BBZ108 Mathematics II

6 ECTS - 3-0 Duration (T+A)- 2. Semester- 3 National Credit

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
Prof. Dr. GÜZİN YÜKSEL (A Group) (Ins. in Charge)


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

Update Time: 04.07.2024 03:29