- The knowledge given during this course will allow the students to progress with further complicated topics such as optimal control theory and like.
- This course will give the students skills for the implementation of mathematical knowledge and expertise.
- Students will develop the ability to apply the knowledge of the differential and difference equations which will enable them to analyze dynamics of the processes.
- Students will develop an understanding of basic concepts of the differential and difference equations.
- Students will be able to solve linear equations with the constant coefficients as well as the systems of such equations.
- Dynamics in economics and natural sciences. Simple first-order equations. Separable equations. Concept of stability of the solution of ODE. Exact equations. General solution as a sum of a general solution of homogeneous equation and a particular solution of a nonhomogeneous equation. Bernoulli equation. Fundamental theorem on existence and uniqueness.
- Qualitative theory of differential equations. Solow’s growth model from macroeconomics.
- Second-order linear differential equations with constant coefficients.
- Refresher on complex numbers and operations on them. Representation of a number. De Moivre and Euler formulas.
- Higher-order linear differential equation with constant coefficients. Characteristic equation. Method of undetermined coefficients for the search of a particular solution. Stability of solutions. Routh theorem (without proof). Systems of DE (linear equations case). Variation of parameters method
- Discrete time economic systems. Difference equations. Method of solving first-order equations. Convergence and oscillations of a solution. Cobweb model. Partial equilibrium model with the inventory.
- Second-order difference equations.
- Higher-order difference equations. Characteristic equation. Undetermined coefficients method. Conditions for the stability of solutions. Markov processes.
- Stability of linear systems via eigenvalues. Stability of nonlinear systems.
- Phase portraits of planar systems.
- First integrals.
- Liapunov functions.
- Home assignmentsEvery second week
- Midterm Test
- Final ExamThe FE lasts for 120 minutes.
- Interim assessment (4 module)0.6 * Final Exam + 0.15 * Home assignments + 0.25 * Midterm Test
- Mathematics for economists, Simon C. P., Blume L., 1994
- Курс дифференциальных уравнений и вариационного исчисления : учеб. пособие для вузов, Романко В. К., 2001
- Сборник задач по дифференциальным уравнениям и вариационному исчислению, Романко В. К., Агаханов Н. Х., 2002