2024/2025
Математические методы для экономистов 2
Статус:
Майнор
Кто читает:
Международный институт экономики и финансов
Где читается:
Международный институт экономики и финансов
Охват аудитории:
для всех кампусов НИУ ВШЭ
Преподаватели:
Букин Кирилл Александрович
Язык:
английский
Кредиты:
5
Course Syllabus
Abstract
Mathematical Methods for Economists is a two-semester course for the second year students studying at ICEF which specialize in “Mathematics and Economics”. This course is an important part of the bachelor stage in education of the future economists. It has give students skills for implementation of the mathematical knowledge and expertise to the problems of economics. In the fall semester this course is is dedicated to “Multivariate Calculus and Optimization” (MCO). MCO continues beyond and from January onwards incorporates also the chapters of “Methods of Optimization” course.
Learning Objectives
- Students are supposed: to acquire knowledge in the field of higher mathematics and become ready to analyze simulated as well as real economic situations;
- to develop ability to apply the knowledge of the differential and difference equations which will enable them to analyze dynamics of the processes.
Expected Learning Outcomes
- Able to handle second-order difference equations
- Apply difference equations to macroeconomics
- Apply Euler’s equation to microeconomics
- Apply FOC to an objective function and checking definiteness of Hessian
- Apply IFT to microeconomic and macroeconomic problems
- Apply Kuhn-Tucker method for solving problems from primarily microeconomics
- Apply Lagrange method for equality constrained type of problems
- Apply method of undetermined coefficients for the search of a particular solution
- Apply Nash equilibrium concept to economic problems
- Apply the basic techniques of solving first-order equations
- Apply the notion of level curve to microeconomics
- Be able to classify bilinear and quadratic forms
- be able to classify forms and apply such a knowledge to conic sections
- Be able to find a limit of a function at a point
- Be able to handle derivatives
- Be able to invert a matrix either by finding cofactors or by Gaussian elimination method
- Classify the sets in n-dimensional space
- define and give examples of spaces and subspaces, explain notions of basis and dimension, axioms of vector spaces
- define rank, range of a matrix, column, row spaces and null space of a matrix, be able to apply rank-nullity theorem
- define rank, range of a matrix, column, row spaces and null space of a matrix, be able to apply rank-nullity theorem
- Explain and apply gradient and related directional derivative
- Explain and apply linear programming
- Explain and apply Solow’s model
- explain and use linear independence, bases and dimension
- explain and use properties of Markov chains along with the technique enabling to find steady-state solutions
- explain and use rotation, projection and basic properties of transformations, introduce a change of basis formula that enables to switch the basis and find the corresponding matrix of a transformation
- Explain orthogonality of vectors, properties of a dot product, Gram-Schmidt procedure, eigenvalues, eigenvectors
- explain relationship between Cartesian, parametric equations for planes and lines, be able to find normal vector to a plane
- Explain the meaning of a multiplier and be ready to demonstrate the applicability of envelope theorems
- Find derivatives of implicit functions
- Outline complex numbers theory
- Practice techniques of matrix operations
- practice techniques of matrix operations, be able to to invert a matrix either by finding cofactors or by Gaussian elimination method; use formula for determinants based on cofactor expansion, outline properties of determinants helping to reduce calculations
- practice techniques of matrix operations, be able to to invert a matrix either by finding cofactors or by Gaussian elimination method; use formula for determinants based on cofactor expansion, outline properties of determinants helping to reduce calculations
- Provide examples of differential equations especially in economics
- Solve equations by Gaussian elimination method
- solve equations by Gaussian elimination method, be able to express solution as a sum of a particular solution and a general solution from the null space of the matrix
- Use integration mostly dealing with the linear equations with constant coefficients and quasipolynomials in the right side
- Use maxmin/minmax techniques
- Use techniques of solving first-order equations
Course Contents
- Optimization
- Algebra
- Systems of linear equations in matrix form. Linear space. Linear independence. Linear subspace. Matrix as a set of columns and as a set of rows. Determinant of a set of vectors Inverse matrix. Linear operator as a geometric object. Eigenvalues, eigenvectors and their properties. Bilinear and quadratic form.s Dot product in linear spaces.
- 1. Lines, planes in R2 and R3. Lines and hyperplanes in Rn 2. Homogeneous systems and null space. Consistent and inconsistent systems. Linear systems with free variables. Solution sets 3. Matrix inversion and determinants 4. Rank, range and linear equations 5. Vector spaces 6. Linear independence, bases and dimension 7. Linear transformations, change of basis 8. Diagonalization 9. Markov chains
- Methods of optimization
- Differential and difference equations
- Multi-dimensional calculus
Assessment Elements
- Home assignments
- Control work
- ExamIn order to get a passing grade for the course, the student must sit (all parts) of the final examination
