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أهلا وسهلا بكم في موقع مادة نظرية المعادلات التفاضلية
Course Syllabus
(I) Linear Systems
Linear systems with constant coefficients:
Uncoupled linear systems
Diagonalization
Exponentials of operators
The fundamental theorem for linear systems
Linear systems in R2 (phase portraits)
Complex and multiple eigenvalues
Stability of solutions
Nonhomogeneous linear systems
Higher order systems
Linear systems with variable coefficients:
The space of solutions ofx'=A(t)x
Solution matrices and the fundamental matrix
The state transition matrix
Nonhomogeneous linear systems with variable coefficients
Linear systems with periodic coefficients
:II) Nonlinear Systems)
Some preliminary concepts and definitions
The Fundamental Existence-Uniqueness theorem
Dependence on initial conditions
The maximal interval of existence
The flow defined by the differential equation
Linearization and stability of equilibria
:List of References
1. Differential Equations and Dynamical Systems
By: Lawrence Perko Differential Equations,
2. Dynamical Systems and Linear Algebra
By: Morris Hirsch and Stephen Smale
3. Ordinary Differential Equations.
By: Richard K. Miller and Anthony N. Michel
4. Ordinary Differential Equations.
By: D. K Arrowsmith and C.M. Place
Course Portfolio
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