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OF FACULTY of TECHNOLOGY / DEPARTMENT of SOFTWARE ENGINEERING /
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YZM3007Numerical Analysis2+2+0ECTS:5
Year / SemesterFall Semester
Level of CourseFirst Cycle
Status Compulsory
DepartmentDEPARTMENT of SOFTWARE ENGINEERING
Prerequisites and co-requisitesNone
Mode of Delivery
Contact Hours14 weeks - 2 hours of lectures and 2 hours of practicals per week
LecturerDoç. Dr. Esma ULUTAŞ
Co-Lecturer
Language of instructionTurkish
Professional practise ( internship ) None
 
The aim of the course:
To give fundamental methods of numerical analysis.
 
Learning OutcomesCTPOTOA
Upon successful completion of the course, the students will be able to :
LO - 1 : Understand about the errors resulting from the making of approximations while applying various numerical methods, and the ways to minimizing of these errors.1,21,
LO - 2 : Understand about the weak and powerful sides, and skills of numerical methods and the computers.1,21,
LO - 3 : Choose the appropriate numerical method depend on the problem to be1,21,
LO - 4 : Obtain the basic numerical solution of ordinary differential equations.1,21,
CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), LO : Learning Outcome

 
Contents of the Course
Mathematical modeling concept, approximations and errors. Roots of equations. Systems of algebraic equations. Curve fitting. Interpolations. Tables of Finite Differences.Numerical differentiation and numerical integration. Solution of ODE's.
 
Course Syllabus
 WeekSubjectRelated Notes / Files
 Week 1Motivation. Numerical methods and engineering practice. Mathematical modeling concept.
 Week 2 Taylor series. Approximations and error definitions. Numerical errors; relative, absolute, approximation, truncation and truncation errors.
 Week 3 Roots of equations. Barcketing methods: Bisection and false-position methods.
 Week 4Open methods: Simple iteration, Newton-Raphson and Secant methods. Multiple roots. Comparison of various methods.
 Week 5Lineer cebirsel denklemler. Küçük denklem sistemlerinin çözümü: Grafik yöntemler, Cramer kuralı ve bilinmeyenlerin yok edilmesi.
 Week 6 Gauss elimination, Gauss-Jordan, Matrix inverse methods. Gauss-Saidel method. Weak and powerful sides of solution methods.
 Week 7Table of Finite Differences. Forward finite differences, backward finite differences and central differences.
 Week 8Interpolation. Linear and higher order interpolations with Newton and Lagrange interpolating polynomials.
 Week 9Mid-term Exam
 Week 10 Numerical differentiation. Forward, backward and central approximations of differentiations. High order differentiation formulas.
 Week 11 Numerical integration. Newton-Cotes integration formulas. Trapezoid rule. 1/3 ve 3/8 Simpson rules.
 Week 12Numerical integration. Newton-Cotes integration formulas. Trapezoid rule. 1/3 ve 3/8 Simpson rules.
 Week 13Ordinary differential equations and engineering practice
 Week 14Numerical solutions of ordinary differential equations. Euler's and Runge-Kutta methods
 Week 15 Multistep methods; Adams, Newton-cotes, Milne methods.
 Week 16End-of-term exam
 
Textbook / Material
1Atkinson, K. 1989 An introduction to Numerical Analysis, John Wiley Pub.
 
Recommended Reading
1Bayram, Mustafa 2002; Nümerik Analiz, Aktif Yayınevi, Ankara.
 
Method of Assessment
Type of assessmentWeek NoDate

Duration (hours)Weight (%)
Mid-term exam 9 29.11.2023 2 50
End-of-term exam 16 15.01.2024 2 50
 
Student Work Load and its Distribution
Type of workDuration (hours pw)

No of weeks / Number of activity

Hours in total per term
Yüz yüze eğitim 4 14 56
Sınıf dışı çalışma 4 14 56
Laboratuar çalışması 0 0 0
Arasınav için hazırlık 5 2 10
Arasınav 2 1 2
Uygulama 0 0 0
Klinik Uygulama 0 0 0
Ödev 0 0 0
Proje 0 0 0
Kısa sınav 0 0 0
Dönem sonu sınavı için hazırlık 12 2 24
Dönem sonu sınavı 2 1 2
Diğer 1 0 0 0
Diğer 2 0 0 0
Total work load150