CEN106 Mathematics 2

5 ECTS - 4-0 Duration (T+A)- 2. Semester- 4 National Credit

Information

Code CEN106
Name Mathematics 2
Term 2024-2025 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 Lisans Dersi
Type Normal
Mode of study Yüz Yüze Öğretim
Catalog Information Coordinator Prof. Dr. ŞEHMUS FINDIK
Course Instructor
1 2
Arş.Gör.Dr. Mehmet GÜRSUL (A Group) (Ins. in Charge)


Course Goal / Objective

To teach the student the topics of infinite series, functions of several variables, multiple integrals and integral theorems, which are the main topics of engineering mathematics, in a functional integrity.

Course Content

Sequence and series of numbers, power series, Taylor series. Quadratic curves, polar coordinates. Analytic geometry in R , vector functions. Functions of several variables, partial derivatives, minimum and maximum problems. Multiple integrals and applications. Line integral, Green's theorem. Surface integral, divergence theorem, Stokes' theorem.

Course Precondition

None.

Resources

Calculus, J. Stewart

Notes

None.


Course Learning Outcomes

Order Course Learning Outcomes
LO01 Analyzes infinite series in conjuction with convergence and divergence concepts
LO02 Derives the Taylor-Maclaurin expansion of a given function.
LO03 Calculates and comments on the partial derivatives of multivariable functions.
LO04 Calculates multiple integrals,


Relation with Program Learning Outcome

Order Type Program Learning Outcomes Level
PLO01 Bilgi - Kuramsal, Olgusal Adequate knowledge of mathematics, science and related engineering disciplines; ability to use theoretical and applied knowledge in these fields in solving complex engineering problems. 5
PLO02 Bilgi - Kuramsal, Olgusal Ability to identify, formulate and solve complex engineering problems; ability to select and apply appropriate analysis and modeling methods for this purpose. 4
PLO03 Bilgi - Kuramsal, Olgusal Ability to design a complex system, process, device or product to meet specific requirements under realistic constraints and conditions; ability to apply modern design methods for this purpose.
PLO04 Bilgi - Kuramsal, Olgusal Ability to select and use modern techniques and tools necessary for the analysis and solution of complex problems encountered in engineering practice; ability to use information technologies effectively.
PLO05 Bilgi - Kuramsal, Olgusal Ability to design and conduct experiments, collect data, analyze and interpret results to investigate complex engineering problems or discipline-specific research topics.
PLO06 Bilgi - Kuramsal, Olgusal Ability to work effectively in interdisciplinary and multidisciplinary teams; individual working skills.
PLO07 Bilgi - Kuramsal, Olgusal Ability to communicate effectively verbally and in writing; knowledge of at least one foreign language; ability to write effective reports and understand written reports, prepare design and production reports, make effective presentations, and give and receive clear and understandable instructions.
PLO08 Bilgi - Kuramsal, Olgusal Awareness of the necessity of lifelong learning; ability to access information, follow developments in science and technology, and constantly renew oneself.
PLO09 Bilgi - Kuramsal, Olgusal Knowledge of ethical principles, professional and ethical responsibility, and standards used in engineering practice.
PLO10 Bilgi - Kuramsal, Olgusal Knowledge of business practices such as project management, risk management and change management; awareness of entrepreneurship and innovation; knowledge of sustainable development.
PLO11 Bilgi - Kuramsal, Olgusal Knowledge of the effects of engineering practices on health, environment and safety in universal and social dimensions and the problems of the age reflected in the field of engineering; awareness of the legal consequences of engineering solutions.


Week Plan

Week Topic Preparation Methods
1 Integral applications, arc length, volume and surface area calculation Reading the lecture notes Öğretim Yöntemleri:
Anlatım
2 Parametric curves Reading the lecture notes Öğretim Yöntemleri:
Anlatım
3 Polar coordinates, polar curves Reading the lecture notes Öğretim Yöntemleri:
Anlatım
4 Infinite series, convergence tests Reading the lecture notes Öğretim Yöntemleri:
Anlatım
5 Convergence tests (continued) Reading the lecture notes Öğretim Yöntemleri:
Anlatım
6 Taylor and Maclaurin expansions, Taylor approximation Reading the lecture notes Öğretim Yöntemleri:
Anlatım
7 Introduction to multivariable functions, partial derivatives and the chain rule Reading the lecture notes Öğretim Yöntemleri:
Anlatım
8 Mid-Term Exam Reading the lecture notes Ölçme Yöntemleri:
Yazılı Sınav
9 Double integrals over general regions Reading the lecture notes Öğretim Yöntemleri:
Anlatım
10 Triple integrals, change of variables in multiple integrals Reading the lecture notes Öğretim Yöntemleri:
Anlatım
11 Double and triple integrals in polar coordinates Reading the lecture notes Öğretim Yöntemleri:
Anlatım
12 Surface area calculation, line integrals Reading the lecture notes Öğretim Yöntemleri:
Anlatım
13 Surface integrals, Green's theorem Reading the lecture notes Öğretim Yöntemleri:
Anlatım
14 Stokes and Divergence theorems Reading the lecture notes Öğretim Yöntemleri:
Anlatım
15 FINAL Reading the lecture notes Ölçme Yöntemleri:
Yazılı Sınav
16 Term Exams Reading the lecture notes Ölçme Yöntemleri:
Yazılı Sınav
17 Term Exams Reading the lecture notes 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 8 8
Final Exam 1 16 16
Total Workload (Hour) 122
Total Workload / 25 (h) 4,88
ECTS 5 ECTS

Update Time: 21.11.2024 12:20