald, C.F., Whewatley, P.O., Applied Numerical Analysis, Addison-Wesley Publishing Company, 1984.

3. Cengel, Y. A., ve Palm, W. J., (Turkish translation: Tahsin Engin), Differential Equations for Engineers and Scientist, Guven bookstore, Izmir, 2012.


Döküman Paylaşımı


Dersin Program Çıktılarına Katkısı

No Program Öğrenme Çıktıları KatkıDüzeyi
1 2 3 4 5
1 Engineering graduates with sufficient theoretical and practical background for a successful profession and with application skills of fundamental scientific knowledge in the engineering practice X
2 Engineering graduates with skills and professional background in describing, formulating, modeling and analyzing the engineering problem, with a consideration for appropriate analytical solutions in all necessary situations X
3 Engineering graduates with the necessary technical, academic and practical knowledge and application confidence in the design and assessment of machines or mechanical systems or industrial processes with considerations of productivity, feasibility and environmental and social aspects. X
4 Engineering graduates with the practice of selecting and using appropriate technical and engineering tools in engineering problems, and ability of effective usage of information science technologies X
5 Ability of designing and conducting experiments, conduction data acquisition and analysis and making conclusions
6 Ability of identifying the potential resources for information or knowledge regarding a given engineering issue
7 The abilities and performance to participate multi-disciplinary groups together with the effective oral and official communication skills and personal confidence
8 Ability for effective oral and official communication skills in Turkish Language and, at minimum, one foreign language
9 Engineering graduates with motivation to life-long learning and having known significance of continuous education beyond undergraduate studies for science and technology
10 Engineering graduates with well-structured responsibilities in profession and ethics
11 Engineering graduates who are aware of the importance of safety and healthiness in the project management, workshop environment as well as related legal issues

Değerlendirme Sistemi

YARIYIL İÇİ ÇALIŞMALARI SIRA KATKI YÜZDESİ
AraSinav 1 60
KisaSinav 1 10
Odev 1 20
KisaSinav 2 10
Toplam 100
Yıliçinin Başarıya Oranı 55
Finalin Başarıya Oranı 45
Toplam 100

AKTS - İş Yükü

Etkinlik Sayısı Süresi(Saat) Toplam İş yükü(Saat)
Course Duration (Including the exam week: 16x Total course hours) 16 3 48
Hours for off-the-classroom study (Pre-study, practice) 16 3 48
Mid-terms 1 6 6
Quiz 2 2 4
Assignment 2 6 12
Final examination 1 10 10
Toplam İş Yükü 128
Toplam İş Yükü /25(s) 5.12
Dersin AKTS Kredisi 5.12
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