課程信息
5.0
1 個評分
100% 在線

100% 在線

立即開始,按照自己的計劃學習。
可靈活調整截止日期

可靈活調整截止日期

根據您的日程表重置截止日期。
中級

中級

完成時間(小時)

完成時間大約為29 小時

建議:8 weeks of study...
可選語言

英語(English)

字幕:英語(English)...
100% 在線

100% 在線

立即開始,按照自己的計劃學習。
可靈活調整截止日期

可靈活調整截止日期

根據您的日程表重置截止日期。
中級

中級

完成時間(小時)

完成時間大約為29 小時

建議:8 weeks of study...
可選語言

英語(English)

字幕:英語(English)...

教學大綱 - 您將從這門課程中學到什麼

1
完成時間(小時)
完成時間為 4 小時

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....
Reading
11 個視頻(共 116 分鐘), 1 個測驗
Video11 個視頻
Promo1分鐘
1.1. Definitions and examples of sets14分鐘
1.2. Operations on sets9分鐘
1.3. Open balls in Rn9分鐘
1.4. Sequences in Rn. Closed sets.10分鐘
1.5. Bounded and compact sets10分鐘
1.6. Functions and level curves in Rn16分鐘
1.7. Domain and limit of a function. Continuous functions.13分鐘
1.8. Continuity of a function. Weierstrass theorem.13分鐘
1.9. Composite function.12分鐘
1.10. Continuity of a composite function3分鐘
2
完成時間(小時)
完成時間為 5 小時

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....
Reading
13 個視頻(共 115 分鐘), 2 個測驗
Video13 個視頻
2.2. Example of differentiation. Cobb-Douglas function.9分鐘
2.3. Tangent plane.7分鐘
2.4. Total differential.7分鐘
2.5. Chain rule for multivariate functions.8分鐘
2.6. Gradient of the function.9分鐘
2.7. Economic applications of the gradient.9分鐘
2.8. Equation of a circumference. Smooth curves.13分鐘
2.9. Chain rule for differentiation.10分鐘
2.10. Linear approximation. Example of tangent plane for particular function.10分鐘
2.11. Second-order derivatives.10分鐘
2.12. Young's Theorem.5分鐘
2.13. Hessian matrix.5分鐘
Quiz1 個練習
Limits. Derivatives. Continuity分鐘
3
完成時間(小時)
完成時間為 4 小時

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....
Reading
12 個視頻(共 93 分鐘), 1 個測驗
Video12 個視頻
3.2. Implicit Function Theorem.5分鐘
3.3. Applications of the Implicit Function Theorem (part 1).10分鐘
3.4. Applications of the Implicit Function Theorem (part 2).7分鐘
3.5. Gradient is perpendicular to a level curve of a function.11分鐘
3.6. Implicit function theorem for the function of many variables.6分鐘
3.7. Example of application of the IFT for the function of many variables.8分鐘
3.8. Implicit Function Theorem for the system of implicit functions. Jacobian matrix.10分鐘
3.9. Example of application IFT for the system of implicit functions (part 1).8分鐘
3.10. Example of application IFT for the system of implicit functions (part 2).7分鐘
3.11. Example of application in microeconomics.6分鐘
3.12. Cramer's rule.2分鐘
4
完成時間(小時)
完成時間為 5 小時

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....
Reading
15 個視頻(共 112 分鐘), 2 個測驗
Video15 個視頻
4.2. Global max. Local max. Saddle point.9分鐘
4.3. Unconstrained optimization.9分鐘
4.4. Critical point. Taylor's formula.12分鐘
4.5. Quadratic forms. Positive definiteness. Negative definiteness.7分鐘
4.6. Sylvester's criterion (part 1).7分鐘
4.7. Sylvester's criterion (part 2).5分鐘
4.8. Examples of Hessians (part 1).7分鐘
4.9. Example of Hessians (part 2).4分鐘
4.10. Sufficient condition for a critical point to be a local maximum, a local minimum and neither of both.7分鐘
4.11. Examples of finding and classification of critical points (part 1).6分鐘
4.12. Examples of finding and classification of critical points (part 2).4分鐘
4.13. Constrained optimization.9分鐘
4.14. Lagrangian.5分鐘
4.15. Example of constrained optimization problem.4分鐘
Quiz1 個練習
Partial derivatives and unconstrained optimization.分鐘

講師

Avatar

Kirill Bukin

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

關於 National Research University Higher School of Economics

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 communications, IT, mathematics, engineering, and more. Learn more on www.hse.ru...

常見問題

  • 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。

還有其他問題嗎?請訪問 學生幫助中心