Mathematics I

Code:

M1014

Acronym:

M1014

Level:

100

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2019/2020 - 1S

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

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:B	0	Official Study Plan	3	-	6	56	162
L:EG	30	The study plan from 2019	1	-	6	56	162
L:F	0	Official Study Plan	2	-	6	56	162
			3
L:Q	53	study plan from 2016/17	1	-	6	56	162
			3

Teaching language

Portuguese

Objectives

By completing this course, the students should master the concepts of derivative, primitive and integral; they should know how to solve some cases of differential equations and know how to use them to model specific situations; and they must understand the concept of matrix and to know how to use it.

Learning outcomes and competences

By completing this course, the student should be able to: find derivatives, primitives and integrals; use the properties of these concepts; solve some particular cases of differential equations (linear and separable equations of 1st order and 2nd order linear equations with constant coefficients); model some situations through differential equations; perform matrix operations; calculate determinants of square matrices; determine eigenvectors and eigenvalues of matrices; diagonalize a matrix (if possible); use some diagonalization properties of matrices.

Working method

Presencial

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

Basic knowledge of the set of real numbers and functions.

Program

1. Pre-Calculus: trigonometric functions and its inverses; exponencial functions and logarithms.


2. Derivatives: concept, results and applications.


3. Primitives: concept and primitivation roles.


4. Integrals: concept, Fundamental Theorem of Calculus, evaluation of areas, improper integrals.


5. Differential equations: separable and linear first order equations, examples of second order differential equations, applications.


6. Matrices: concept, algebra of matrices, inverse matrix, matrix rank.


7. Determinants: evaluation, identification of invertible matrices, determination of the inverse matrix.


8. Diagonalization: matriz diagonalization, applications.

Mandatory literature

Adams Robert A.; Calculus. ISBN: 0-201-39607-6
Anton Howard; Álgebra linear com aplicações. ISBN: 978-85-7307-847-3

Teaching methods and learning activities

Contact hours are divided into theoretical and practical classes. In the first, the contents of the course are presented using examples to illustrate them and to guide the students. In the practical classes some exercises will be solved. Support materials are made available on the course webpage at FCUP's information system (Sigarra). In addition to the classes, there are periods of attendance per week where students have the opportunity to ask questions.

keywords

Physical sciences > Mathematics > Applied mathematics

Evaluation Type

Distributed evaluation without final exam

Assessment Components

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

Amount of time allocated to each course unit

designation	Time (hours)
Estudo autónomo	106,00
Frequência das aulas	56,00
Total:	162,00

Eligibility for exams

Not applicable.

Calculation formula of final grade

During the semester there will be two "tests" each one with tha maximum classification of 10 valores and  wiith 1 hour of duration. The first one will be realized n the lective part of the semestre and the second one will be realized in the date previewed for the wxam of the curricular unit. To pass using classifications obtained in the rwo tests, the sum of these classifications must be at least 10 valores with a minimum of 4 valores in each test.

The exam in the second season have two parts, corresponding to the two tests. The classification in each part is the best of the classifcation of the part in the exam and the classification of the corresponding test. If a student realized a test and did not the corresponding part in the exam the classification of that part will be the one obtained in the corresponding test.

The classification in the exam  for  improvement of the classification of a student that passed in a previious examiinantion is the sum of classifcations obtained in the two parts of the exam.

Special assessment (TE, DA, ...)

Any special examination can take one of the following forms: an oral examinantion, or a written examinanion. The decision of which  form will be used is  full responsabilfy of  teachers of the curricular unit:

Classification improvement

See "formula for final classification".