MAT2062 Differential EquationsBahçeşehir UniversityDegree Programs FILM AND TELEVISIONGeneral Information For StudentsDiploma SupplementErasmus Policy StatementNational QualificationsBologna Commission
FILM AND TELEVISION
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 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) Being familiar to the main concepts and methods of the social sciences and the fine arts devoted to understanding the world and the society 4
2) Having comprehensive knowledge regarding different media and branches of art 3
3) Knowing the historical background of audio-visual moving images in the world and in Turkey and keeping pace with the new developments in the area 1
4) Having a good command of the language and the aesthetics of audio-visual moving images in the world and in Turkey 1
5) Being able to create a narrative that could be used in a fiction or a non-fiction audio-visual moving image product 2
6) Being able to write a script ready to be shot 2
7) Having the skills to produce the photoboard of a script in hand and to shoot the film using the camera, the lights and other necessary equipment
8) Being able to transfer the footage of a film to the digital medium, to edit and do other post-production operations
9) Being able to create a documentary audio visual moving image from the preliminary sketch stage to shooting, editing and post-production stages
10) Being able to produce an audio visual moving image for television and audio products for radio from preliminary stages through shooting and editing to the post-production stage
11) Being culturally and theoretically equipped to make sense of an audio-visual moving image, to approach it critically with regard to its language and narration and being able to express his/her approach in black and white 3
12) Having ethical values and a sense of social responsibility 5