Course aims:

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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Course Entry Requirements:

Mathematical Analysis

Course contents:

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.

Teaching methods:

Lecture, conversation, exemplification

Learning outcomes:

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.

Learning outcomes verification and assessment criteria:

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

Recommended reading:

-, • 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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