Differential Equations (AN5)
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 Department of Mathematics
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General
School  School of Science 

Academic Unit  Department of Mathematics 
Level of Studies  Graduate 
Course Code  AN5 
Semester  2 
Course Title  Differential Equations 
Independent Teaching Activities  Lectures (Weekly Teaching Hours: 3, Credits: 7.5) 
Course Type  Special Background 
Prerequisite Courses   
Language of Instruction and Examinations 
Greek 
Is the Course Offered to Erasmus Students  Yes 
Course Website (URL)  See eCourse, the Learning Management System maintained by the University of Ioannina. 
Learning Outcomes
Learning outcomes 
This course is aiming at familiarizing the students with a variety of advanced subjects related to differential equations. Both classical and modern subjects are studied. After attending this course, the students should be able to:


General Competences 

Syllabus
Second order linear ordinary differential equations: Sturmtype theorems, oscillation and nonoscillation theorems. Reducing differential equation problems to integral ones. Volterra integral equations: existence and uniqueness of solutions. Existence of solutions. The linear equation. The first order linear equation. Some problems on the semiaxis. Fredholm theory for linear integral equations: the resolvent kernel. The entire functions of Fredholm and their applications. Eigenvalues, eigenfunctions and conjugate functions. Some integral inequalities: Gronwall and Bihari Lemmas, and their applications. Delay differential equations: Introduction, Examples and the stepping method. Some remarkable examples and some "wrong" questions. Lipschitz condition and uniqueness for the basic initial problem. Notations and uniqueness for systems with bounded delay. Existence for systems with bounded delay. Linear delay differential systems: superposition. Fixed coefficients. Variation of parameters. Stability for delayed differential systems: Definitions and examples. Asymptotic stability. Linear and almost linear differential systems. Fractional differential equations: Definitions and basic calculus. Initial and boundary systems. Dynamical systems: definitions and calculus. Equations and problems. Various subjects.
Teaching and Learning Methods  Evaluation
Delivery 
Lectures on class  

Use of Information and Communications Technology    
Teaching Methods 
 
Student Performance Evaluation 
The students can choose one of the following options:
If both methods are used, then the final grade is the maximum of the two. The criteria regarding the grading are publised in the "ECourse" platform. 
Attached Bibliography
 C. Corduneanu, Principles of Differential and Integral Equations
 R. D. Driver, Ordinary and Delay Differential Equations
 T. A. Burton, Volterra Integral and Differential Equations
 R. K. Miller, Nonlinear Volterra Integral Equations
 P. Hartman, Ordinary Differential Equations
 Κ. Diethelm, The Analysis of Fractional Differential Equations
 Y. Zhou, Basic Theory of Fractional Differential Equations
 M. Bohner and A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications.