ENERGY SYSTEMS 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)	Build up a body of knowledge in mathematics, science and Energy Systems Engineering subjects; use theoretical and applied information in these areas to model and solve complex engineering problems.	4
2)	Ability to identify, formulate, and solve complex Energy Systems Engineering problems; select and apply proper modeling and analysis methods for this purpose.	4
3)	Ability to design complex Energy systems, processes, devices or products under realistic constraints and conditions, in such a way as to meet the desired result; apply modern design methods for this purpose.
4)	Ability to devise, select, and use modern techniques and tools needed for solving complex problems in Energy Systems Engineering practice; employ information technologies effectively.
5)	Ability to design and conduct numerical or pysical experiments, collect data, analyze and interpret results for investigating the complex problems specific to Energy Systems Engineering.	3
6)	Ability to cooperate efficiently in intra-disciplinary and multi-disciplinary teams; and show self-reliance when working on Energy Systems-related problems
7)	Ability to communicate effectively in English and Turkish (if he/she is a Turkish citizen), both orally and in writing. Write and understand reports, prepare design and production reports, deliver effective presentations, give and receive clear and understandable instructions.
8)	Recognize the need for life-long learning; show ability to access information, to follow developments in science and technology, and to continuously educate oneself.
9)	Develop an awareness of professional and ethical responsibility, and behave accordingly. Be informed about the standards used in Energy Systems Engineering applications.
10)	Learn about business life practices such as project management, risk management, and change management; develop an awareness of entrepreneurship, innovation, and sustainable development.
11)	Acquire knowledge about the effects of practices of Energys Systems Engineering on health, environment, security in universal and social scope, and the contemporary problems of Energys Systems engineering; is aware of the legal consequences of Energys Systems engineering solutions.