Publication in the Diário da República: Despacho n.º 9184/2020 - 25/09/2020
6 ECTS; 1º Ano, 2º Semestre, 28,0 T + 42,0 TP + 5,0 OT , Cód. 81435.
Lecturer
- Maria Helena Morgado Monteiro (1)
(1) Docente Responsável
(2) Docente que lecciona
Prerequisites
Not applicable.
Objectives
a) Know and apply basic mathematical procedures used in the degree programme;
b) Interpret data, formulate and solve problems involving derivation and integration of functions of one variable;
c) Represent functions as a power series and calculate approximate values.
Program
1.Real functions.
1.1 Definition, properties and graph of a real function;
1.2 Algebraic functions;
1.3 Exponential function and logarithmic function;
1.4 Trigonometric functions (direct and inverse).
2.Differential calculus in R
2.1 Derivative of a function at a point and derivative function;
2.2 Derivation Rules and derivative function of elementary functions;
2.3 The chain rule for differentiating composite functions
2.4 Applications of the derivative: differentials, monotony and extremes of a function; optimization problems.
3. Integral Calculus in R
3.1 Undefined integral
3.1.1 Primitives and indefinite integral - definition and properties;
3.1.2 Immediate primitives;
3.1.3 Methods of primitivation: primitivation by parts, primitivation of rational functions and primitivation of powers of trigonometric functions;
3.2 Integral definite
3.2.1 Definition and geometric interpretation of the Riemann simple integral;
3.2.2 The fundamental theorem of integral calculus and properties of the definite integral;
3.2.3 Applications of the definite integral: calculation of area of a region between two graphs, volume of a solid of revolution and length of a plane curve.
4.Series
4.1 Infinite series
4.1.1 Definitions and tests for convergence;
4.1.2 Alternating series;
4.2 Series of functions;
4.2.1 Power series and convergence intervals;
4.2.2 Taylor's series and calculation of the value of a transcendental function at a point.
Evaluation Methodology
Exam assessment: a written test (0-20).
Minimum mark to pass the exam is 10.
Bibliography
- Larson, R. e Hostetler, R. e Edwards, B. (2006). Cálculo. (Vol. I). São Paulo: McGraw-Hill
- Monteiro, H. (2023). Apontamentos de Cálculo. Abrantes: ESTA
- Stewart, J. (2012). Calculus. Belmont, USA: Brooks/Cole, Cengage Learning
- Tavares, J. (0). Temas de Matemática Elementar. Acedido em 14 de fevereiro de 2019 em http://cmup.fc.up.pt/cmup/apoiomat/manual_apoiomat_v1.pdf
(0). Khan Academy. Acedido em 1 de fevereiro de 2019 em http://www.fundacao.telecom.pt/Home/KhanAcademy
Teaching Method
Tutorial methodology.
Software used in class
Not applicable.
