5.0
6 ratings

#### 100% online

Start instantly and learn at your own schedule.

#### Approx. 30 hours to complete

Suggested: 8 weeks of study...

#### English

Subtitles: English

#### 100% online

Start instantly and learn at your own schedule.

#### Approx. 30 hours to complete

Suggested: 8 weeks of study...

#### English

Subtitles: English

### Syllabus - What you will learn from this course

Week
1
4 hours to complete

## 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 videos (Total 116 min), 1 quiz
11 videos
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
Week
2
5 hours to complete

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 videos (Total 115 min), 2 quizzes
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
2.7. 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. Continuitys
Week
3
4 hours to complete

## 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 videos (Total 93 min), 1 quiz
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
5 hours to complete

## 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 videos (Total 112 min), 2 quizzes
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.s

## Instructor

### Kirill Bukin

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

## About 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 communicamathematics, engineering, and more. Learn more on www.hse.ru...

• Once you enroll for a Certificate, you’ll have access to all videos, quizzes, and programming assignments (if applicable). Peer review assignments can only be submitted and reviewed once your session has begun. If you choose to explore the course without purchasing, you may not be able to access certain assignments.