Elements of Mathematics

Code:

M1021

Acronym:

M1021

Level:

100

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2021/2022 - 1S

Active?	Yes
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Bachelor in Biochemistry

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:BQ	121	Official Study Plan	1	-	6	56	162

Teaching language

Portuguese

Objectives

The aim of this course is that the student:

- masters some basic techniques of differential and integral calculus of one variable (calculation of derivatives, primitives and integrals, solution of differential equations) and recognizes some of its applications;

- Master some basic concepts of Probability and Statistics, necessary for the development of this subject in the course of the second year.

Learning outcomes and competences

Familiarity with basic techniques of Differential and Integral Calculus, Differential Equations and its applications, and Probability and Statistics.

Working method

Presencial

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

Basic knowledge of mathematics acquired in high school education (12º year of Matemática A).

Program

1 – Differential Calculus

Review of limits, continuity and derivatives of real functions of real variable. Inverse trigonometric functions and their derivatives. Rule of L'Hôpital. Primitives. Integration by substitution and integration by parts. Primitives of rational functions (some cases). Area and integrals. Fundamental Theorem of Calculus. Areas of regions bounded by curves. Improper integrals.

2. Differential Equations:

First order differential equations: separable and linear. Examples of modeling with differential equations.

3. Probability Theory:

Fundamental concepts, interpretations of the concept of probability, independence of events and conditional probability, Bayes theorem and the total probability.

4. Random variables:

Discrete and continuous random variables, probability function, probability density function and distribution function; expected value and its properties, variance and their properties.

Mandatory literature

Stewart James; Cálculo. ISBN: 0-534-39-321-7

Complementary Bibliography

Anton Howard; Calculus. ISBN: 0-471-48273-0
Samuels Myra L.; Statistics for the life sciences. ISBN: 978-0-13-122811-5 0-13-122811-0

Comments from the literature

All the supporting material made available for lectures is the most important "bibliography".

Teaching methods and learning activities

1. Lectures: presentation of the course material and of examples.


2. Exercise sessions: solution of exercises by the students with the advice of the teachers; the exercises are published in advance to stimulate student work.

Classes will be in person or online, according to the instructions of the Board of FCUP.

Evaluation Type

Evaluation with final exam

Assessment Components

designation	Weight (%)
Exame	100,00
Total:	100,00

Amount of time allocated to each course unit

designation	Time (hours)
Estudo autónomo	110,00
Frequência das aulas	56,00
Total:	166,00

Eligibility for exams

Course registration is the only requirement.

Calculation formula of final grade

Avaliação por exame final

The final classification is the mark obtained in the normal examination period (Época Normal) or eventually in the second examination period (Época de Recurso).

In any case, a student with a final grade ≥ 17.5 may eventually be subjected to an extra oral or written test.

All registered students are admitted, without restrictions, to the exams.

Internship work/project

Any type of special examination can be from one the following types: exclusively by an oral examination, only a written exam, one oral examination and a written exam.

The decision about which of the types of special examination is chosen, is exclusively the responsability of the teacher assigned to the curricular unit.