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Information
| Code | CMZ108 |
| Name | Mathematics II |
| Semester | 2. Semester |
| Duration (T+A) | 4-0 (T-A) (17 Week) |
| ECTS | 6 ECTS |
| National Credit | 4 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. ZERRİN GÜL ESMERLİGİL |
Course Goal
Area, volume calculation with the mathematical and physical quantities, the theory of functions of several variables input, first-order and first-order differential equations. We also train the students to think analytically and to solve problems in the future issues will form their own interest to teach the methods of solution for the models. Analysis is considered as one of the greatest achievements of the human mind is an exciting topic. Our hope is that students with usage analysis is not only to discover her inner beauty as well.
Course Content
Polar coordinates, indefinite and definite integrals and applications, functions of several variables ,1. degrees and 1. order differential equations.
Course Precondition
None
Resources
Analize Giriş Cilt II Prof. Dr. Fikri AKDENİZ Prof.Dr. Yusuf ÜNLÜ
Notes
Lecture Notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Identifies and draws on different curves. Definite integral accounts. Using the Definite Integral area, volume, surface area, and center of gravity finds the arc length. Finds the limits of functions of several variables. Finds partial derivatives of func |
| LO02 | Definite integral accounts. Using the Definite Integral area, volume, surface area, and center of gravity finds the arc length. Finds the limits of functions of several variables. Finds partial derivatives of func |
| LO03 | Using the Definite Integral area, volume, surface area, and center of gravity finds the arc length. |
| LO04 | Finds the limits of functions of several variables. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Becomes equipped with adequate knowledge in mathematics, science, environment and engineering sciences | 4 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Becomes able to apply theoretical knowledge in mathematics, science, environment and engineering sciences | 5 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Determines, describes, formulates and gains capabilities in solving engineering problems | 3 |
| PLO04 | Bilgi - Kuramsal, Olgusal | Analyzes a system, components of the system or process, gains the designing capabilities of the system under the real restrictive conditions. | 5 |
| PLO05 | Bilgi - Kuramsal, Olgusal | Chooses ans uses the ability to apply modern tools and design technics, suitable analytical methods, modeling technics for the engineering applications | 3 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Designs and performs experiments, data collection, has the ability of analyzing results | 5 |
| PLO07 | Bilgi - Kuramsal, Olgusal | Works individually and in inter-disciplinary teams effectively | 5 |
| PLO08 | Beceriler - Bilişsel, Uygulamalı | Becomes able to reach knowledge and for this purpose does literature research and to uses data base and other information sources | |
| PLO09 | Beceriler - Bilişsel, Uygulamalı | Becomes aware of the necessity of lifelong learning and continuously self renewal | |
| PLO10 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Capable of effective oral and written skills in at least one foreign language for technical or non-technical use | |
| PLO11 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Effective use of Information and communication technologies | 1 |
| PLO12 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Defines necessities in learning in scientific, social, cultural and artistic areas and improves himself/herself accordingly. | 1 |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Professional and ethical responsibility | 4 |
| PLO14 | Yetkinlikler - Öğrenme Yetkinliği | Project management, workplace practices, environmental and occupational safety; awareness about the legal implications of engineering applications | |
| PLO15 | Yetkinlikler - Öğrenme Yetkinliği | Becomes aware of universal and social effects of engineering solutions and applications, entrepreneurship and innovation and to have idea of contemporary issues |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Polar Koordinatlar.Some major curves. Curves drawings. Parametric representation of the slope of the tangent formula.Parametric representation of curves. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 2 | The Indefinite Integral definition, properties. Variable Change and Integration by Parts. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 3 | Integration of rational functions. Integration of some trigonometric functions. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 4 | Some algebraic functions integralnable with algebraic substitution .Trigonometrik and algebraic special integrals. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 5 | Problem-solving. Specific definition of integral, properties. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 6 | Fundamental theorems of differential-integral calculus. Change of variables in the definite integral. Improper Integrals. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 7 | Convergence of Improper integrals. Perpendicular to the polar coordinates and finding. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 8 | Mid-Term Exam | Review of the relevant pages from sources | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | The volume of solids of revolution. Arc length. Surface area. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 10 | Finding the center of gravity. Pappus theorem. Problem-solving. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 11 | Functions of several variables. Limits and continuity. Partial Derivatives, Chain Rule. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 12 | Finding the maximum, minimum, functions of several variables. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 13 | Introduction to differential equations. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 14 | Finding solutions to first-order and first-order differential equations. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 15 | First-order and first-order differential equations continue to find solutions and problem-solving. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 16 | Term Exams | Review of the relevant pages from sources | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Review of the relevant pages from sources | Ölçme Yöntemleri: Yazılı Sınav |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 4 | 56 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 4 | 56 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 12 | 12 |
| Final Exam | 1 | 28 | 28 |
| Total Workload (Hour) | 152 | ||
| Total Workload / 25 (h) | 6,08 | ||
| ECTS | 6 ECTS | ||