Description

Theory
2

Theory/Practice
2

Instructors

Gisela Vieira Ramadas

Contents

I - Differential calculus in IR - 4,5 weeks
A complement of the study of functions of one real variable;
Inverse circular functions approach;
Derivatives of composite, implicit and inverse functions.
Differential.

II - Integral calculus - 7 weeks
Indefinite integrals: Def., geometric interpretation and properties.
Integration by: algebraic decomposition, parts, and substitution.
Definite Integral: Definition, geometric interpretation, and properties;
The fundamental theorem of integral calculus; Application to the calculation of plane areas.
Improper integrals.

III - Series - 3,5 weeks
Infinite series: Definition. The sum of a series. Series of non-negative terms. The main convergence tests. Alternating series. Absolute and conditional convergence. The Leibniz test.
Series of functions: Definition. Power series. Radius and interval of convergence. MacLaurin and Taylor series.

Learning Outcomes

OB1: Analyse real functions of one variable and apply mathematical concepts to solve problems.

OB2: Apply derivative concepts and differentiation techniques in problem-solving contexts.

OB3: Understand and apply indefinite and definite integral concepts and their relationship with derivatives.

OB4: Apply different integration techniques and use definite integrals in practical applications.

OB5: Analyse improper integrals and evaluate their convergence.

OB6: Analyse numerical series and apply appropriate convergence criteria.

OB7: Apply power series concepts and use Taylor and MacLaurin series for function representation.

OB8: Formulate structured mathematical solutions, simplify results, and critically interpret obtained solutions.