32,998 recent views
Shareable Certificate
Earn a Certificate upon completion
100% online
Start instantly and learn at your own schedule.
Reset deadlines in accordance to your schedule.
Intermediate Level
Approx. 25 hours to complete
English

### Instructor

Shareable Certificate
Earn a Certificate upon completion
100% online
Start instantly and learn at your own schedule.
Reset deadlines in accordance to your schedule.
Intermediate Level
Approx. 25 hours to complete
English

Week
1

## Week 1

3 hours to complete

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

3 hours to complete
12 videos (Total 117 min), 2 readings, 1 quiz
12 videos
Promo1m
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
Rules on the academic integrity in the course10m
Week
2

## Week 2

4 hours to complete

## Differentiation. Gradient. Hessian.

4 hours to complete
13 videos (Total 115 min)
13 videos
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
1 practice exercise
Limits. Derivatives. Continuity1h
Week
3

## Week 3

3 hours to complete

## Implicit Function Theorems and their applications.

3 hours to complete
12 videos (Total 93 min)
12 videos
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
Week
4

## Week 4

4 hours to complete

## Unconstrained and constrained optimization.

4 hours to complete
15 videos (Total 112 min)
15 videos
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
1 practice exercise
Partial derivatives and unconstrained optimization.1h

## Frequently Asked Questions

More questions? Visit the Learner Help Center.