Presentation with practical methods for solving of ordinary differential equations, systems of differential equations, higher order differential equations and with partial derivates of order 1 and 2
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Mathematical Analysis

1. First order differential equations: Basic concepts. Cauchy problem. 2. Separable differential equations. Homogeneous equations. 3. Linear differential equations. 4. Bernoulli, Riccati, Lagrange, Clairaut Differential equations. 5. Exact differential equations; Solutions existence and uniqueness 6. Higher order differential equations: Cases and modalities for reduction the order of an equation; Linear differential equations with variable coefficients. Fundamental sets of solutions. 7. Method of undetermined coefficients . Differential equations with constant coefficients. 8. Systems of differential equations: Systems of first order differential equations, the equivalence with higher order differential equations. Cauchy problem. 9. The fundamental matrix of a system of first order linear differential equations with variable coefficients. 10. Systems of first order linear differential equations with constant coefficients. Matrix exponential 11. Autonomous systems 12. Partial derivates equations: Linear , homogeneousand nonhomogeneous first order partial derivates equations. 13. Second order partial derivates equations. 14. Equations of mathematical physics. Laplace equation.

Lecture, conversation, exemplification

Learning the basic techniques of solving differential calculus problems; knowledge and application of theorems, models, their properties and methods of work in the field of differential equations and partial derivatives.

Written paper – 50%; continuous assessment – 50%.

-, • R. Redheffer, Diffwerential Equations. Theory and applications, Jones and Bartleft Publishers, Boston, 1991., - , - , - , -
-, • J. C. Robinson, An introduction to ordinary differential equations, Cambridge University Press, Cambridge, 2004., - , - , - , -
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