TÜRKÇE
ENGLISH
Information
| Unit | FACULTY OF SCIENCE AND LETTERS |
| ARTIFICIAL INTELLIGENCE AND MACHINE LEARNING PR. (ENGLISH) | |
| Code | YZZ102 |
| Name | Mathematics II |
| Term | 2025-2026 Academic Year |
| Semester | 2. Semester |
| Duration (T+A) | 4-0 (T-A) (17 Week) |
| ECTS | 5 ECTS |
| National Credit | 4 National Credit |
| Teaching Language | İngilizce |
| Level | Belirsiz |
| Type | Normal |
| Label | C Compulsory |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Doç. Dr. Ayşe Gül KAPLAN |
| Course Instructor |
The current term course schedule has not been prepared yet.
|
Course Goal / Objective
The aim of this course is to provide students with detailed information about integrals, their usage areas, and series in order to provide them with the foundation of the information they will use in the future and to help them gain an analytical thinking structure.
Course Content
This course covers partial derivatives and finding extreme values in multivariable functions. Multiple integrals in Cartesian, polar, cylindrical, and spherical coordinates. Change of variables. Green's and Stokes' theorems. Sequences, series, power series, and Taylor series.
Course Precondition
None
Resources
Robert A. Adams, Cristopher Essex, Calculus A Complete Course Seventh Edition, Pearson Education.
Notes
Stewart James, Calculus: concepts and contexts 2nd ed.,TECH-arts of Colorado, Inc.
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 | Explains power series of elementary functions. |
| LO06 | Uses the power series of fundamental functions for derivation and integration. |
| LO07 | Applies extreme values in multivariable functions using partial derivatives, gradients, and directional derivatives. |
| LO08 | Apply it to double integrals using Cartesian and polar coordinates. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | It provides a broad range of knowledge about fundamental Computer Science concepts, algorithms and data structures. | |
| PLO02 | Bilgi - Kuramsal, Olgusal | Learns basic computer topics such as software development, programming languages, and database management. | |
| PLO03 | Bilgi - Kuramsal, Olgusal | Understands advanced computing fields such as data science, artificial intelligence, and machine learning. | |
| PLO04 | Belirsiz | Learn about topics such as computer networks, cyber security, and database design. | |
| PLO05 | Beceriler - Bilişsel, Uygulamalı | Develops skills in designing, implementing and analyzing algorithms. | 4 |
| PLO06 | Beceriler - Bilişsel, Uygulamalı | Gains the ability to use different programming languages effectively | |
| PLO07 | Beceriler - Bilişsel, Uygulamalı | Learns data analysis, database management and big data processing skills. | |
| PLO08 | Beceriler - Bilişsel, Uygulamalı | Gains practical experience by working on software development projects. | |
| PLO09 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Strengthens collaboration and communication skills within the team. | 3 |
| PLO10 | Yetkinlikler - Alana Özgü Yetkinlik | It provides a mindset open to technological innovations. | 4 |
| PLO11 | Yetkinlikler - Öğrenme Yetkinliği | Encourages continuous learning and self-improvement competence. | 4 |
| PLO12 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Develops 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 | Mid-Term Exam | 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 | Term Exams | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Term Exams | 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 | 3 | 42 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 12 | 12 |
| Final Exam | 1 | 26 | 26 |
| Total Workload (Hour) | 136 | ||
| Total Workload / 25 (h) | 5,44 | ||
| ECTS | 5 ECTS | ||