Mathematics I

Code:

M191

Acronym:

M191

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2012/2013 - 1S

Active?	Yes
Web Page:	http://moodle.up.pt/course/view.php?id=932
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Bachelor in Computer Science

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:CC	70	Plano de estudos de 2008 até 2013/14	1	-	7,5	-
MI:ERS	130	Plano de Estudos a partir de 2007	1	-	7,5	-

Teaching language

Portuguese

Objectives

Understand and use the notions and results of the program below.

Learning outcomes and competences

Understand and use the notions and results of the program below.

Working method

Presencial

Program

1. Systems of linear equations and matrices. 1.1 Solving systems of linear equations using Gauss's method and matrices. 1.2 Matrices: sum of matrices, scalar multiplication, multiplication of two matrices, inverse of a matrix, the rank of a matrix. 1.3 Determinants and Cramer's Rule. 2. Calculus - Preliminaries 2.1 Functions, domain, codomain and image ; injective, surjective and bijective functions; graphs of functions; composite functions; the inverse of a bijective function. 2.2 Trigonometric functions; properties. Inverse trigonometric functions. Exponential and Logarithmic functions. 2.3 Limits; definition and properties. 2.4 Continuous functions; definitions and properties, the Intermediate-Value Theorem, the Max-Min Theorem. 3. Differentiation 3.1 Definition of derivative, differentiation rules (sums and constant multiples, the product rule, the quotient rule, inverse functions). Derivatives of Trigonometric functions and of their inverse functions. Derivatives of exponential and logarithmic functions. 3.2 Mean value Theorem (Rolle, Lagrange and Cauchy). Increasing and decreasing functions, maximum and minimum values. 3.3 Extreme-value problems. 3.4 Concavity and inflexictions. 3.5 Sketching the graph of a function. 4. Taylor polynomials. 5. Integration 5.1 The definite integral: definition and properties. 5.2 The fundamental Theorem of Calculus.The method of substitution, integration by parts. Integral of rational functions. 5.3 Improper integrals. 5.4 Areas of plane regions, volumes of solids of revolution. The arc length of the graph of a function. 6. Sequences and Series 6.1 Sequences and Convergence 6.2 Convergence tests: the ratio test, the integral test, the alternating series test.

Mandatory literature

000052624. ISBN: 0-914098-89-6
000097905. ISBN: 978-0-495-38273-7
000093351. ISBN: 0-471-66959-8
000054372. ISBN: 972-773-106-6

Teaching methods and learning activities

1. All classes will be permeated with explanatory examples and overview exercises. 2. An adequate list of updated references will be recommended; all books and texts are available at the Mathematics Department' s library. Besides the exercises list, the slides with the course's content may be looked up or printed from the unit description page. 3. During some of the pratical classes it will be proposed that the students solve written short tests (taking around 30 minutes) to attest their learning outcome. These tests, however, will not be eligible for the calculation of the final grade. Each witten test will be proofread and mended by a classmate; on a following class the questions will be thoroughly solved by the teacher and the solutions attached to the course unit page.

Evaluation Type

Evaluation with final exam

Assessment Components

Description	Type	Time (hours)	Weight (%)	End date
	Exame	3,00	100,00
	Total:	-	100,00

Amount of time allocated to each course unit

Description	Type	Time (hours)	End date
	Frequência das aulas	28
	Total:	28,00

Eligibility for exams

All the student missing more than 4 TP will be excluded. Students who ere eligible in 2008/09, 2009/10 or 2010/11 may be excused from attending TP classes. For this, they must send a request by email to gchaves@fc.up.pt until 15th October.

Calculation formula of final grade

1. Final Exam 2. Extra exam: any student whose mark on the final exam has lain in the interval ]8, 9.5[ may apply for an additional exam; its granting depends on a full assessment of the previous written test. 3. Extra exam: any student who had obtained more than 16 out of 20 can be asked to write an extra exam. If the student does not take the extra exam, the fibnal grade will be 16. 4. Any student may have to take an oral exam in order to clarify any doubts in relation to the written exam.

Examinations or Special Assignments

Any special exam is written. Any student applying for this exam can be asked to do a small oral or written test to decide if he/she is prepared to take the exam; in case the student is not prepared he/she will have his/her admission to the special exam refused.

Observations

Board of examiners: Maria Gabriela Chaves Maria Pires de Carvalho José Carlos Santos Maria Eugénia de Sá