ARCHITECTURE
Bachelor	TR-NQF-HE: Level 6	QF-EHEA: First Cycle	EQF-LLL: Level 6

Course Introduction and Application Information

Course Code	Course Name	Semester	Theoretical	Practical	Credit	ECTS
MAT2062	Differential Equations	Spring Fall	3	0	3	6

This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester.

Basic information

Language of instruction:	English
Type of course:	Non-Departmental Elective
Course Level:	Bachelor’s Degree (First Cycle)
Mode of Delivery:	Face to face
Course Coordinator :	Dr. Öğr. Üyesi GÜLSEMAY YİĞİT
Course Lecturer(s):	Prof. Dr. NAFİZ ARICA
Recommended Optional Program Components:	None
Course Objectives:	This course covers the fundamental concepts of an introductory level of elementary differential equations with basic concepts, theory, solution methods and applications. Main goal is to develop the basics of modeling at an introductory level and connect this step to the theoretical and methodological resource of mathematics.

Learning Outcomes

The students who have succeeded in this course;
1. Classify differential equations and determine the existence and uniqueness of solutions of Initial Value Problems
2. Solve first order separable and linear differential equations
3. Use substitution methods to solve homogeneous and Bernoulli equations
4. Solve exact differential equations
5. Solve the higher order linear homogeneous and nonhomogeneous differential equations
6. Solve the systems of linear differential equations
7. Solve differential equations by using Laplace transform method

Course Content

In this course basic concepts of elementary differential equations will be covered. The solution techniques for the different types of first order differential equations will be given and the solution methods will be taught. The higher order linear differential equations and solution methods will be discussed. The systems of linear equations will be covered with different techniques. Finally, the Laplace Transform method will be taught to solve linear differential equations.

Weekly Detailed Course Contents

Week	Subject	Related Preparation
1)	Classification of differential equations, Explicit solution, implicit solution, Initial Value Problems, Integrals as General and Particular Solutions.
2)	Existence and Uniqueness of Solution. Separable Differential Equations.
3)	First Order Linear Differential Equations.
4)	Substitutions methods. Homogeneous Differential Equations. Bernoulli Differential Equations.
5)	Exact Differential Equations.
6)	Population models. Reducible second order equations.
7)	Theory of Higher Order Linear Differential Equations, Existence and Uniqueness Theorem, Linear Dependence and Independence, Representation of Solutions for Homogeneous and Nonhomogeneous Cases.
8)	Homogeneous Linear Equations with Constant Coefficients. Euler Equations.
9)	Solution of Nonhomogeneous Linear Differential Equations. Method of Undetermined Coefficients.
10)	Solution of Nonhomogeneous Linear Differential Equations. Method of Variation of Parameters.
11)	Theory of Systems of Linear Differential Equations.
12)	The Eigenvalue Method for Systems of Linear Differential Equations.
13)	Laplace Transforms: Definition of the Laplace Transform, Properties of the Laplace Transform. Inverse Laplace Transform.
14)	Solution of Differential Equations by using Laplace Transform.

Sources

Course Notes / Textbooks:	Differential Equations with Boundary Value Problems by C. Henry Edwards & D. E.Penney, sixth edition
References:	Introduction to Ordinary Differential Equations” by Shepley L. Ross. Fourth Edition, John Wiley and Sons.

Evaluation System

Semester Requirements	Number of Activities	Level of Contribution
Quizzes	2	% 20
Midterms	1	% 35
Final	1	% 45
Total		% 100
PERCENTAGE OF SEMESTER WORK		% 55
PERCENTAGE OF FINAL WORK		% 45
Total		% 100

Contribution of Learning Outcomes to Programme Outcomes

No Effect	1 Lowest	2 Low	3 Average	4 High	5 Highest

	Program Outcomes	Level of Contribution
1)	Using the theoretical/conceptual and practical knowledge acquired for architectural design, design activities and research.
2)	Identifying, defining and effectively discussing aesthetic, functional and structural requirements for solving design problems using critical thinking methods.
3)	Being aware of the diversity of social patterns and user needs, values and behavioral norms, which are important inputs in the formation of the built environment, at local, regional, national and international scales.
4)	Gaining knowledge and skills about architectural design methods that are focused on people and society, sensitive to natural and built environment in the field of architecture.
5)	Gaining skills to understand the relationship between architecture and other disciplines, to be able to cooperate, to develop comprehensive projects; to take responsibility in independent studies and group work.
6)	Giving importance to the protection of natural and cultural values in the design of the built environment by being aware of the responsibilities in terms of human rights and social interests.
7)	Giving importance to sustainability in the solution of design problems and the use of natural and artificial resources by considering the social, cultural and environmental issues of architecture.
8)	Being able to convey and communicate all kinds of conceptual and practical thoughts related to the field of architecture by using written, verbal and visual media and information technologies.
9)	Gaining the ability to understand and use technical information about building technology such as structural systems, building materials, building service systems, construction systems, life safety.
10)	Being aware of legal and ethical responsibilities in design and application processes.