Code | Name of the Course Unit | Semester | In-Class Hours (T+P) | Credit | ECTS Credit |
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MAT106 | MATHEMATICS II | 2 | 5 | 4 | 6 |
GENERAL INFORMATION |
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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 |
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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) |
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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 |
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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 |
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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 |
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Assessment & Grading of In-Term Activities | Number of Activities | Degree of Contribution (%) | Description |
Level of Contribution | |||||
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0 | 1 | 2 | 3 | 4 | 5 |
KNOWLEDGE |
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Theoretical |
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Programme Learning Outcomes | Level of Contribution | ||||||
0 | 1 | 2 | 3 | 4 | 5 | ||
1 |
Ability to apply mathematics, science and engineering knowledge.
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5 |
KNOWLEDGE |
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Factual |
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Programme Learning Outcomes | Level of Contribution | ||||||
0 | 1 | 2 | 3 | 4 | 5 | ||
1 |
Ability to apply mathematics, science and engineering knowledge.
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5 |
SKILLS |
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Cognitive |
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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.
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0 |
SKILLS |
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Practical |
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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.
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2 |
OCCUPATIONAL |
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Autonomy & Responsibility |
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Programme Learning Outcomes | Level of Contribution | ||||||
0 | 1 | 2 | 3 | 4 | 5 | ||
1 |
Ability to work in teams with different disciplines
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1 |
OCCUPATIONAL |
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Learning to Learn |
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Programme Learning Outcomes | Level of Contribution | ||||||
0 | 1 | 2 | 3 | 4 | 5 | ||
1 |
Ability to identify, formulate and solve engineering problems
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3 |
OCCUPATIONAL |
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Communication & Social |
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Programme Learning Outcomes | Level of Contribution | ||||||
0 | 1 | 2 | 3 | 4 | 5 | ||
1 |
Awareness of having professional and ethical responsibilities.
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1 | |||||
2 |
Ability to communicate effectively verbally and in writing.
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1 |
OCCUPATIONAL |
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Occupational and/or Vocational |
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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.
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1 | |||||
2 |
Awareness of the necessity of lifelong learning and the ability to do so.
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1 | |||||
3 |
The ability to have knowledge about current/contemporary issues.
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3 | |||||
4 |
Ability to use the techniques required for engineering applications and modern engineering and calculation equipment.
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2 |
WORKLOAD & ECTS CREDITS OF THE COURSE UNIT |
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Workload for Learning & Teaching Activities |
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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 |