Course Details

DIFFERENTIAL EQUATIONS

MATH205

Course Information

Semester	Course Unit Code	Course Unit Title	T+P+L	Credit	Number of ECTS Credits
3	MATH205	DIFFERENTIAL EQUATIONS	4+0+0	4	5

Course Details

Language of Instruction	English
Level of Course Unit	Bachelor's Degree
Department / Program	BIOENGINEERING
Type of Program	Formal Education
Type of Course Unit	Compulsory
Course Delivery Method	Face To Face
Objectives of the Course	This course aims to teach the differential equations and their applications by - Providing fundamental knowledge and skills to analyze the behavior of a Ordinary Differential Equations in an introductory level in detail -Constructing theoretical and conceptual understanding of essential mathematical tools to study Ordinary Differential Equations. - Developing the ability of using the notions and tools of basic mathematics to recognize and analyze a problem deduced from real life/nature and offering solutions to these problems by applying relevant computation and analytic techniques.
Course Content	This course is an introduction to Differential Equations and their applications for engineering students and covers the fundamentals and broad applications in engineering and sciences. In this context, different types of differentials equations, Ordinary Differential Equations, and their solution finding procedures with existence and uniqueness conditions, first, second and higher order ordinary differential equations with their specific solution techniques, series solution of ordinary differential equations, systems of ordinary differential equations, Fourier Series details, Partial Differential Equations and their different types with basic applications will be covered during the one semester course.
Course Methods and Techniques
Prerequisites and co-requisities	( MATH152 )
Course Coordinator	None
Name of Lecturers	Associate Prof.Dr. Abdülkadir Doğan abdulkadir.dogan@agu.edu.tr Associate Prof.Dr. Mehmet Tarık Atay mehmettarik.atay@agu.edu.tr
Assistants	None
Work Placement(s)	No

Recommended or Required Reading

Resources	W. E. Boyce, R. C. DiPrima, D. B. Meade, Elementary Differential Equations and Boundary Value Problems, 11th Edition

Course Category

Mathematics and Basic Sciences

%100

Planned Learning Activities and Teaching Methods

Activities are given in detail in the section of "Assessment Methods and Criteria" and "Workload Calculation"

Assessment Methods and Criteria

In-Term Studies	Quantity	Percentage
Yarıyıl İçi Çalışmalarının Başarı Notunun Katkısı	2	% 40
Final examination	1	% 60
Total	3	% 100

ECTS Allocated Based on Student Workload

Activities	Quantity	Duration	Total Work Load
Yazılı Sınav	2	2	4
F2F Dersi	14	4	56
Okuma	14	2	28
Araştırma	14	2	28
Kişisel Çalışma	14	2	28
Final Sınavı	1	2	2
Total Work Load			Number of ECTS Credits 5 146

Course Learning Outcomes: Upon the successful completion of this course, students will be able to:

No	Learning Outcomes
1	Understand the concepts of different types of differentials equations
2	Establish the theoretical understanding of Ordinary Differential Equations, and their solution finding procedures with existence and uniqueness conditions interpretation of it and to derive required solutions for given Ordinary Differential Equations
3	Gain the ability of sketching a graph of a solution of a given differential equations
4	Apply derivation and integration rules to derive and find the required solution
5	Calculate the solution(s) of a given differential equation by using different numerical methods
6	Solve the real-world related case problems seen as Ordinary and Partial Differential Equations by using analytical and numerical methods

Weekly Detailed Course Contents

Week	Topics	Study Materials	Materials
1	Introduction to basic First order ODEs, Basic definitions, Seperable Eqauations, Linear Equations, Bernoulli Diff Equations, Ricatti Diff Equations
2	Modelling of Differential Equations, Homogenous Diff. Equations, Exact Diff. Equations and Integrating Factors
3	General theory of linear differential equations, Reduction of order method, Homogenous Constant Coefficient Equations, Method of Undetermined Coefficients, Method of Variation of Parameters
4	Method of Undetermined Coefficients, Method of Variation of Parameters, Cauchy - Euler Equations, Applications of ODEs
5	Applications of ODEs, Series solutions
6	Series solutions
7	Series solutions
8	Laplace transform
9	Laplace transform
10	Systems of Differential Equations
11	Systems of Differential Equations
12	Fourier series
13	The Wave Equation, The Heat Equation, Laplace’s Equation, Separation of variables solutions to PDEs - PDEs in Rectangular Coordinates
14	Separation of variables solutions to PDEs - PDEs in Rectangular Coordinates

Contribution of Learning Outcomes to Programme Outcomes

	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11	P12
C1
C2
C3
C4
C5
C6

Contribution: 1: Very Slight 2:Slight 3:Moderate 4:Significant 5:Very Significant

https://sis.agu.edu.tr/oibs/bologna/progCourseDetails.aspx?curCourse=70796&lang=en

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