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YZM1005Mathematics - I4+0+0ECTS:5
Year / SemesterFall Semester
Level of CourseFirst Cycle
Status Compulsory
DepartmentDEPARTMENT of SOFTWARE ENGINEERING
Prerequisites and co-requisitesNone
Mode of DeliveryFace to face
Contact Hours14 weeks - 4 hours of lectures per week
LecturerÖğr. Gör. Dr Şenol DEMİR
Co-Lecturer
Language of instructionTurkish
Professional practise ( internship ) None
 
The aim of the course:
The aim of the course is to teach the basic mathematical techniques, introducing at the same time a number of mathematical skills which can be used for the analysis of problems. The emphasis is on the practical usability of mathematics; this goal is mainly pursued via a large variety of examples and applications from these disciplines
 
Learning OutcomesCTPOTOA
Upon successful completion of the course, the students will be able to :
LO - 1 : clasify numbers and understand functions and their properties 1,2,3,4,5,6,7,8,9,10,11,12,131
LO - 2 : know the concepts of limit and continuity of functions 1,21
LO - 3 : know the concepts of derivatives of functions 1,21
LO - 4 : apply of the derivative to some engineering problems 1,21
LO - 5 : know the concepts of integral of functions 1,21
LO - 6 : apply the integration to some engineering problems and to some applications 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
Functions, inverse functions, plotting the graphs of basic curves, transformation of graphs. Trigonometric functions, inverse trigonometric functions, logarithmic and exponential functions . Limit, rules of limit, continuity . Derivative of function, geometric meaning of derivative, rules of derivative, derivative of trigonometric functions, inverse trigonometric functions, logarithmic and exponential functions. Higher order derivative, chain rules, derivative of implicit functions, applications of derivative, concept of derivation. L?hospital rule, limit at infinity, Rolle Theorem and Mean Value Theorem, extrema of functions . Asymptotes, plotting graphs by observation of changes in functions . Indefinite integrals . Methods of integration, change of variable, integration by parts, integration of polynomials, algebraic and trigonometric (rational) functions . Riemann sums, definite integration and properties, fundamental theorem of analysis. Applications of definite integrals: areas of regions, length of curves, volumes of rotating objects, surface arease, calculation of mass, moment, gravitational center and work. Change of variables for definite integrals. Generalization of integration . Sequences, series, alternating series, power series, series expansion of functions (Taylor and Maclaurin series)
 
Course Syllabus
 WeekSubjectRelated Notes / Files
 Week 1Functions, inverse functions, plotting the graphs of basic curves, transformation of graphs.
 Week 2Trigonometric functions, inverse trigonometric functions, logarithmic and exponential functions.
 Week 3Limit, rules of limit, continuity.
 Week 4Derivative of a function, geometric meaning of derivative, rules of derivative, derivative of trigonometric functions, inverse trigonometric functions, logarithmic and exponential functions
 Week 5Higher order derivative, chain rules, derivative of implicit functions, applications of derivative, concept of derivation.
 Week 6L'hospital rule, limit at infinity, Rolle Theorem and Mean Value Theorem, extrema of functions.
 Week 7Asymptotes, plotting graphs by observation of changes in functions
 Week 8Asymptotes, plotting graphs by observation of changes in functions
 Week 9Mid-term exam
 Week 10Methods of integration, change of variable, integration by parts, integration of polynomials, algebraic and trigonometric (rational) functions
 Week 11Riemann sums, definite integration and properties, fundamental theorem of analysis
 Week 12Change of variables for definite integrals. Short Exam.
 Week 13Applications of definite integrals: areas of regions, length of curves, volumes of rotating objects, surface arease, calculation of mass, moment, gravitational center and work.
 Week 14Generalization of integration
 Week 15Sequences, series, alternating series, power series, series expansion of functions (Taylor and Maclaurin series)
 Week 16End-of-term exam
 
Textbook / Material
1Temel Matematik, Mustafa Balcı, Balcı Yayınları, 2008, 457 s., ISBN:9756683187.
 
Recommended Reading
1Temel ve Genel Matematik 1?2, Kolektif, Üniversite Kitabevi, Elazığ, 2006.
2Temel Matematik, İrfan Ertuğrul, Ekin Kitabevi Yayınları, 2006.
3Genel Matematik, Ahmet Dernek, Nobel Yayın Dağıtım, 2005.
4Çözümlü ve Alıştırmalı Genel Matematik, Ali Dönmez, Üniversiteli Kitabevi, 2007.
5Matematik Analiz ve Analitik Geometri ?1, C. Henry Edwards, çev.: Ömer Akın, Palme Yayın Dağıtım, 2008.
 
Method of Assessment
Type of assessmentWeek NoDate

Duration (hours)Weight (%)
Mid-term exam 9 50
End-of-term exam 16 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 5 14 70
Arasınav için hazırlık 12 1 12
Arasınav 2 1 2
Uygulama 1.5 1 1.5
Dönem sonu sınavı için hazırlık 15 1 15
Dönem sonu sınavı 2 1 2
Total work load158.5