Publication in the Diário da República: Despacho n.º 12419/2016 - 14/10/2016
6 ECTS; 1º Ano, 2º Semestre, 30,0 T + 45,0 TP + 5,0 OT , Cód. 81435.
Lecturer
- Maria Helena Morgado Monteiro (1)(2)
(1) Docente Responsável
(2) Docente que lecciona
Prerequisites
Knowledge of secondary school Algebra is assumed.
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
Ongoing assessment: three written tests (0-20) with minimum mark of 5.
Exam assessment: a written test (0-20).
Minimum mark to pass the exam is 10. Pass mark for ongoing assessment is the weighted average of the 3 tests and must total 10.
Bibliography
- , . (0). Khan Academy. Acedido em 1 de fevereiro de 2019 em http://www.fundacao.telecom.pt/Home/KhanAcademy
- Larson, R. e Hostetler, R. e Edwards, B. (2006). Cálculo. (Vol. I). São Paulo: McGraw-Hill
- Monteiro, H. (2020). Apontamentos de Cálculo. (Vol. ). Abrantes: ESTA
- Stewart, J. (2002). Cálculo. (Vol. 1). São Paulo: Pioneira Thomson 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
Teaching Method
Lectures dealing with the fundamentals principles and its applications. Practical classes involve practising with calculus techniques and the application of skills and knowledge.
Software used in class
Productivity tools.
