#### DIFFERENTIAL AND PARTIAL DERIVATES EQUATIONS

###### Domain: Computer Science • Field of study: Computer Science (in English)
 Type of course: Compulsory Language of instruction: English Erasmus Language of instruction: English Name of lecturer: Mihaela Aldea Seminar tutor: Pax Dorin Wainberg-Drăghiciu Form of education Full-time
 Form of instruction: Class Number of teaching hours per semester: 56 Number of teaching hours per week: 4 Semester: Autumn Form of receiving a credit for a course: Grade Number of ECTS credits allocated 4

#### 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%.