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OF FACULTY of TECHNOLOGY / DEPARTMENT of CIVIL ENGINEERING /
Katalog Ana Sayfa
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OINS2034Numerical Analysis2+0+0ECTS:4
Year / SemesterSpring Semester
Level of CourseFirst Cycle
Status Elective
DepartmentDEPARTMENT of CIVIL ENGINEERING
Prerequisites and co-requisitesNone
Mode of Delivery
Contact Hours14 weeks - 2 hours of lectures per week
LecturerDr. Öğr. Üyesi Emin TUĞCU
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.1,2,3,4,5,11
LO - 2 : Understand about the weak and powerful sides, and skills of numerical methods1,4,5
LO - 3 : Choose the appropriate numerical method depend on the problem to be s1,4,5
LO - 4 : Obtain the basic numerical solution of ordinary differential equations.1,4,5
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 2Taylor series. Approximations and error definitions. Numerical errors; relative, absolute, approximation, truncation and truncation errors.
 Week 3Roots 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 6Gauss 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 9 Mid-term Exam
 Week 10Numerical differentiation. Forward, backward and central approximations of differentiations. High order differentiation formulas.
 Week 11Numerical 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 14 Numerical solutions of ordinary differential equations. Euler's and Runge-Kutta methods
 Week 15Multistep methods; Adams, Newton-cotes, Milne methods.
 Week 16End-of-term exam
 
Textbook / Material
 
Recommended Reading
 
Method of Assessment
Type of assessmentWeek NoDate

Duration (hours)Weight (%)
Mid-term exam 9 2 50
End-of-term exam 16 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 2 14 28
Sınıf dışı çalışma 4 14 56
Laboratuar çalışması 0 0 0
Arasınav için hazırlık 8 1 8
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 load120