Description

Theory
2

Theory/Practice
2

Instructors

Ana Cristina Meira

Contents

P1 Multivariable functions:
- Definition, domain, and geometric interpretation
- Limits and continuity
- Partial derivatives
- Total differential
- Derivative of composite functions
- Derivatives of implicit functions
- Maxima and minima

P2 Laplace Transform
- Definition and existence
- Properties
- Laplace transform of some functions
- Inverse Laplace Transform
- Solving differential equations

P3 Ordinary Differential Equations (ODEs):
- Definition, classification, and generalization
- First-order ODE: Equations with separated and separable variables, Homogeneous equations, Linear equations
- Second-order ODE: Linear equation of constant coefficients (homogeneous and non-homogeneous). Lagrange's method
- Brief reference to resolution systems of ODEs

P4 Double Integrals
- Definition, properties, and geometric interpretation
- Calculus
- Applications

Learning Outcomes

The classes in this course aim to contribute to developing students' reasoning, abstraction, and critical thinking skills, providing them with essential mathematical tools for understanding and interpreting topics taught in the different disciplines of the course. Thus, at the end of the semester, the student must be able to:

PO1. Study domains, limits and continuity of real functions of several real variables.

PO2. Apply the Laplace Transform operator to functions and solve differential equations with this operator.

PO3. Identify the most common types of Ordinary Differential Equations (ODE) and apply the appropriate resolution method to 1st-order and 2nd-order linear ODEs.

PO4. Apply integration techniques to double integrals and apply integral calculus to determine areas of plane regions and volumes of solids.

PO5 Acquire habits of rigor and detail in presenting problem resolutions, as well as routines for synthesizing, analyzing and interpreting the results obtained.