Description

Theory
2

Theory/Practice
2

Instructors

Alzira Mota

Contents

1. Multivariable functions:
Definition, domain, and geometric interpretation (CP1).
Partial derivatives, Total differential (CP2).
Derivative of a composite function (CP3).
Derivatives of implicit functions (CP4).
Maxima and Minima (CP5)
2. Ordinary differential equations (ODEs).
Definition, classification, and generalities (CP6).
First-order differential equations: equations with separate and separable variables, homogeneous equations, and linear equations. (CP7)
Second-order differential equations: Linear equations with constant coefficients (homogeneous and non-homogeneous); Lagrange's method. (CP8)
3. Multiple integrals:
Definition, properties, and geometric interpretation. (CP9)
Calculation of the double integral. (CP10)
Calculating the triple integral.(CP11)
Applications. (CP12)

Learning Outcomes

This course aims to develop the capacity for abstraction, logical deduction, and analysis; to acquire techniques that foster critical and mathematical thinking; to master multivariable differential and integral calculus, as well as ordinary differential equations; and to apply mathematical knowledge to solve engineering problems.
Students are expected to be able to:
- manipulate functions of several variables, understanding the importance of these functions in their application to engineering problems; (OB1)
- Identify and determine the general and particular solutions of first- and second-order ordinary differential equations. (OB2)
- Apply integration techniques to solve multiple integrals. (OB3)