MAT2062 Differential EquationsBahçeşehir UniversityDegree Programs INTERIOR ARCHITECTURE AND ENVIRONMENTAL DESIGNGeneral Information For StudentsDiploma SupplementErasmus Policy StatementNational QualificationsBologna Commission
INTERIOR ARCHITECTURE AND ENVIRONMENTAL DESIGN
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 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) Setting up various spaces in national and international contexts, carrying out designs, planning and applications that could satisfy various user groups and respond various requirements in the field of Interior Architecture,
2) Analyzing the information gathered from the framework of actual physical, social and economical constraints and user requirements, and synthesizing these with diverse knowledge and considerations in order to create innovative spatial solutions,
3) Generating creative, innovative, aesthetic and unique spatial solutions by using tangible and abstract concepts,
4) Using at least one of the illustration and presentation technologies competently, that the field of interior architecture requires,
5) Reporting, presenting and transferring the design, practice and research studies to the specialists or laymen by using visual, textual or oral communication methods, efficiently and accurately,
6) Embracing and prioritizing man-environment relationships, user health, safety and security, and universal design principles in the field of interior architecture,
7) Design understanding and decision making that respects social and cultural rights of the society, cultural heritage and nature,
8) Being aware of national and international values, following developments and being equipped about ethical and aesthetical subjects in the fields of interior architecture, design and art,
9) Having absolute conscious about legal regulations, standards and principles; and realizing professional ethics, duties and responsibilities in the field of Interior Architecture,