6 ECTS; 1º Ano, 1º Semestre, 28,0 T + 28,0 TP + 5,0 OT , Cód. 814342.
Lecturer
- Maria Helena Morgado Monteiro (1)(2)
(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 Sequencies;
4.2 Infinite series and tests for convergence;
4.3 Alternating series;
4.4 Taylor's series and series and their applications.
Evaluation Methodology
Ongoing assessment: two written tests (0-9) with minimum mark of 2; four homeworks with presentation in class of one homeworks (0-0.5).
Pass mark for ongoing assessment is the sum of the tests with the homeworks and the presentations and must total 10.
Exam assessment: a written test (0-20).
Minimum mark to pass the exam is 10.
Bibliography
- Monteiro, H. (2024). Apontamentos de Cálculo I. Abrantes: ESTA
(0). Khan Academy. Acedido em 1 de fevereiro de 2019 em http://www.fundacao.telecom.pt/Home/KhanAcademy
(0). Temas de Matemática Elementar. Acedido em 14 de fevereiro de 2019 em http://cmup.fc.up.pt/cmup/apoiomat/manual_apoiomat_v1.pdf
(2006). Cálculo. (Vol. I). São Paulo: McGraw-Hill
(2012). Calculus. Belmont, USA: Brooks/Cole, Cengage Learning
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, Geogebra, Wolframalpha and Moodle platform.
