Information Package / Course Catalogue
Analysis II
Course Code: MAT102
Course Type: Required
Couse Group: First Cycle (Bachelor's Degree)
Education Language: Turkish
Work Placement: N/A
Theory: 4
Prt.: 2
Credit: 5
Lab: 0
ECTS: 7
Objectives of the Course

The aim of this course is to construct a basis of information which learners will use in the future by giving detailed information about integral, applications of integral and series, and to assist learners to grasp an analytical thought.

Course Content

Riemann integrals and its properties, Main-Value Theorem for integrals, change of variables, indefinite integral and method of finding primitive, Exponential and logarithmic functions, the concept of inverse functions, inverse trigonometric functions, hyperbolic and inverse hyperbolic functions, applications of definite integrals, area, volume, length of arc, areas of surfaces of revolution, improper integrals, sequences, convergence, convergence tests.

Name of Lecturer(s)
Prof. İnci EGE
Learning Outcomes
1.To be able to comprehend the base of the definite integral principle.
2.To be able to comprehend the cause and effect relation between indefinite and definite integral.
3.To be able to comprehend the use of integral in real life applications.
4.To be able to comprehend series and convergence tests.
5.To be able to make connection between power series and functions
Recommended or Required Reading
1.Addams R. A., Essex C., Kalkülüs, Eksiksiz Bir Ders, Cilt I., Palme Yayınevi, 2024
2.Silverman R. A. Calculus ve Analitik Geometri I, Alkım Yayınları, 1992
3.Dennis G. Zill - Warren S. Wright, Matematik Cilt II - Calculus Early Transcendentals, Nobel Akademik Yayıncılık, 2017
4.Balcı M. Genel Matematik I, Palme Yayınevi, 2022
5.Weir M. D., Hass J., Thomas’ Calculus Early Transcendentals, 12th Ed., Pearson Education, 2004
Weekly Detailed Course Contents
Week 1 - Theoretical & Practice
Indefinite integral and method of finding primitive
Week 2 - Theoretical & Practice
Partition, upper and lower sums, Riemannian integral and its properties
Week 3 - Theoretical & Practice
Theorems of integrals, Area in definite integral
Week 4 - Theoretical & Practice
Inverse functions and properties
Week 5 - Theoretical & Practice
Exponential and logarithmic functions
Week 6 - Theoretical & Practice
Hyperbolic and inverse hyperbolic functions
Week 7 - Theoretical & Practice
Method of change of variables and partial integral
Week 8 - Theoretical & Practice
Trigonometric integrals, integrals of polynomials with second degree, Partial fractions, half angle formulas (MIDTERM EXAM)
Week 9 - Theoretical & Practice
Improper integrals and tests in improper integrals
Week 10 - Theoretical & Practice
Volume in definite integral, Arc length and area of surfaces of revolution
Week 11 - Theoretical & Practice
Series, Convergence tests for series with positive terms
Week 12 - Theoretical & Practice
Convergence tests for series with positive terms, absolute and conditionally convergences
Week 13 - Theoretical & Practice
Power Series, power series representation of functions
Week 14 - Theoretical & Practice
Taylor and Maclaurin series
Assessment Methods and Criteria
Type of AssessmentCountPercent
Midterm Examination1%40
Final Examination1%60
Workload Calculation
ActivitiesCountPreparationTimeTotal Work Load (hours)
Lecture - Theory140456
Lecture - Practice140228
Individual Work140456
Midterm Examination115217
Final Examination120222
TOTAL WORKLOAD (hours)179
Contribution of Learning Outcomes to Programme Outcomes
PÇ-1
PÇ-2
PÇ-3
PÇ-4
PÇ-5
PÇ-6
PÇ-7
PÇ-8
PÇ-9
PÇ-10
PÇ-11
PÇ-12
PÇ-13
PÇ-14
PÇ-15
PÇ-16
PÇ-17
PÇ-18
OÇ-1
4
4
OÇ-2
4
4
OÇ-3
4
4
4
OÇ-4
4
4
OÇ-5
Adnan Menderes University - Information Package / Course Catalogue
2026