Description

Theory
2

Theory/Practice
2

Instructors

Teresa Araujo

Contents

Infinite Series
Introduction to series analysis
Analysis of positive-term and alternating series convergence - main tests.
Absolute convergence.

Functional Series
Power series.
Convergence.
Harmonic representation and analysis
Magnitude and phase spectrum

Multi-variable Functions
- Definition and domain
- Contours and forms of representation
- Continuity and differentiability
- Partial derivatives and differential
- Derivative of composite and implicit functions

Ordinary Differential Equations
- Definition, classification and generalities
- Ordinary Differential Equations of 1st order
- Ordinary Differential Equations of 2nd order

Double Integrals
- Definition and properties
- Calculus
- Application to calculus of areas and volumes

Learning Outcomes

Classes are oriented to contribute to the development of students reasoning and abstraction capabilities, to provide them the basic concepts and methods of Mathematical Analysis and to allow their application in new situations.
O1 Understand the numerical series concept;
O2 Study the numerical series convergence using appropriate criteria;
O3 Understand the functional series concept;
O4 Represent periodic functions by their Fourier series.
O5 - Understand the concept of multi-variable functions
O6 - Identify multi-variable functions in its direct, compose and implicit form
O7 - Calculate multi-variable functions derivatives
O8 - Understand the differential concept;
O9 - Understand the differential equation concept;
O10 - Identify different types of differential equations
O11 - Solve differential equations using the appropriate method;
O12 - Understand the concept of double integral;
O13 - Correctly use different integration techniques to compute double integrals;
O14 - Use double integrals to compute areas and volumes.

Students should be able to realize the importance of thought subjects in engineering and perform the proposed tasks in the teachers presence, in practical classes. They also should meet the success criteria underlying the assessment of the proposed tasks.