Applied mathematics I

Knowledge and mastery of the subjects taught in Mathematics of the secondary school.

The expository method will be accompanied by the resolution of exercises, individually or in teams, with the coordination of the teacher. In a more practical aspect, open source software (GeoGebra, Symbolab,…) will be used to solve exercises.

Development of critical thinking, coordination and exposition skills, attitudes of reflection and research, rigor in the interpretation, use and description of mathematical concepts, aiming at the acquisition of indispensable knowledge for the understanding of the subjects, namely functions, differential  and integral calculus, together with  its applications. All the topics will also be addressed in practical classes using Geogebra, WolframAlpha and Symbolab, promoting the capacity for autonomous learning.

1. Real functions of real variables
Brief review of real numbers, powers of rational exponents, equations and inequalities; real function of real variable: practical examples, properties, domain, range and graph; inverse function; polynomial function; rational function; irrational function; function defined by branches; limit and continuity; direct and inverse trigonometric functions and applications; exponential function and logarithm function; compound interest and exponential models.

2. Differential calculus
Average rate of change; derivative of a function at a point; derivative applications; derived function and properties; analytical study of functions: monotony, extremes, direction of concavities and asymptotes; optimization problems.

3. Integral calculus
Immediate integrals: table of integrals. Definite integral, properties, fundamental theorem of calculus, applications of the definite integral: area of a plane region, volume of a solid of revolution and length of an arc of curve.

4. Introduction to GeoGebra
Introduction; operating with real numbers; equations and inequalities and their geometric interpretation; curves and analytical study of functions.

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NAO

Anton, H. (2000), Cálculo – um novo horizonte (6ª ed.), Volume 1. Bookman. (Two books available at Library of ISEC: 3-2-150 e 3-2-242)

Rodrigues, R. (2019). ­ Notas Teóricas de Análise Matemática. DFM, ISEC.

Swokowski, Earl W. (1983). Cálculo com geometria analítica, Volume 1. McGraw­Hill (many books available at the Library of ISEC) 

Material available on Moodle (notes of Pré-­Cálculo, problem solving sheets, …)