Mathematics I

Code:

M1014

Acronym:

M1014

Level:

100

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2018/2019 - 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:F	0	Official Study Plan	2	-	6	56	162
			3
L:Q	59	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; exponencials 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	162,00
Frequência das aulas	56,00
Total:	218,00

Eligibility for exams

Not applicable.

Calculation formula of final grade

The final mark is either the sum of the classifications in 3 tests or approval in exam in the second exam period.

Regular Season:

• The first and second  part will be evaluated by a test, which will be held, respectively, at the end of October and the end of Novembre.
• The third part will be evaluated by a test on the date set for the examination of this UC during the regular season. Then, the student may also try to improve the classification on the first or second tests.
• The first test is for 7 points, the second for 5 points and the third for 8 poinst. For approval the student should obtain a total of at least 9,50 points (out of 20).

Second examination season:

• The examination in the second examination season will be divided into three parts, each corresponding to one of the tests.
• At the second examination season, the final classification of each part will always be the best between the classifications obtained in the regular season and the second examination season.
• An additional test, either written or oral, may be asked of students aiming at marks over 18 out of 20.

Special assessment (TE, DA, ...)

Written exam.

Classification improvement

• Students wishing to take a grade improvement examination in the regular season will have to follow the rules indicated above for the evaluation of the remaining students during the regular season.


• Students who want to improve their grades at the second examination season will do the exam.