Civil Engineering (English)
Bachelor TR-NQF-HE: Level 6 QF-EHEA: First Cycle EQF-LLL: Level 6

General course introduction information

Course Code: MATH216
Course Name: Mathematics IV
Course Semester: Spring
Course Credits:
Theoretical Practical Credit ECTS
2 2 3 6
Language of instruction: EN
Course Requisites: MATH114 - Mathematics II
Does the Course Require Work Experience?: No
Type of course: Compulsory
Course Level:
Bachelor TR-NQF-HE:6. Master`s Degree QF-EHEA:First Cycle EQF-LLL:6. Master`s Degree
Mode of Delivery: Face to face
Course Coordinator : Dr.Öğr.Üyesi MESERET TUBA GÜLPINAR
Course Lecturer(s): Prof. Dr. HASAN ÖZEKES
Course Assistants:

Course Objective and Content

Course Objectives: The aim of this course is to gain basic knowledge and abilities about classification of differential equations, first order differential equations: solution of separable, linear and exact differential equations, substitution methods and order reduction, higher order differential equations: linear, homogeneous equations with constant coefficients, nonhomogeneous equations, method of undetermined coefficients, method of variation of parameters, Laplace transform solution of initial value problems, linear systems of differential equations: homogeneous differential equations in R2, homogeneous differential equations in R3, matrix exponential and fundamental matrix solution, solution of systems of nonhomogeneous equations, Laplace transform methods to the students.
Course Content: This course will investigate classification of differential equations, first order differential equations: solution of separable, linear and exact differential equations, substitution methods and order reduction, higher order differential equations: linear, homogeneous equations with constant coefficients, nonhomogeneous equations, method of undetermined coefficients, method of variation of parameters, Laplace transform solution of initial value problems, linear systems of differential equations: homogeneous differential equations in R2, homogeneous differential equations in R3, matrix exponential and fundamental matrix solution, solution of systems of nonhomogeneous equations, Laplace transform methods

Learning Outcomes

The students who have succeeded in this course;
Learning Outcomes
1 - Knowledge
Theoretical - Conceptual
1) Able to classify the given differential equations and solve the first order linear differential equations and some nonlinear differential equations.
2) Able to determine the general solution of the higher order homogeneous and non-homogeneous constant coefficient linear differential equations.
3) Able to calculate the Laplace Transform of functions and inverse Laplace Transform of rational expressions of Laplace Transform and solve homogeneous and non-homogeneous linear differential equations with constant coefficients by using Laplace Transformation.
4) Able to use eigenvalues and eigenvectors of square matrices to calculate the solution of the systems of the homogeneous and non-homogeneous differential equations in R^2 and R^3.
2 - Skills
Cognitive - Practical
3 - Competences
Competence to Work Independently and Take Responsibility
Field Specific Competence
Learning Competence
Communication and Social Competence

Lesson Plan

Week Subject Related Preparation
1) Some Basic Mathematical Models; Direction Fields Classification of Differential Equations Lecture Notes
2) First Order Differential Equations Lecture Notes
3) First Order Differential Equations Lecture Notes
4) Higher Order Linear Equations Lecture Notes
5) Higher Order Linear Equations Lecture Notes
6) The Laplace Transform Lecture Notes
7) The Laplace Transform Lecture Notes
8) The Laplace Transform Lecture Notes
9)
10) Systems of First Order Linear Differential Equations Lecture Notes
11) Systems of First Order Linear Differential Equations Lecture Notes
12) Systems of First Order Linear Differential Equations Lecture Notes
13) Systems of First Order Linear Differential Equations Lecture Notes
14) Systems of First Order Linear Differential Equations Lecture Notes

Sources

Course Notes / Textbooks: Elementary Differential Equations and Boundary Value Problems, 10th Edition with WileyPlus Card
William E. Boyce, Richard C. DiPrima
John Wiley & Sons Pte Ltd
References: Lecture notes- Ders notu

Course-Program Learning Outcome Relationship

Learning Outcomes

1

2

3

4
Program Outcomes
1) Adequate knowledge in mathematics, science and engineering subjects pertaining to the relevant discipline; ability to use theoretical and applied information in these areas to model and solve engineering problems.
2) Ability to identify, formulate, and solve complex engineering problems; ability to select and apply proper analysis and modelling methods for this purpose.
3) Ability to design a complex system, process, device or product under realistic constraints and conditions, in such a way so as to meet the desired result; ability to apply modern design methods for this purpose. (Realistic constraints and conditions may include factors such as economic and environmental issues, sustainability, manufacturability, ethics, health, safety issues, and social and political issues according to the nature of the design.)
4) Ability to select and use modern techniques and tools needed for analyzing and solving complex problems encountered in engineering practice; ability to employ information technologies effectively.
5) Ability to design and conduct experiments, gather data, analyze and interpret results for investigating complex engineering problems or discipline specific research questions.
6) Ability to work efficiently in intra-disciplinary and multi-disciplinary teams; ability to work individually.
7) Ability to communicate effectively, both orally and in writing; knowledge of a minimum of one foreign language; ability to write effective reports and comprehend written reports, prepare design and production reports, make effective presentations, and give and receive clear and intelligible instructions.
8) Recognition of the need for lifelong learning; ability to access information, to follow developments in science and technology, and to continue to educate him/herself.
9) Knowledge on behavior according ethical principles, professional and ethical responsibility and standards used in engineering practices.
10) Knowledge about business life practices such as project management, risk management, and change management; awareness in entrepreneurship, innovation; knowledge about sustainable development.
11) Knowledge about contemporary issues and the global and societal effects of engineering practices on health, environment, and safety; awareness of the legal consequences of engineering solutions.

Course - Learning Outcome Relationship

No Effect 1 Lowest 2 Low 3 Average 4 High 5 Highest
           
Program Outcomes Level of Contribution
1) Adequate knowledge in mathematics, science and engineering subjects pertaining to the relevant discipline; ability to use theoretical and applied information in these areas to model and solve engineering problems. 5
2) Ability to identify, formulate, and solve complex engineering problems; ability to select and apply proper analysis and modelling methods for this purpose.
3) Ability to design a complex system, process, device or product under realistic constraints and conditions, in such a way so as to meet the desired result; ability to apply modern design methods for this purpose. (Realistic constraints and conditions may include factors such as economic and environmental issues, sustainability, manufacturability, ethics, health, safety issues, and social and political issues according to the nature of the design.)
4) Ability to select and use modern techniques and tools needed for analyzing and solving complex problems encountered in engineering practice; ability to employ information technologies effectively.
5) Ability to design and conduct experiments, gather data, analyze and interpret results for investigating complex engineering problems or discipline specific research questions.
6) Ability to work efficiently in intra-disciplinary and multi-disciplinary teams; ability to work individually.
7) Ability to communicate effectively, both orally and in writing; knowledge of a minimum of one foreign language; ability to write effective reports and comprehend written reports, prepare design and production reports, make effective presentations, and give and receive clear and intelligible instructions.
8) Recognition of the need for lifelong learning; ability to access information, to follow developments in science and technology, and to continue to educate him/herself.
9) Knowledge on behavior according ethical principles, professional and ethical responsibility and standards used in engineering practices.
10) Knowledge about business life practices such as project management, risk management, and change management; awareness in entrepreneurship, innovation; knowledge about sustainable development.
11) Knowledge about contemporary issues and the global and societal effects of engineering practices on health, environment, and safety; awareness of the legal consequences of engineering solutions.

Learning Activity and Teaching Methods

Lesson
Reading
Problem Solving
Q&A / Discussion

Assessment & Grading Methods and Criteria

Written Exam (Open-ended questions, multiple choice, true-false, matching, fill in the blanks, sequencing)

Assessment & Grading

Semester Requirements Number of Activities Level of Contribution
Midterms 2 % 50
Final 1 % 50
total % 100
PERCENTAGE OF SEMESTER WORK % 50
PERCENTAGE OF FINAL WORK % 50
total % 100

Workload and ECTS Credit Grading

Activities Number of Activities Duration (Hours) Workload
Course Hours 15 4 60
Study Hours Out of Class 15 4 60
Midterms 2 15 30
Final 1 20 20
Total Workload 170