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FACULTY of SCIENCE / DEPARTMENT of STATISTICS and COMPUTER SCIENCES

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FACULTY of SCIENCE / DEPARTMENT of STATISTICS and COMPUTER SCIENCES /
Katalog Ana Sayfa
  Katalog Ana Sayfa  KTÜ Ana Sayfa   Katalog Ana Sayfa
 
 

MAT1004Mathematics-II4+2+0ECTS:8
Year / SemesterSpring Semester
Level of CourseFirst Cycle
Status Compulsory
DepartmentDEPARTMENT of STATISTICS and COMPUTER SCIENCES
Prerequisites and co-requisitesNone
Mode of DeliveryFace to face
Contact Hours14 weeks - 4 hours of lectures and 2 hours of practicals per week
LecturerProf. Dr. İdris ÖREN
Co-LecturerAll stuff of the departmant
Language of instructionTurkish
Professional practise ( internship ) None
 
The aim of the course:
The aim of the course is to teach the basic mathematical techniques. Analyzing the two and three dimensional problems in engineering sciencies and introducing 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 : apply the integration to some engineering problems and to some applications 2,4,51
LO - 2 : analize convergence of improper integrals.2,4,51
LO - 3 : analize convergence of sequences and series.2,4,51
LO - 4 : understand functions of two and three variables and their properties2,4,51
LO - 5 : know the concepts of limit and continuity of functions of two and three variables2,4,51
LO - 6 : know the concepts of derivative of functions of two variables and apply it to engineering problems2,4,51
LO - 7 : know the concepts of integration of functions of two variables and apply it to engineering problems2,4,51
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
Riemann sums, definite integrals and their properties, Fundamental Theorem of Calculus.Change of variables in definite integrals Applications of definite integrals: areas of plane regions,Applications of definite integrals: Volume computations (disk and cross-section methods) length of parametric curves, areas of surfaces of revolution.Improper integrals (Type 1 and Type 2).Sequences and infinite series, (definitions of convergence and divergence, geometric series, n-th term test, p-series, alternating series).Series(absolute convergence, ratio and root tests) Power series and their convergence, Taylor and Maclaurin series. Multivariable functions, limit, continuity and partial derivatives.Chain rule, directional derivatives, Maximum and minimum, Lagrange Multipliers (Single constraint case) Double integrals and their applications (Area). Polar Coordinates ,Double integrals in Polar Coordinates and their applications (mass and density, center of mass ).
 
Course Syllabus
 WeekSubjectRelated Notes / Files
 Week 1Riemann sums, definite integrals and their properties, Fundamental Theorem of Calculus
 Week 2Change of variables in definite integrals and Area Between Curves
 Week 3Applications of definite integrals: Volume computations (disk, cross-section, the washer, the shell methods)
 Week 4Length of parametric curves, areas of surfaces of revolution
 Week 5Improper integrals (Type 1 and Type 2)
 Week 6Sequences and infinite series, (definitions of convergence and divergence, geometric series, n-th term test, integral test, ratio and root tests)
 Week 7Alternating series, absolute and conditional convergence, power series
 Week 8Taylor and Maclaurin series
 Week 9Mid-term exam
 Week 10Multivariable functions, limit, continuity and partial derivatives.
 Week 11Chain rule, directional derivatives and gradient
 Week 12Extreme values, absolute maxima and minima,Lagrange multipliers (Single constraint case)
 Week 13Double integrals and their applications (Area)
 Week 14Substitutions in Double Integrals, Double integrals in Polar Coordinates and polar curves and their applications (mass and density, center of mass ),
 Week 15General assessment
 Week 16End-of-term exam
 
Textbook / Material
1Thomas, G.B., Finney, R.L.. (Çev: Korkmaz, R.), 2001; Calculus ve Analitik Geometri, Cilt II, Beta Yayınları, İstanbul.
2Thomas, G.B., Finney, R.L.. (Çev: Korkmaz, R.), 2001; Calculus ve Analitik Geometri, Cilt II, Beta Yayınları, İstanbul.
3Kolman, B., Hill, D.L. (Çev Edit: Akın, Ö.) 2002; Uygulamalı lineer cebir. Palme Yayıncılık, Ankara.
4Kolman, B., Hill, D.L. (Çev Edit: Akın, Ö.) 2002; Uygulamalı lineer cebir. Palme Yayıncılık, Ankara.
 
Recommended Reading
1Balcı, M. 2009; Genel Matematik 2, Balcı Yayınları, Ankara
2Balcı, M. 2009; Genel Matematik 2, Balcı Yayınları, Ankara
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4
5Balcı, M. 2009; Genel Matematik 2, Balcı Yayınları, Ankara
6Balcı, M. 2009; Genel Matematik 2, Balcı Yayınları, Ankara
 
Method of Assessment
Type of assessmentWeek NoDate

Duration (hours)Weight (%)
Mid-term exam 9 06/04/2020 1,5 50
End-of-term exam 16 04/06/2020 1,5 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 7 14 98
Arasınav için hazırlık 9 1 9
Arasınav 1.5 1 1.5
Uygulama 2 14 28
Dönem sonu sınavı için hazırlık 10 1 10
Dönem sonu sınavı 1.5 1 1.5
Total work load204