38,154 次近期查看

100% 在线

100% 在线

1

## The basics of the set theory. Functions in Rn

12 个视频 （总计 117 分钟）, 2 个阅读材料, 1 个测验
12 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 个阅读材料
Rules on the academic integrity in the course10分钟
2

## 周 2

13 个视频 （总计 115 分钟）
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
2.7. 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. Continuity1小时
3

## Implicit Function Theorems and their applications.

12 个视频 （总计 93 分钟）
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

## Unconstrained and constrained optimization.

15 个视频 （总计 112 分钟）
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.1小时