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MAT1011Mathematics - I4+0+0ECTS:5
Year / SemesterFall Semester
Level of CourseFirst Cycle
Status Compulsory
Prerequisites and co-requisitesNone
Mode of Delivery
Contact Hours14 weeks - 4 hours of lectures per week
LecturerProf. Dr. Erhan COŞKUN
Co-LecturerOther instructor assigned for the course
Language of instructionTurkish
Professional practise ( internship ) None
The aim of the course:
The course aims to provide the basic information about functions, limit, derivative, integral as well as their appicaitons in various disciplines including physical and engineering sciences.
Learning OutcomesCTPOTOA
Upon successful completion of the course, the students will be able to :
LO - 1 : learn how to model with functions1,21
LO - 2 : learn about limit, derivative and applications 1,21
LO - 3 : learn about integral and their 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 (polynomials, rational, trigonometric, hyperbolic, exponential, logarithmic and inverse trigonometric functions) graphs of basic functions, shifting and scaling graphs, limit, continuity, differentiation and applications (Intermediate Value Theorem, L'hopital's rule, Mean Value Theorem, Optimization problems, sketching the graph of a function), integration techniques
Course Syllabus
 WeekSubjectRelated Notes / Files
 Week 1Functions and their graphs, composite functions, polynomial and rational functions, transcendental functions
 Week 2Inverse functions, exponential and logarithmic functions, functions derived from verbal expressions, applications
 Week 3Limits-an intuitive approach, limit theorems, continuity, trigonometric limits
 Week 4limits at infinity, limits-a mathematical approach, tangent line problem, application
 Week 5Derivative, power and sum rules, product and division rules, trigonometric functions
 Week 6Chain rule, implicit differentiation, derivative of inverse functions, exponential functions
 Week 7Logarithmic functions, hyperbolic functions, rectilinear motion, related rates
 Week 8Extrema of functions, mean value theorem, limits with L'Hopital rule, drawing graphs, first and second derivative test
 Week 9Midterm exam
 Week 10Optimization, linearization and differentials, applications
 Week 11Indefinite integral, integration by a change of variable, area, definite integral
 Week 12Main theorem of calculus, rectilinear motion, area, volumes of solids: slicing method
 Week 13Volumes of solids: cylindirical shells, arch length, area of a surface of revolution, mean value of a function(work, fluid pressure and force, mass and center of weight)
 Week 14Integral, integration by a change of variable, integration by parts, powers of trigonometric functions
 Week 15Trigonometric change of variables, simple fractions, improper integrals
 Week 16Final exam
Textbook / Material
1Zill, D.G, Wright, W.S., 2012; Matematik Cilt I (Calculus Early Transcendentals), Çeviri Editörü Prof. Dr. İsmail Naci Cangül, Nobel Yayıncılık, Ankara.
Recommended Reading
1Thomas, G.B., Weir, M.D., Hass, J., 2009; Thomas' Calculus, 12th Edition, Pearson, USA.
2Adams, R.A., Essex, C., Calculus a Complete Course, 2012, Pearson, USA.
Method of Assessment
Type of assessmentWeek NoDate

Duration (hours)Weight (%)
Mid-term exam 9 28.11.2023 50
End-of-term exam 16 22.01.2024 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
Laboratuar çalışması 0 0 0
Arasınav için hazırlık 12 1 12
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 15 1 15
Dönem sonu sınavı 2 1 2
Diğer 1 0 0 0
Diğer 2 0 0 0
Total work load157