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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 Prof. OSMAN KOPMAZ
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

CONTRIBUTION OF THE COURSE UNIT TO THE PROGRAMME LEARNING OUTCOMES

KNOWLEDGE

Theoretical

Programme Learning Outcomes Level of Contribution
0 1 2 3 4 5
1
Ability to apply mathematics, science and engineering knowledge.
5

KNOWLEDGE

Factual

Programme Learning Outcomes Level of Contribution
0 1 2 3 4 5
1
Ability to apply mathematics, science and engineering knowledge.
5

SKILLS

Cognitive

Programme Learning Outcomes Level of Contribution
0 1 2 3 4 5
1
Ability to design experiments, conduct experiments, collect data, analyze and interpret results.
0

SKILLS

Practical

Programme Learning Outcomes Level of Contribution
0 1 2 3 4 5
1
A system, product or process has economic, environmental, social, political, ethical, health and safety, under realistic constraints and conditions such as feasibility and sustainability, Ability to design to meet requirements.
2

OCCUPATIONAL

Autonomy & Responsibility

Programme Learning Outcomes Level of Contribution
0 1 2 3 4 5
1
Ability to work in teams with different disciplines
1

OCCUPATIONAL

Learning to Learn

Programme Learning Outcomes Level of Contribution
0 1 2 3 4 5
1
Ability to identify, formulate and solve engineering problems
3

OCCUPATIONAL

Communication & Social

Programme Learning Outcomes Level of Contribution
0 1 2 3 4 5
1
Awareness of having professional and ethical responsibilities.
1
2
Ability to communicate effectively verbally and in writing.
1

OCCUPATIONAL

Occupational and/or Vocational

Programme Learning Outcomes Level of Contribution
0 1 2 3 4 5
1
The ability to have a comprehensive education to understand the impact of engineering solutions on global and social dimensions.
1
2
Awareness of the necessity of lifelong learning and the ability to do so.
1
3
The ability to have knowledge about current/contemporary issues.
3
4
Ability to use the techniques required for engineering applications and modern engineering and calculation equipment.
2

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
Total Workload of the Course Unit 148
Workload (h) / 25.5 5,8
ECTS Credits allocated for the Course Unit 6,0