Base Knowledge
Basic knowledge is acquired at the level of secondary education.
Teaching Methodologies
The teaching methodologies used in this course are:
1) Verbal Methodologies (say), making use of pedagogical resources: Exposition, Explanation, Dialogue and Interrogation;
2) Intuitive Methodologies (show), making use of pedagogical resources: Demonstration, Audiovisuals and Written Texts.
Learning Results
It is intended to provide students with the basic mathematical knowledge required in the professional training of a senior professional technician in the area of Computer Science and it is expected that, at the end of the course unit, the student will be able to:
1. understand analytically and geometrically the concept of derivative of a function at a point,
2. derive real functions of real variable using appropriate rules;
3. analyze and apply the rules and methods of primitivation in IR appropriately,
4. compute indefinite integrals, definite integrals and improper integrals in IR ,
5. analyze, synthesize and articulate information to solve problems using differential and integral calculus.
Program
1. Real functions of real variable – reviews: affine, quadratic, exponential, logarithmic and trigonometric functions.
2. Differential calculus in R: derivation of functions.
3. Primitivation of real functions of real variable: definition and properties; immediate primitivation; methods of primitivation: primitivation by parts; primitivation of rational functions; primitivation of trigonometric functions; primitivation by substitution.
4. Integral calculus: definite integral; applications of definite integral: calculating areas, volumes and arc lengths of curves; improper integrals.
Grading Methods
1) The Periodic Evaluation comprises the mandatory completion of three tests. Students who obtain a score less than seven at some test are automatically disapproved by this method. In other cases, the final rating is obtained by calculating the arithmetic average of the classifications obtained.
2) The Evaluation by Exam includes an exam.
Internship(s)
NAO
Bibliography
Campos Ferreira, J. (2014). Introdução à Análise Matemática (11ªEd). Fundação Calouste Gulbenkian.
James, G. (2020). Modern Engineering Mathematics (6th Ed). Pearson.
Lima, E. L.(2016). Análise no Espaço lR^n (2.ª ed.). Instituto Nacional de Matemática Pura e Aplicada.
Lima, E.L. (2016). Análise Real – Vol. 2 (6.ª ed.). Instituto Nacional de Matemática Pura e Aplicada.
Kreyszig, E. (2011). Advanced Engineering Mathematics (10th Ed). John Wiley & Sons.
Stewart, J. (2017). Cálculo, Vol. 2 (8ª Ed.). São Paulo: Cengage Learning.