SOFTWARE ENGINEERING
Bachelor TR-NQF-HE: Level 6 QF-EHEA: First Cycle EQF-LLL: Level 6

Course Introduction and Application Information

Course Code Course Name Semester Theoretical Practical Credit ECTS
MAT1052 Calculus II Spring 3 2 4 7

Basic information

Language of instruction: English
Type of course: Must Course
Course Level: Bachelor’s Degree (First Cycle)
Mode of Delivery: Face to face
Course Coordinator : Dr. Öğr. Üyesi GÜLSEMAY YİĞİT
Course Lecturer(s): Prof. Dr. SÜREYYA AKYÜZ
Prof. Dr. İRİNİ DİMİTRİYADİS
RA DUYGU ÜÇÜNCÜ
Dr. Öğr. Üyesi LAVDİE RADA ÜLGEN
RA AYSUN SOYSAL
Dr. Öğr. Üyesi MÜRÜVVET ASLI AYDIN
Assoc. Prof. HALE GONCE KÖÇKEN
Prof. Dr. MURAT SARI
Dr. Öğr. Üyesi DOĞAN AKCAN
Recommended Optional Program Components: None
Course Objectives: The objective of the course is to give to the students an understanding of the integral and its applications as well as introducing them to sequences and series so as to improve their ability to think critically, and enrich the tools they can use in analyzing and solving problems.

Learning Outcomes

The students who have succeeded in this course;

1) Calculate the approximate area under the curve using the sigma notation and Riemann sums over infinite number of partition
2) Calculate the definite and indefinite integrals using substitution, fractional integral, trigonometric substitution, partial fraction and anti-derivative tables
3) Solve the problems of area finding and volume and arc length using definitions of definite integral
4) Define the irregular integrals and calculate the results of irregular integrals by defining the concepts of limit, convergence and divergence.
5) Determine the convergence or divergence by applying ratio, integral, limit comparison, alternative series and root tests to geometric, alternative, telescopic and power series.
6) Use the Taylor and MacLaurin series to represent functions
7) Find the limit, continuity, partial derivatives, tangent surfaces and normal lines in multivariable functions
8) Calculate the double integrals in multivariable functions, understand the change the integral sequence, find a volume limited to a region determined under a surface

Course Content

Definite integral, fundemantal theorem, indefinite integral and techniques of integration, application of the integral, areas, arc length, volumes and area of surfaces of revolution, numerical integration and improper integrals.

Sequences and series, convergence tests of series, alternating series, power series, Taylon, MacLaurin series and their applications.

Finding limit, continuity, partial derivatives, tangent surfaces and normal lines in multivariable functions.

Calculating double integrals in multivariable functions, changing the integral sequence, finding a volume limited to a region determined under a surface

Weekly Detailed Course Contents

Week Subject Related Preparation
1) Antiderivatives, Estimating areas with finite sums.Riemann sum, upper and lower sums.
2) Definite Integral. The Fundamental Theorem of Calculus. Properties of the definite integral.
3) Indefinite integral, substitution rule. Area Between Curves.
4) Basic Integration Formulas and integration by parts. Integrals of logaritmic and exponential functions. Integration of Rational Functions
5) Trigonometric Integrals,Trigonometric substitution and additional methods of integration. Improper Integrals,
6) Applications of Integrations, Volumes of Solids Revolution.
7) Arc Length and Surface Area, Sequences and Convergence
8) Review for Midterm
9) Infinite Series, Convergence Tests for Positive Series, Integral Test , comparison ratio and root tests.
10) Alternating Series, Absolute and Conditional Convergence, Power Series
11) Taylor and Maclaurin Series, Convergence of Taylor Series; error estimates, applications of power series.
12) Functions of Several Variables, Level Curves, Limits and Continuity, Partial Derivative, Higher Order Derivatives
13) Multiple Integration, Double Integrals, Iteration of Double Integrals in Cartesian Coordinates, Improper Integrals and a Mean Value Theorem
14) Review for Final Exam

Sources

Course Notes / Textbooks: Thomas' Calculus International Edition 12th Edition George Thomas, Maurice Weir, Joel Hass, Frank Giordano
References: James Stewart Calculus, 5th Ed. Brooks/Cole Publishing Company

C.H. Edwards,Jr. David E. Penney, Calculus with Analytic Geometry

Richard Silverman, Calculus with Analytic Geometry, Prentice Hall

Evaluation System

Semester Requirements Number of Activities Level of Contribution
Midterms 1 % 40
Final 1 % 60
Total % 100
PERCENTAGE OF SEMESTER WORK % 40
PERCENTAGE OF FINAL WORK % 60
Total % 100

ECTS / Workload Table

Activities Number of Activities Duration (Hours) Workload
Course Hours 14 3 42
Application 14 2 28
Study Hours Out of Class 47 1 47
Midterms 1 15 15
Final 1 25 25
Total Workload 157

Contribution of Learning Outcomes to Programme Outcomes

No Effect 1 Lowest 2 Low 3 Average 4 High 5 Highest
           
Program Outcomes Level of Contribution
1) Be able to specify functional and non-functional attributes of software projects, processes and products. 4
2) Be able to design software architecture, components, interfaces and subcomponents of a system for complex engineering problems. 1
3) Be able to develop a complex software system with in terms of code development, verification, testing and debugging.
4) Be able to verify software by testing its program behavior through expected results for a complex engineering problem.
5) Be able to maintain a complex software system due to working environment changes, new user demands and software errors that occur during operation. 2
6) Be able to monitor and control changes in the complex software system, to integrate the software with other systems, and to plan and manage new releases systematically. 1
7) Be able to identify, evaluate, measure, manage and apply complex software system life cycle processes in software development by working within and interdisciplinary teams. 2
8) Be able to use various tools and methods to collect software requirements, design, develop, test and maintain software under realistic constraints and conditions in complex engineering problems. 1
9) Be able to define basic quality metrics, apply software life cycle processes, measure software quality, identify quality model characteristics, apply standards and be able to use them to analyze, design, develop, verify and test complex software system. 1
10) Be able to gain technical information about other disciplines such as sustainable development that have common boundaries with software engineering such as mathematics, science, computer engineering, industrial engineering, systems engineering, economics, management and be able to create innovative ideas in entrepreneurship activities. 5
11) Be able to grasp software engineering culture and concept of ethics and have the basic information of applying them in the software engineering and learn and successfully apply necessary technical skills through professional life.
12) Be able to write active reports using foreign languages and Turkish, understand written reports, prepare design and production reports, make effective presentations, give clear and understandable instructions.
13) Be able to have knowledge about the effects of engineering applications on health, environment and security in universal and societal dimensions and the problems of engineering in the era and the legal consequences of engineering solutions.