About this Course
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지금 바로 시작해 나만의 일정에 따라 학습을 진행하세요.

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일정에 따라 마감일을 재설정합니다.

중급 단계

완료하는 데 약 30시간 필요

권장: 8 weeks of study...

영어

자막: 영어

100% 온라인

지금 바로 시작해 나만의 일정에 따라 학습을 진행하세요.

탄력적인 마감일

일정에 따라 마감일을 재설정합니다.

중급 단계

완료하는 데 약 30시간 필요

권장: 8 weeks of study...

영어

자막: 영어

강의 계획 - 이 강좌에서 배울 내용

1
완료하는 데 4시간 필요

The basics of the set theory. Functions in Rn

Week 1 of the Course is devoted to the main concepts of the set theory, operation on sets and functions in Rn. Of special attention will be level curves. Also in this week introduced definitions of sequences, bounded and compact sets, domain and limit of the function. Also from this week students will grasp the concept of continuous function....
11 videos (Total 116 min), 1 quiz
11개의 동영상
1.1. Definitions and examples of sets14m
1.2. Operations on sets9m
1.3. Open balls in Rn9m
1.4. Sequences in Rn. Closed sets.10m
1.5. Bounded and compact sets10m
1.6. Functions and level curves in Rn16m
1.7. Domain and limit of a function. Continuous functions.13m
1.8. Continuity of a function. Weierstrass theorem.13m
1.9. Composite function.12m
1.10. Continuity of a composite function3m
2
완료하는 데 5시간 필요

Differentiation. Gradient. Hessian.

Week 2 of the Course is devoted to the main concepts of differentiation, gradient and Hessian. Of special attention is the chain rule. Also students will understand economic applications of the gradient....
13 videos (Total 115 min), 2 quizzes
13개의 동영상
2.2. Example of differentiation. Cobb-Douglas function.9m
2.3. Tangent plane.7m
2.4. Total differential.7m
2.5. Chain rule for multivariate functions.8m
2.6. Gradient of the function.9m
2.7. Economic applications of the gradient.9m
2.8. Equation of a circumference. Smooth curves.13m
2.9. Chain rule for differentiation.10m
2.10. Linear approximation. Example of tangent plane for particular function.10m
2.11. Second-order derivatives.10m
2.12. Young's Theorem.5m
2.13. Hessian matrix.5m
1개 연습문제
Limits. Derivatives. Continuity
3
완료하는 데 4시간 필요

Implicit Function Theorems and their applications.

Week 3 of the Course is devoted to implicit function theorems. In this week three different implicit function theorems are explained. This week students will grasp how to apply IFT concept to solve different problems....
12 videos (Total 93 min), 1 quiz
12개의 동영상
3.2. Implicit Function Theorem.5m
3.3. Applications of the Implicit Function Theorem (part 1).10m
3.4. Applications of the Implicit Function Theorem (part 2).7m
3.5. Gradient is perpendicular to a level curve of a function.11m
3.6. Implicit function theorem for the function of many variables.6m
3.7. Example of application of the IFT for the function of many variables.8m
3.8. Implicit Function Theorem for the system of implicit functions. Jacobian matrix.10m
3.9. Example of application IFT for the system of implicit functions (part 1).8m
3.10. Example of application IFT for the system of implicit functions (part 2).7m
3.11. Example of application in microeconomics.6m
3.12. Cramer's rule.2m
4
완료하는 데 5시간 필요

Unconstrained and constrained optimization.

Week 4 of the Course is devoted to the problems of constrained and unconstrained optimization. Of special attention are quadratic forms, critical points and their classification....
15 videos (Total 112 min), 2 quizzes
15개의 동영상
4.2. Global max. Local max. Saddle point.9m
4.3. Unconstrained optimization.9m
4.4. Critical point. Taylor's formula.12m
4.5. Quadratic forms. Positive definiteness. Negative definiteness.7m
4.6. Sylvester's criterion (part 1).7m
4.7. Sylvester's criterion (part 2).5m
4.8. Examples of Hessians (part 1).7m
4.9. Example of Hessians (part 2).4m
4.10. Sufficient condition for a critical point to be a local maximum, a local minimum and neither of both.7m
4.11. Examples of finding and classification of critical points (part 1).6m
4.12. Examples of finding and classification of critical points (part 2).4m
4.13. Constrained optimization.9m
4.14. Lagrangian.5m
4.15. Example of constrained optimization problem.4m
1개 연습문제
Partial derivatives and unconstrained optimization.
5
완료하는 데 4시간 필요

Constrained optimization for n-dim space. Bordered Hessian.

Week 5 of the Course is devoted to the extension of the constrained optimization problem to the n-dimensional space. This week students will grasp how to apply bordered Hessian concept to classification of critical points arising in different constrained optimization problems....
13 videos (Total 99 min), 1 quiz
13개의 동영상
5.2. Weierstrass theorem. Compact sets.7m
5.3. Bordered Hessian.9m
5.4. Constrained optimization in general case (part 1).5m
5.5. Constrained optimization in general case (part 2).6m
5.6. Application of the bordered Hessian in the constrained optimization.7m
5.7. Generalization of the constrained optimization problem for the n variables case.8m
5.8. Example of constrained optimization for the case of more than two variables (part 1).7m
5.9. Example of constrained optimization for the case of more than two variables (part 2).9m
5.10. Example of constrained optimization problem on non-compact set.5m
5.11. Theorem for determining definiteness (positive or negative) or indefiniteness of the bordered matrix.5m
5.12. Example of application bordered Hessian technique for the constrained optimization problem.8m
5.13. Example of violating NDCQ.10m
6
완료하는 데 3시간 필요

Envelope theorems. Concavity and convexity.

Week 6 of the Course is devoted to envelope theorems, concavity and convexity of functions. This week students will understand how to interpret Lagrange multiplier and get to learn the criteria of convexity and concavity of functions in n-dimensional space....
11 videos (Total 85 min), 1 quiz
11개의 동영상
6.2. Envelope Theorem for constrained optimization.4m
6.3. Examples of the Envelope Theorem application (part 1).7m
6.4. Examples of the Envelope Theorem application (part 2).6m
6.5. Interpretation of the Lagrangian multiplier.10m
6.6. Relaxing assumptions using second order conditions.8m
6.7. Concave and convex functions.7m
6.8. Concave and convex functions in n-dimensional case.7m
6.9. Inequality for concave function in n-dimensional space.9m
6.10. Criteria of concavity and convexity of the function in n-dimensional space.5m
6.11. Properties of concave functions.7m
7
완료하는 데 4시간 필요

Global extrema. Constrained optimization with inequality constraints.

Week 7 of the Course is devoted to identification of global extrema and constrained optimization with inequality constraints. This week students will grasp the concept of binding constraints and complementary slackness conditions....
11 videos (Total 96 min), 1 quiz
11개의 동영상
7.2. How to identify global extrema? (part 2)10m
7.3. How to identify global extrema? (part 3)12m
7.4. How to identify global extrema? (part 4)10m
7.5. Constrained optimization with inequality constraints.8m
7.6. Binding constraints. Complementary slackness conditions.5m
7.7. Constrained optimization problem with inequalities for n-dimensional space.7m
7.8. Constrained optimization problem with inequalities. Theorem.6m
7.9. Example of solving constrained optimization problem with inequalities (part 1).9m
7.10. Example of solving constrained optimization problem with inequalities (part 2).10m
7.11. Example of solving constrained optimization problem with inequalities (part 3).3m
8
완료하는 데 4시간 필요

Kunh-Tucker conditions. Homogeneous functions.

Week 8 of the Course is devoted to Kuhn-Tucker conditions and homogenous functions. This week students will find out how to use Kuhn-Tucker conditions for solving various economic problems....
9 videos (Total 80 min), 2 quizzes
9개의 동영상
8.2. Solving consumer choice problem using Kuhn-Tucker conditions (part 1).9m
8.3. Solving consumer choice problem using Kuhn-Tucker conditions (part 2).11m
8.4. Solving minimization costs problem using Kuhn-Tucker conditions (part 1).9m
8.5. Solving minimization costs problem using Kuhn-Tucker conditions (part 2).7m
8.6. Homogeneous functions.6m
8.7. Homogeneous functions. Two propositions.5m
8.8. Income-consumption curve.10m
8.9. Euler's Theorem.12m
1개 연습문제
Kuhn-Tucker conditions. Concavity, convexity.

강사

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Kirill Bukin

Associate Professor, Candidate of sciences (phys.-math.)
Faculty of Economic Sciences, Department of Theoretical Economics

국립 연구 고등 경제 대학 정보

National Research University - Higher School of Economics (HSE) is one of the top research universities in Russia. Established in 1992 to promote new research and teaching in economics and related disciplines, it now offers programs at all levels of university education across an extraordinary range of fields of study including business, sociology, cultural studies, philosophy, political science, international relations, law, Asian studies, media and communicamathematics, engineering, and more. Learn more on www.hse.ru...

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  • 강좌에 등록하면 바로 모든 비디오, 테스트 및 프로그래밍 과제(해당하는 경우)에 접근할 수 있습니다. 상호 첨삭 과제는 이 세션이 시작된 경우에만 제출하고 검토할 수 있습니다. 강좌를 구매하지 않고 살펴보기만 하면 특정 과제에 접근하지 못할 수 있습니다.

  • 수료증을 구매하면 성적 평가 과제를 포함한 모든 강좌 자료에 접근할 수 있습니다. 강좌를 완료하면 전자 수료증이 성취도 페이지에 추가되며, 해당 페이지에서 수료증을 인쇄하거나 LinkedIn 프로필에 수료증을 추가할 수 있습니다. 강좌 콘텐츠만 읽고 살펴보려면 해당 강좌를 무료로 청강할 수 있습니다.

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