MAT2062 Differential EquationsBahçeşehir UniversityDegree Programs PERFORMING ARTSGeneral Information For StudentsDiploma SupplementErasmus Policy StatementNational QualificationsBologna Commission
PERFORMING ARTS
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) They acquire theoretical, historical and aesthetic knowledge specific to their field by using methods and techniques related to performing arts (acting, dance, music, etc.). 2
2) They have knowledge about art culture and aesthetics and they provide the unity of theory and practice in their field. 2
3) They are aware of national and international values in performing arts. 2
4) Abstract and concrete concepts of performing arts; can transform it into creative thinking, innovative and original works. 1
5) They have the sensitivity to run a business successfully in their field. 3
6) Develops the ability to perceive, think, design and implement multidimensional from local to universal. 3
7) They have knowledge about the disciplines that the performing arts field is related to and can evaluate the interaction of the sub-disciplines within their field. 2
8) They develop the ability to perceive, design, and apply multidimensionality by having knowledge about artistic criticism methods. 3
9) They can share original works related to their field with the society and evaluate their results and question their own work by using critical methods. 1
10) They follow English language resources related to their field and can communicate with foreign colleagues in their field. 1
11) By becoming aware of national and international values in the field of performing arts, they can transform abstract and concrete concepts into creative thinking, innovative and original works. 3
12) They can produce original works within the framework of an interdisciplinary understanding of art. 2
13) Within the framework of the Performing Arts Program and the units within it, they become individuals who are equipped to take part in the universal platform in their field. 3
14) Within the Performing Arts Program, according to the field of study; have competent technical knowledge in the field of acting and musical theater. 2
15) They use information and communication technologies together with computer software that is at least at the Advanced Level of the European Computer Use License as required by the field. 3