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Information
| Code | BBZ108 |
| Name | Mathematics II |
| Term | 2024-2025 Academic Year |
| Semester | 2. Semester |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 6 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Belirsiz |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. GÜZİN YÜKSEL |
| Course Instructor |
1 2 |
Course Goal / Objective
To provide students with detailed information about integrals, areas of use of integrals and series in order to form a basis for the knowledge they will use in the future and to provide them with an analytical mindset.
Course Content
Partial derivatives, finding extrema of multivariable functions. Double and triple integrals in Cartesian, polar, cylindrical and spherical coordinates. Change of variables. Green's and Stokes's Theorems. Sequences, series, power series, Taylor series.
Course Precondition
None
Resources
Ayşe Peker Dobie, Matematik I Çözümlü Problemleri Calculus and Analytic Geometry, Sherman K. Stein, Anthony Barcellos.Lecture notes.
Notes
Lecture notes.
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Calculates partial derivatives, gradients and direction derivatives. |
| LO02 | Uses Cartesian and polar coordinates. |
| LO03 | Uses cartesian, cylindrical and spherical coordinates. |
| LO04 | Uses Green's and Stokes' Theorems to calculate curve and surface integrals. |
| LO05 | Calculates power series of fundamental functions |
| LO06 | Uses the power series of fundamental functions for derivation and integration. |
| LO07 | Finds extreme values in multivariable functions using partial derivative, gradient and directional derivative. |
| LO08 | Calculates double integrals using Cartesian and polar coordinates. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Gain comprehensive knowledge of fundamental concepts, algorithms, and data structures in Computer Science. | |
| PLO02 | Bilgi - Kuramsal, Olgusal | Learn essential computer topics such as software development, programming languages, and database management | |
| PLO03 | Bilgi - Kuramsal, Olgusal | Understand advanced computer fields like data science, artificial intelligence, and machine learning. | |
| PLO04 | Bilgi - Kuramsal, Olgusal | Acquire knowledge of topics like computer networks, cybersecurity, and database design. | |
| PLO05 | Beceriler - Bilişsel, Uygulamalı | Develop skills in designing, implementing, and analyzing algorithms | 4 |
| PLO06 | Beceriler - Bilişsel, Uygulamalı | Gain proficiency in using various programming languages effectively | |
| PLO07 | Beceriler - Bilişsel, Uygulamalı | Learn skills in data analysis, database management, and processing large datasets. | |
| PLO08 | Beceriler - Bilişsel, Uygulamalı | Acquire practical experience through working on software development projects. | |
| PLO09 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Strengthen teamwork and communication skills. | 3 |
| PLO10 | Yetkinlikler - Alana Özgü Yetkinlik | Foster a mindset open to technological innovations. | 4 |
| PLO11 | Yetkinlikler - Öğrenme Yetkinliği | Encourage the capacity for continuous learning and self-improvement. | 4 |
| PLO12 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Enhance the ability to solve complex problems | 4 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Multivariable functions, partial derivatives, the Chain Rule, implicit differentiation | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 2 | Gradients, maximum/minimum in the multivariable case, Lagrange multipliers | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama |
| 3 | Polar, cylindrical and spherical coordinate systems; curves and surfaces in R^2 and R^3 | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 4 | Double integrals, Fubini's Theorem | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 5 | Double integrals in polar coordinates | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 6 | Triple integrals in Cartesian, cylindrical and spherical coordinates | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 7 | Change of variables | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama |
| 8 | Mid-Term Exam | Review and problem Solving | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Path integrals | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 10 | Green's Theorem | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama |
| 11 | Surface integrals, curl and divergence | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 12 | Stokes's Theorem | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama |
| 13 | Sequences and series | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 14 | Convergence tests, power series | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 15 | Taylor series and their applications | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 16 | Term Exams | Review and problem Solving | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Review and problem Solving | Ölçme Yöntemleri: Yazılı Sınav |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 3 | 42 |
| 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 | 15 | 15 |
| Final Exam | 1 | 30 | 30 |
| Total Workload (Hour) | 143 | ||
| Total Workload / 25 (h) | 5,72 | ||
| ECTS | 6 ECTS | ||