MATHEMATICS II PROGRAMME COURSE DESCRIPTION

Code	Name of the Course Unit	Semester	In-Class Hours (T+P)	Credit	ECTS Credit
MAT106	MATHEMATICS II	2	5	4	6

GENERAL INFORMATION
Language of Instruction :	Turkish
Level of the Course Unit :	BACHELOR'S DEGREE, TYY: + 6.Level, EQF-LLL: 6.Level, QF-EHEA: First Cycle
Type of the Course :	Compulsory
Mode of Delivery of the Course Unit	-
Coordinator of the Course Unit	Assist.Prof. OĞUZHAN ÖZTAŞ
Instructor(s) of the Course Unit
Course Prerequisite	No

OBJECTIVES AND CONTENTS
Objectives of the Course Unit:	It is aimed for students to recognize multivariable functions, to be able to transfer the concepts of limit continuity and derivatives obtained in univariate functions to multivariable functions, to interpret their graphs, and to calculate surface area and volume with different methods with the help of integral.
Contents of the Course Unit:	Area Between Curves, Lengths of Plane Curves, Finding Volume by Slicing and Rotation around an Axis, Finding Volume with Cylindrical Shells, Areas of Rotational Surfaces, Generalized Integrals, Multivariable Functions, Limits and Continuity in High Dimensions, Partial Derivatives, Chain Rule, Direction Derivatives and Gradient Vectors. , Tangent Planes and Differentials, Extreme Values ​​and Saddle Points, Second Derivative Test for Extreme Values, Double Integrals and Area, Volume Applications, Double Integrals in Polar Form, Variable Conversion in Multiple Integrals

KEY LEARNING OUTCOMES OF THE COURSE UNIT (On successful completion of this course unit, students/learners will or will be able to)
Recognizes multivariable functions and their graphs. (Bloom 1, Knowledge)
Uses partial derivative steps correctly. (Bloom 3, Application)
Defines and interprets Directional Derivative and Gradient Vector. (Bloom 1, Knowledge, Bloom 2, Understand)
Solves the problems of finding extrema and saddle points of graphs of two-variable functions. (Bloom 3, Application)
Transfers a given function to polar form. (Bloom 3, Application)
Compares different methods of calculating volume with the help of integral. (Bloom 2, Understand)
Solves area, volume and arc length calculation problems with the help of definite integral. (Bloom 3, Application)
Solves area and volume calculation problems with the help of double integral. (Bloom 3, Application)

WEEKLY COURSE CONTENTS AND STUDY MATERIALS FOR PRELIMINARY & FURTHER STUDY
Week	Preparatory	Topics(Subjects)	Method
1	Students create a positive impression in the preparatory work related to course topics	Sigma Notation and Limits of Finite Sums,The Definite Integral, The Fundamental Theorem of Calculus, Basic Integration Formulas, Integration by Parts,	Lecture-Discussion
2	Topic started on the preparation of problems and solutions	Integration of Rational Functions by Partial Fractions, Trigonometric Integrals, Trigonometric Substitutions	Lecture-Discussion
3	Topic started on the preparation of problems and solutions	Substitution and Area Between Curves, Lengths of Plane Curves	Lecture-Discussion
4	Topic started on the preparation of problems and solutions	Volumes by Slicing and Rotation About an Axis, Volumes by Cylindrical Shells, Areas of Surfaces of Revolution	Lecture-Discussion
5	Topic started on the preparation of problems and solutions	Improper Integrals	Lecture-Discussion
6	Topic started on the preparation of problems and solutions	Functions of Several Variables	Lecture-Discussion
7	Topic started on the preparation of problems and solutions	Limits and Continuity in Higher Dimensions	Lecture-Discussion
8	-	MID-TERM EXAM	-
9	Topic started on the preparation of problems and solutions	Partial Derivatives, The Chain Rule	Lecture-Discussion
10	Topic started on the preparation of problems and solutions	Directional Derivatives and Gradient Vectors, Tangent Planes and Differentials	Lecture-Discussion
11	Topic started on the preparation of problems and solutions	Extreme Values and Saddle Points	Lecture-Discussion
12	Topic started on the preparation of problems and solutions	Double Integrals, Area and Volume	Lecture-Discussion
13	Topic started on the preparation of problems and solutions	Double Integrals in Polar Form, Substitutions in Multiple Integrals	Lecture-Discussion
14	Topic started on the preparation of problems and solutions	Applications	Lecture-Discussion
15	-	-	-
16	-	FINAL EXAM	-
17	-	FINAL EXAM	-

SOURCE MATERIALS & RECOMMENDED READING
P.F.Smith, W.R. Congley, Diferansiyel ve İntegral Hesap.
Prof.Dr.Ahmet Karadeniz, Yüksek Matematik Problemleri.
Murtaza Çalı, Diferansiyel ve İntegral Hesap.
George B. Thomas, Calculus and Analytic Geometry.
Naci İskender, Yüksek Matematik.

ASSESSMENT
Assessment & Grading of In-Term Activities	Number of Activities	Degree of Contribution (%)	Description

Level of Contribution
0	1	2	3	4	5

KNOWLEDGE
Theoretical
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Explains the fundamental engineering concepts of computer science and relates them to the groundwork of computer science.

KNOWLEDGE
Factual
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Uses theoretical and practical knowledge coming from mathematics, probability, statistics and various other branches of life sciences, to find solutions to engineering problems.

SKILLS
Cognitive
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Determines the components and the underlying process of a system and designs an appropriate computational model under reasonable constraints.
2	Designs a computer-aided conceptual model with modern techniques.

SKILLS
Practical
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Determines, detects and analyzes the areas of computer science applications and develops appropriate solutions.
2	Identifies, models and solves computer engineering problems by applying appropriate analytical methods.
3	Determines and uses the necessary information technologies in an efficient way for engineering applications.

OCCUPATIONAL
Autonomy & Responsibility
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Possess the responsibility and ability to design and conduct experiments for engineering problems by collecting, analyzing and interpreting data.
2	Possess the ability to conduct effective individual study.
3	Takes responsibility as a team work and contributes in an effective way.

OCCUPATIONAL
Learning to Learn
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Monitors the developments in the field of information technologies by means of internet and related journals and possess the required knowledge for the management, control, development and security of information technologies.
2	Develops positive attitude towards lifelong learning.

OCCUPATIONAL
Communication & Social
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Communicates effectively by oral and/or written form and uses at least one foreign language.
2	Possess sufficient consciousness about the issues of project management, practical applications and also environmental protection, worker's health and security.

OCCUPATIONAL
Occupational and/or Vocational
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Possess professional and ethical responsibility and willingness to share it.
2	Possess sufficient consciousness about the universality of engineering solutions and applications and be well aware of the importance of innovation.

WORKLOAD & ECTS CREDITS OF THE COURSE UNIT
Workload for Learning & Teaching Activities
Type of the Learning Activites	Learning Activities (# of week)	Duration (hours, h)	Workload (h)
Lecture & In-Class Activities	14	4	56
Preliminary & Further Study	14	2	28
Land Surveying	0	0	0
Group Work	0	0	0
Laboratory	0	0	0
Reading	0	0	0
Assignment (Homework)	4	6	24
Project Work	0	0	0
Seminar	0	0	0
Internship	0	0	0
Technical Visit	0	0	0
Web Based Learning	0	0	0
Implementation/Application/Practice	4	4	16
Practice at a workplace	0	0	0
Occupational Activity	0	0	0
Social Activity	0	0	0
Thesis Work	0	0	0
Field Study	0	0	0
Report Writing	0	0	0
Final Exam	1	2	2
Preparation for the Final Exam	1	10	10
Mid-Term Exam	1	2	2
Preparation for the Mid-Term Exam	1	10	10
Short Exam	0	0	0
Preparation for the Short Exam	0	0	0
TOTAL	40	0	148