Continuing Education Department - Universidad del Azuay
University of Azuay
University of Azuay
Continuing Education Department - Universidad del Azuay Continuing Education Department - Universidad del Azuay
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Functions of several variables and applications

5 of January to 16 2026

Face-to-face modality
40 hours (20 hours in person and 20 hours independent study)

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Course

About this course

This course strengthens the skills of teachers and related professionals in using multivariable differential and integral calculus to solve real-world problems. Through practical exercises, it covers maxima and minima, areas, volumes, and applications in physics and other disciplines.

Through guided activities and independent work, participants develop skills applicable to their academic practice. The practical approach allows them to integrate multivariable calculus into real-world and multidisciplinary contexts with greater clarity and mastery.

 

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Objectives

Acquire the necessary knowledge to develop the ability to analyze functions of several variables and apply multivariable calculus tools to solve optimization, modeling, and integration problems in scientific and engineering contexts.

Specific objectives

  • Interpret and represent functions of two variables, their domains and graphical behavior.
  • Calculate limits, partial derivatives, differentials, and local extrema.
  • Apply double integrals to determine areas, volumes, and physical properties of plane regions.
ODS

Sustainable development goals

Quality education

Quality education

Methodology

The methodology combines active learning, brief presentations, and practical workshops to solve contextualized problems. It integrates independent work, teacher reflection, and the exchange of experiences to effectively apply multivariable calculus in real-world and interdisciplinary situations.

Duration

Duration

Duration

40 hours (20 hours in person and 20 hours independent study)

Opening hours

Monday to Friday from 17:00 to 19:00

Mode

In‑person

Teachers)

Teachers)

Juan Carlos Malo

Juan Carlos Malo

Instructor

  • Master in University Teaching
  • Master in Applied Mathematics

Content

Content

  • Week 1
  • Week 2
Syllabus

  • 5 moons: Domain, range, and graphical representation of functions of two variables.
  • 6 Tuesday: Limits and continuity of functions of two variables.
  • Wednesday 7: Partial derivatives and higher-order partial derivatives.
  • Thursday 8: Total differential and total derivative.
  • Viernes 9: Maxima and minima of functions of two variables.

Syllabus

  • 12 moons: Double integrals: definition, interpretation and limits of integration.
  • 13 Tuesday: Change in integration order and type I and II regions.
  • Wednesday 14: Polar coordinates and conversion to polar coordinates in double integrals.
  • Thursday 15: Calculation of areas and volumes using double integrals.
  • Viernes 16: Centers of mass, moments of inertia and final integrative activity.

Recipients

Recipients

Aimed at university professors in basic areas such as linear algebra, calculus, statistics, physics, computer science and related disciplines.

Date

Dates

5 of January to 16 2026

Investment

Investment

UDA Teachers

$ Free

Permanent teaching update program

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Certificates

Certificates

Once the activities and requirements for the development of the course have been fulfilled, the participants will receive the certificate of approval , based on what is established in the Regulations of the Department of Continuing Education, that is, that the participant obtains a minimum of 70% in the academic evaluation and 80% attendance at the face-to-face or synchronous classes.

Information

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