﻿ Calculus - Informática e Tecnologias MultimédiaInstituto Politécnico de Tomar

# IPT   Ano Letivo: 2021/22

# Informática e Tecnologias Multimédia

## Calculus

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

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
Ongoing assessment: two written tests (0-8) with minimum mark of 2; three homeworks (0-1); presentation in class of one exercise solved(0-1).
Exam assessment: a written test (0-20).
Minimum mark to pass the exam is 10. Pass mark for ongoing assessment is the sum of the tests with the homeworks and the presentation and must total 10.

Bibliography
- Larson, R. e Hostetler, R. e Edwards, B. (2006). Cálculo. (Vol. I). São Paulo: McGraw-Hill
- Monteiro, H. (2020). Apontamentos de Cálculo. Abrantes: ESTA
- Stewart, J. (2012). Calculus. Belmont, USA: Brooks/Cole, Cengage Learning
(0). Khan Academy. Acedido em 1 de fevereiro de 2019 em http://www.fundacao.telecom.pt/Home/KhanAcademy
- 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 and Moodle platform.   