MATHEMATICS II PROGRAMME COURSE DESCRIPTION

Code	Name of the Course Unit	Semester	In-Class Hours (T+P)	Credit	ECTS Credit
MAT142	MATHEMATICS II	2	3	3	4

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. BANU KAYINOVA
Instructor(s) of the Course Unit	Assist.Prof. BEDİA MERİH ÖZÇETİN VATANSEVER
Course Prerequisite	No

OBJECTIVES AND CONTENTS
Objectives of the Course Unit:	The objective is for students to become familiar with multivariable functions, apply the concepts of limits, continuity, and derivatives—which they have learned in the context of single-variable functions—to multivariable functions, interpret their graphs, and calculate surface area and volume using various methods involving integrals.
Contents of the Course Unit:	Definite and Indefinite Integrals: Solutions and Applications, Area Between Curves, Lengths of Curves in the Plane, Finding Volume by Slicing and Rotation Around an Axis, Finding Volume Using Cylindrical Shells, Areas of Surfaces of Revolution, Generalized Integrals, Multivariable Functions, Limits and Continuity in Higher Dimensions, Partial Derivatives, the Chain Rule, Directional Derivatives and Gradient Vectors, Tangent Planes and Differentials, Extremum Values and Saddle Points, the Second Derivative Test for Extremum Values Translated with DeepL.com (free version)

KEY LEARNING OUTCOMES OF THE COURSE UNIT (On successful completion of this course unit, students/learners will or will be able to)
Can solve problems involving indefinite integrals.
Recognizes multivariable functions and their graphs.
Correctly uses partial differentiation steps.
Definitions and interpretations of directional derivatives and gradient vectors.
Solves problems involving finding extrema and saddle points on the graphs of functions of two variables.
Solves problems involving the calculation of area, volume, and arc length using definite integrals.
Compares different methods for calculating volume using integrals.

WEEKLY COURSE CONTENTS AND STUDY MATERIALS FOR PRELIMINARY & FURTHER STUDY
Week	Preparatory	Topics(Subjects)	Method
1	The relevant unit in the course book	Introductions, overview of the course, information on teaching methods, definition of the integral, formulas	Explanation, problem-solving, practical application
2	The relevant unit in the course book	Integration methods, substitution method, integration by parts, and applications of integration using the method of reducing to simple fractions	Explanation, problem-solving, practical application
3	The relevant unit in the course book	Trigonometric integrals, trigonometric transformations, Riemann sums, properties of the sigma (sum) symbol, fundamental theorem of definite integrals	Explanation, problem-solving, practical application
4	The relevant unit in the course book	Sum Notation and Limits of Finite Sums, Definite Integral, Fundamental Theorem of Calculus, Basic Integration Formulas for Definite Integrals	Explanation, problem-solving, practical application
5	The relevant unit in the course book	Variable Substitution and Area Between Curves, Lengths of Curves in the Plane	Explanation, problem-solving, practical application
6	The relevant unit in the course book	Finding Volume by Slicing and Rotation Around an Axis, Finding Volume Using Cylindrical Shells, Areas of Surfaces of Revolution	Explanation, problem-solving, practical application
7	The relevant unit in the course book	Generalized Integrals	Explanation, problem-solving, practical application
8	The relevant unit in the course book	Multivariable Functions	Explanation, problem-solving, practical application
9	The relevant unit in the course book	Limits and Continuity in Higher Dimensions	Explanation, problem-solving, practical application
10	-	MID-TERM EXAM	-
11	The relevant unit in the course book	Partial Derivatives, Chain Rule	Explanation, problem-solving, practical application
12	The relevant unit in the course book	Partial Derivatives, Chain Rule	Explanation, problem-solving, practical application
13	The relevant unit in the course book	Directional Derivatives and Gradient Vectors, Tangent Planes and Differentials	Explanation, problem-solving, practical application
14	The relevant unit in the course book	Extremum Values and Saddle Points, Second Derivative Test for Extremum Values	Explanation, problem-solving, practical application
15	The relevant unit in the course book	General Review	Explanation, problem-solving, practical application
16	-	FINAL EXAM	-
17	-	FINAL EXAM	-

SOURCE MATERIALS & RECOMMENDED READING
George B. Thomas, Calculus, (11. baskıdan çeviri).
Stewart Calculus.

ASSESSMENT
Assessment & Grading of In-Term Activities	Number of Activities	Degree of Contribution (%)	Description	Examination Method
Mid-Term Exam	1	40		Classical Exam
Homework Assessment	1	10
Final Exam	1	50		Classical Exam
TOTAL	3	100

Level of Contribution
0	1	2	3	4	5

KNOWLEDGE
Theoretical
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1							5
2							5

KNOWLEDGE
Factual
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1						4
2						4

SKILLS
Cognitive
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1						4
2						4

SKILLS
Practical
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1						4
2					3

OCCUPATIONAL
Autonomy & Responsibility
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1					3
2					3

OCCUPATIONAL
Learning to Learn
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1					3
2							5

OCCUPATIONAL
Communication & Social
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1							5
2				2

OCCUPATIONAL
Occupational and/or Vocational
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1					3
2					3

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	3	42
Preliminary & Further Study	9	2	18
Land Surveying	0	0	0
Group Work	0	0	0
Laboratory	0	0	0
Reading	0	0	0
Assignment (Homework)	11	1	11
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	9	3	27
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	1	1
Preparation for the Final Exam	0	0	0
Mid-Term Exam	1	1	1
Preparation for the Mid-Term Exam	0	0	0
Short Exam	0	0	0
Preparation for the Short Exam	0	0	0
TOTAL	45	0	100