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中級

完成時間大約為30 小時

建議:8 weeks of study...

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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

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中級

完成時間大約為30 小時

建議:8 weeks of study...

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....
11 個視頻 (總計 116 分鐘), 1 個測驗
11 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....
13 個視頻 (總計 115 分鐘), 2 個測驗
13 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
1 個練習
Limits. Derivatives. Continuity
3
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....
12 個視頻 (總計 93 分鐘), 1 個測驗
12 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....
15 個視頻 (總計 112 分鐘), 2 個測驗
15 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
1 個練習
Partial derivatives and unconstrained optimization.
5
完成時間為 4 小時

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 個視頻 (總計 99 分鐘), 1 個測驗
13 個視頻
5.2. Weierstrass theorem. Compact sets.7分鐘
5.3. Bordered Hessian.9分鐘
5.4. Constrained optimization in general case (part 1).5分鐘
5.5. Constrained optimization in general case (part 2).6分鐘
5.6. Application of the bordered Hessian in the constrained optimization.7分鐘
5.7. Generalization of the constrained optimization problem for the n variables case.8分鐘
5.8. Example of constrained optimization for the case of more than two variables (part 1).7分鐘
5.9. Example of constrained optimization for the case of more than two variables (part 2).9分鐘
5.10. Example of constrained optimization problem on non-compact set.5分鐘
5.11. Theorem for determining definiteness (positive or negative) or indefiniteness of the bordered matrix.5分鐘
5.12. Example of application bordered Hessian technique for the constrained optimization problem.8分鐘
5.13. Example of violating NDCQ.10分鐘
6
完成時間為 3 小時

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 個視頻 (總計 85 分鐘), 1 個測驗
11 個視頻
6.2. Envelope Theorem for constrained optimization.4分鐘
6.3. Examples of the Envelope Theorem application (part 1).7分鐘
6.4. Examples of the Envelope Theorem application (part 2).6分鐘
6.5. Interpretation of the Lagrangian multiplier.10分鐘
6.6. Relaxing assumptions using second order conditions.8分鐘
6.7. Concave and convex functions.7分鐘
6.8. Concave and convex functions in n-dimensional case.7分鐘
6.9. Inequality for concave function in n-dimensional space.9分鐘
6.10. Criteria of concavity and convexity of the function in n-dimensional space.5分鐘
6.11. Properties of concave functions.7分鐘
7
完成時間為 4 小時

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 個視頻 (總計 96 分鐘), 1 個測驗
11 個視頻
7.2. How to identify global extrema? (part 2)10分鐘
7.3. How to identify global extrema? (part 3)12分鐘
7.4. How to identify global extrema? (part 4)10分鐘
7.5. Constrained optimization with inequality constraints.8分鐘
7.6. Binding constraints. Complementary slackness conditions.5分鐘
7.7. Constrained optimization problem with inequalities for n-dimensional space.7分鐘
7.8. Constrained optimization problem with inequalities. Theorem.6分鐘
7.9. Example of solving constrained optimization problem with inequalities (part 1).9分鐘
7.10. Example of solving constrained optimization problem with inequalities (part 2).10分鐘
7.11. Example of solving constrained optimization problem with inequalities (part 3).3分鐘
8
完成時間為 4 小時

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 個視頻 (總計 80 分鐘), 2 個測驗
9 個視頻
8.2. Solving consumer choice problem using Kuhn-Tucker conditions (part 1).9分鐘
8.3. Solving consumer choice problem using Kuhn-Tucker conditions (part 2).11分鐘
8.4. Solving minimization costs problem using Kuhn-Tucker conditions (part 1).9分鐘
8.5. Solving minimization costs problem using Kuhn-Tucker conditions (part 2).7分鐘
8.6. Homogeneous functions.6分鐘
8.7. Homogeneous functions. Two propositions.5分鐘
8.8. Income-consumption curve.10分鐘
8.9. Euler's Theorem.12分鐘
1 個練習
Kuhn-Tucker conditions. Concavity, convexity.

講師

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Kirill Bukin

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

關於 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...

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