Διαφορικές Εξισώσεις

Title:  Διαφορικές Εξισώσεις  Lesson Code:  3212254  Semester:  4  ECTS:  5  Theory Hours:  3  Lab Hours:  2  Faculty:  Kofinas Georgios 


Content outline 
Examples of differential equations. The differential equation x'=f(t). The first order linear differential equation. Extension of the exponential function. Two dimensional linear systems with constant coefficients. Second order linear differential equations with constant coefficients. Solution of x' = A x + f. Solution of x'' + bx' + cx = f. Superposition principle. Linear oscillations x' = A x + f. Linear oscillations x'' + bx' + cx = f. Exact equations. Differential forms and line integrals. Integral curves. Sequences. Series. Improper integration. Fixedpoint theorems and successive approximations. Existenceuniqueness theorem. Series solution of differential equations. Numerical solution of differential equations. Legendre polynomials. Fourier series. Fourier approximations. 

Learning outcomes 
Ability understand what a differential equation is and what is a solution of it. Ability to solve 1st and 2nd order equations and linear systems with constant coefficients. Basic existence theory, series solutions of differential equations, fourier approximation. 

Prerequisites 
Calculus II, Linear Algebra. 

Basic Textbooks 
1. W.E. Boyce and R. C. DiPrima, Elementary differential equations and boundary value problems. 

Additional References 
1. R. Bronson, Differential equations. 

Learning Activities and Teaching Methods 
Systematic development and explanation of the theory, methods of solutions of exercises, use of Mathematica. 

Assessment/Grading Methods 
One final written exam. 

Language of Instruction 
Greek, English (for Erasmus students) 

Μode of delivery 
Facetoface. 