课程信息
5.0
10 个评分
1 个审阅

100% 在线

立即开始,按照自己的计划学习。

可灵活调整截止日期

根据您的日程表重置截止日期。

中级

完成时间大约为30 小时

建议:8 weeks of study...

英语(English)

字幕:英语(English)

100% 在线

立即开始,按照自己的计划学习。

可灵活调整截止日期

根据您的日程表重置截止日期。

中级

完成时间大约为30 小时

建议:8 weeks of study...

英语(English)

字幕:英语(English)

教学大纲 - 您将从这门课程中学到什么

1
完成时间为 4 小时

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 个视频 (总计 116 分钟), 1 个测验
11 个视频
Promo1分钟
1.1. Definitions and examples of sets14分钟
1.2. Operations on sets9分钟
1.3. Open balls in Rn9分钟
1.4. Sequences in Rn. Closed sets.10分钟
1.5. Bounded and compact sets10分钟
1.6. Functions and level curves in Rn16分钟
1.7. Domain and limit of a function. Continuous functions.13分钟
1.8. Continuity of a function. Weierstrass theorem.13分钟
1.9. Composite function.12分钟
1.10. Continuity of a composite function3分钟
2
完成时间为 5 小时

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 个视频 (总计 115 分钟), 2 个测验
13 个视频
2.2. Example of differentiation. Cobb-Douglas function.9分钟
2.3. Tangent plane.7分钟
2.4. Total differential.7分钟
2.5. Chain rule for multivariate functions.8分钟
2.6. Gradient of the function.9分钟
2.7. Economic applications of the gradient.9分钟
2.8. Equation of a circumference. Smooth curves.13分钟
2.9. Chain rule for differentiation.10分钟
2.10. Linear approximation. Example of tangent plane for particular function.10分钟
2.11. Second-order derivatives.10分钟
2.12. Young's Theorem.5分钟
2.13. Hessian matrix.5分钟
1 个练习
Limits. Derivatives. Continuity
3
完成时间为 4 小时

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 个视频 (总计 93 分钟), 1 个测验
12 个视频
3.2. Implicit Function Theorem.5分钟
3.3. Applications of the Implicit Function Theorem (part 1).10分钟
3.4. Applications of the Implicit Function Theorem (part 2).7分钟
3.5. Gradient is perpendicular to a level curve of a function.11分钟
3.6. Implicit function theorem for the function of many variables.6分钟
3.7. Example of application of the IFT for the function of many variables.8分钟
3.8. Implicit Function Theorem for the system of implicit functions. Jacobian matrix.10分钟
3.9. Example of application IFT for the system of implicit functions (part 1).8分钟
3.10. Example of application IFT for the system of implicit functions (part 2).7分钟
3.11. Example of application in microeconomics.6分钟
3.12. Cramer's rule.2分钟
4
完成时间为 5 小时

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 个视频 (总计 112 分钟), 2 个测验
15 个视频
4.2. Global max. Local max. Saddle point.9分钟
4.3. Unconstrained optimization.9分钟
4.4. Critical point. Taylor's formula.12分钟
4.5. Quadratic forms. Positive definiteness. Negative definiteness.7分钟
4.6. Sylvester's criterion (part 1).7分钟
4.7. Sylvester's criterion (part 2).5分钟
4.8. Examples of Hessians (part 1).7分钟
4.9. Example of Hessians (part 2).4分钟
4.10. Sufficient condition for a critical point to be a local maximum, a local minimum and neither of both.7分钟
4.11. Examples of finding and classification of critical points (part 1).6分钟
4.12. Examples of finding and classification of critical points (part 2).4分钟
4.13. Constrained optimization.9分钟
4.14. Lagrangian.5分钟
4.15. Example of constrained optimization problem.4分钟
1 个练习
Partial derivatives and unconstrained optimization.
5
完成时间为 4 小时

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 个视频 (总计 99 分钟), 1 个测验
13 个视频
5.2. Weierstrass theorem. Compact sets.7分钟
5.3. Bordered Hessian.9分钟
5.4. Constrained optimization in general case (part 1).5分钟
5.5. Constrained optimization in general case (part 2).6分钟
5.6. Application of the bordered Hessian in the constrained optimization.7分钟
5.7. Generalization of the constrained optimization problem for the n variables case.8分钟
5.8. Example of constrained optimization for the case of more than two variables (part 1).7分钟
5.9. Example of constrained optimization for the case of more than two variables (part 2).9分钟
5.10. Example of constrained optimization problem on non-compact set.5分钟
5.11. Theorem for determining definiteness (positive or negative) or indefiniteness of the bordered matrix.5分钟
5.12. Example of application bordered Hessian technique for the constrained optimization problem.8分钟
5.13. Example of violating NDCQ.10分钟
6
完成时间为 3 小时

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 个视频 (总计 85 分钟), 1 个测验
11 个视频
6.2. Envelope Theorem for constrained optimization.4分钟
6.3. Examples of the Envelope Theorem application (part 1).7分钟
6.4. Examples of the Envelope Theorem application (part 2).6分钟
6.5. Interpretation of the Lagrangian multiplier.10分钟
6.6. Relaxing assumptions using second order conditions.8分钟
6.7. Concave and convex functions.7分钟
6.8. Concave and convex functions in n-dimensional case.7分钟
6.9. Inequality for concave function in n-dimensional space.9分钟
6.10. Criteria of concavity and convexity of the function in n-dimensional space.5分钟
6.11. Properties of concave functions.7分钟
7
完成时间为 4 小时

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 个视频 (总计 96 分钟), 1 个测验
11 个视频
7.2. How to identify global extrema? (part 2)10分钟
7.3. How to identify global extrema? (part 3)12分钟
7.4. How to identify global extrema? (part 4)10分钟
7.5. Constrained optimization with inequality constraints.8分钟
7.6. Binding constraints. Complementary slackness conditions.5分钟
7.7. Constrained optimization problem with inequalities for n-dimensional space.7分钟
7.8. Constrained optimization problem with inequalities. Theorem.6分钟
7.9. Example of solving constrained optimization problem with inequalities (part 1).9分钟
7.10. Example of solving constrained optimization problem with inequalities (part 2).10分钟
7.11. Example of solving constrained optimization problem with inequalities (part 3).3分钟
8
完成时间为 4 小时

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 个视频 (总计 80 分钟), 2 个测验
9 个视频
8.2. Solving consumer choice problem using Kuhn-Tucker conditions (part 1).9分钟
8.3. Solving consumer choice problem using Kuhn-Tucker conditions (part 2).11分钟
8.4. Solving minimization costs problem using Kuhn-Tucker conditions (part 1).9分钟
8.5. Solving minimization costs problem using Kuhn-Tucker conditions (part 2).7分钟
8.6. Homogeneous functions.6分钟
8.7. Homogeneous functions. Two propositions.5分钟
8.8. Income-consumption curve.10分钟
8.9. Euler's Theorem.12分钟
1 个练习
Kuhn-Tucker conditions. Concavity, convexity.

讲师

Avatar

Kirill Bukin

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

关于 国立高等经济大学

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...

常见问题

  • 注册以便获得证书后,您将有权访问所有视频、测验和编程作业(如果适用)。只有在您的班次开课之后,才可以提交和审阅同学互评作业。如果您选择在不购买的情况下浏览课程,可能无法访问某些作业。

  • 您购买证书后,将有权访问所有课程材料,包括评分作业。完成课程后,您的电子课程证书将添加到您的成就页中,您可以通过该页打印您的课程证书或将其添加到您的领英档案中。如果您只想阅读和查看课程内容,可以免费旁听课程。

还有其他问题吗?请访问 学生帮助中心