Energy Systems Engineering (English)
Bachelor	TR-NQF-HE: Level 6	QF-EHEA: First Cycle	EQF-LLL: Level 6

General course introduction information

Course Code:

MATH114

Course Name:

Mathematics II

Course Semester:

Fall

Course Credits:

Theoretical	Practical	Credit	ECTS
3	2	4	6

Language of instruction:

Course Requisites:

Does the Course Require Work Experience?:

Type of course:

Compulsory

Course Level:

Bachelor

TR-NQF-HE:6. Master`s Degree

QF-EHEA:First Cycle

EQF-LLL:6. Master`s Degree

Mode of Delivery:

Face to face

Course Coordinator :

Dr.Öğr.Üyesi MESERET TUBA GÜLPINAR

Course Lecturer(s):

Dr.Öğr.Üyesi ASUMAN ÖZER
Prof. Dr. VASFİ ELDEM
Prof. Dr. SEZGİN SEZER
Prof. Dr. HASAN ÖZEKES

Course Assistants:

Course Objective and Content

Course Objectives:

The aim of this course to gain basic knowladge and abilities about techniques of Integration, improper integrals, infinite sequences and series, convergence tests, power series, radius of convergence and interval of convergence, term-by-term differentiation and integration of power series, vectors in 3-space, dot product and cross product of vectors, equations of lines and planes in space, quadratic surfaces, functions of several variables and their limits, continuity and partial derivatives, chain rule, directional derivatives, tangent planes and normal lines, local and absolute extrema, Lagrange multipliers, double and triple integrals, polar coordinates, change of variables, cylindrical and spherical coordinates to the students.

Course Content:

This course will investigate techniques of Integration, improper integrals, infinite sequences and series, convergence tests, power series, radius of convergence and interval of convergence, term-by-term differentiation and integration of power series, vectors in 3-space, dot product and cross product of vectors, equations of lines and planes in space, quadratic surfaces, functions of several variables and their limits, continuity and partial derivatives, chain rule, directional derivatives, tangent planes and normal lines, local and absolute extrema, Lagrange multipliers, double and triple integrals, polar coordinates, change of variables, cylindrical and spherical coordinates.

Learning Outcomes

The students who have succeeded in this course;

Learning Outcomes

1 - Knowledge
Theoretical - Conceptual
1) Evaluate integrals, using the basic rules of integration and other techniques such as integration by parts, trigonometric substitution, and partial fraction decomposion and determine the convergence of improper integrals.
2) Able to calculate the limits of infinite sequences and sum of infinite series and use various test to determine the convergence. Able to calculate the radius and interval of convergence of power series.
3) Able to perform vector operations such as dot product, the cross product, and the projection of a vector onto another vector and derive the equations of lines and planes in space.
4) Able to describe and sketch the domain and the range of functions with several variables and determine the existence of the limits and continuity of these functions. Evaluate the partial derivatives, directional derivatives, extreme values, and use them to solve optimization problems.
5) Able to evaluate the multiple integrals over general regions by using substitution and obtain the area of a surface or volume of a solid by using multiple integrals.
2 - Skills
Cognitive - Practical
3 - Competences
Communication and Social Competence
Learning Competence
Field Specific Competence
Competence to Work Independently and Take Responsibility

Lesson Plan

Week	Subject	Related Preparation
1)	Techniques of Integration	Lecture Notes
2)	Techniques of Integration	Lecture Notes
3)	Infinite Sequences and Series	Lecture Notes
4)	Infinite Sequences and Series	Lecture Notes
5)	Infinite Sequences and Series	Lecture Notes
6)	Vectors and Geometry of Space	Lecture Notes
7)	Vectors and Geometry of Space	Lecture Notes
8)	Partial Derivatives	Lecture Notes
9)
10)	Partial Derivatives	Lecture Notes
11)	Multiple Integrals	Lecture Notes
12)	Multiple Integrals	Lecture Notes
13)	Multiple Integrals	Lecture Notes
14)	Review	Lecture Notes

Sources

Course Notes / Textbooks:	Thomas’ Calculus, 13th Edition George B. Thomas, Maurice D. Weir, Joel R. Hass Pearson Education Inc.
References:	A Complete Course Calculus, 8th Edition. Robert A. Adams, Christopher Essex Pearson Canada Inc. ISBN 978: 0321781079

Course-Program Learning Outcome Relationship

Learning Outcomes	1	2	3	4	5
Program Outcomes
1) Closed Department

Course - Learning Outcome Relationship

No Effect	1 Lowest	2 Low	3 Average	4 High	5 Highest

	Program Outcomes	Level of Contribution
1)	Closed Department

Learning Activity and Teaching Methods

Individual study and homework
Reading
Homework
Problem Solving
Q&A / Discussion

Assessment & Grading Methods and Criteria

Written Exam (Open-ended questions, multiple choice, true-false, matching, fill in the blanks, sequencing)
Homework

Assessment & Grading

Semester Requirements	Number of Activities	Level of Contribution
Homework Assignments	5	% 20
Midterms	2	% 40
Final	1	% 40
total		% 100
PERCENTAGE OF SEMESTER WORK		% 60
PERCENTAGE OF FINAL WORK		% 40
total		% 100

Workload and ECTS Credit Grading

Activities	Number of Activities	Duration (Hours)	Workload
Course Hours	15	5	75
Study Hours Out of Class	15	2	30
Homework Assignments	5	5	25
Midterms	2	10	20
Final	1	15	15
Total Workload			165