Subject: Introduction to Calculus

Scientific Area:

Mathematics

96 Hours

Number of ECTS:

7,5 ECTS

Language:

Portuguese

# Overall objectives:

1 - There are two main learning outcomes from this course. First, it is an understanding of basic concepts in applied linear algebra (systems of linear equations, matrices, determinants, eigenvalues and eigenvectors). Students should master properties of matrices including how to use them to solve linear systems of equations.
2 - Second, it is an understanding of the concepts of derivative (rate of change of a function) and integral (which, in particular, provides a way to recover a function from the knowledge of its derivative). The ability to work with these concepts is essential for applications of mathematical techniques in engineering.

# Syllabus:

1 - Real e complex numbers. Inequalities. Absolute values. Intervals.
2 - Matrices. Matrix algebra. Essential properties of matrices.
3 - Determinants. Inverse matrix. Systems of linear equations.
4 - General eigenvalue problems. Properties of eigenvalues and eigenvectors.
5 - Real functions of one variable. Elementary functions. Inverse functions.
6 - Limit and continuity. Indeterminacy. Infinite limits and infinity. Continuous functions.
7 - Derivatives. Geometric interpretation. Rules of differentiation. Chain rule. Implicit differentiation.
8 - Applications of derivatives in engineering. Graphics of functions. Extreme values. Taylor formula.
9 - Integrals. Area concept. Indefinite versus definite integrals. Basic integration techniques.
10 - Applications of integrals in engineering. Work, force and area. Centroids and center of mass.

# Literature/Sources:

Howard Anton, Chris Rorres , 2012 , Algebra linear com aplicações , Porto Alegre: Bookman
James Stewart , 2013 , Cálculo: Volume I , São Paulo: Cengage Learning

# Assesssment methods and criteria:

Classification Type: Quantitativa (0-20)

Evaluation Methodology:
Oral and written presentations of the course syllabus. Offer of practical examples to consolidate the theory. Resolution of exercises to better understand and navigate the theory presented. To pass the course, two written tests (weighting 50% each) must be performed individually during the regular semester term. For the Complimentary and Special periods, an Exam is offered and the final grade is attributed in accordance with the result of the exam.