Fundamentals of Mathematics

Code:

M1012

Acronym:

M1012

Level:

100

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2024/2025 - 1S

Active?	Yes
Web Page:	https://moodle2324.up.pt/course/view.php?id=6729
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Bachelor in Biology

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:B	166	Official Study Plan	1	-	6	48	162
			3
L:CC	1	study plan from 2021/22	2	-	6	48	162
L:CTA	56	Plano estudos a partir do ano letivo 2016/17	1	-	6	48	162
L:F	0	Official Study Plan	2	-	6	48	162
			3
L:G	54	study plan from 2017/18	1	-	6	48	162
			3
L:Q	0	study plan from 2016/17	3	-	6	48	162
SauDInoB	38	Current Studies Plan	1	-	6	48	162

Teaching language

Suitable for English-speaking students

Objectives

The aim of this course is that the student:
- masters some basic techniques of linear algebra (operations with matrices,  solving linear systems) and recognizes some of its applications;
- 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.

Learning outcomes and competences

Familiarity with basic techniques of differential and integral calculus, differential equations, and matrix theory, and their applications.

Working method

Presencial

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

Prerequisites: basic knowledge of Mathematics acquired in the secondary education system.

Program

I. Linear Algebra
1. Real matrices; matrix operations.
2. Systems of linear equations; Gaussian elimination; chacteristic of a matrix; matrix inversion.
3. Markov chains as a mathematical model; regular chains andstationary state vector.
4. Linear regression by the least squares method.

II. Calculus
4. Polynomial, exponential, logarithmic, and trigonometric functions(review). Inverse trigonometric functions, their derivatives; l'Hôpital's rule.
5. Primitivation by substitution, change of variable, and by parts; primitivation of rational functions.
6. Area and definite integral; Fundamental Theorem of Calculus; area of regions bounded by curves; improper integrals.
7. First order differential equations: separable or linear.
8. Examples of modelling by differential equations.

Mandatory literature

J. Stewart; Cálculo - Volumes I e II, Pioneira Thomson Learning, 2006

Complementary Bibliography

Anton Howard; Álgebra linear com aplicações. ISBN: 978-85-7307-847-3
W. Nicholson; Álgebra Linear, McGraw-Hill, 2006
F. Ayres e E. Mendelson; Schaum's Outline of Calculus, McGraw-Hill, 1999
Anton Howard; Calculus. ISBN: 0-471-48273-0

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.
3. Regular office hours for student advice and clarification of doubts.
4. Besides the bibliography list, slides of the lecture notes  and exercises are published on moodleUP.

keywords

Physical sciences > Mathematics > Mathematical analysis > Differential equations
Physical sciences > Mathematics > Mathematical analysis > Functions

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

Course registration is the only requirement.

Calculation formula of final grade

There will be two optional midterm tests during the semester, with equal weight, and duration of 1h00m, the first durin the classes period of the semester an the second on the day of the exams calendar.

To be approved by midterm tests, the sum of the corresponding ratings must be greater than or equal to 9.5.

The final exam at "época de recurso" consists of two parts, corresponding to the tests. The classification of each part is the best between that of the test and that of the corresponding exam part. These rules do not apply to all remaining exams.

Grade improvement can be attempted only through exam at "época de recurso".

Examinations or Special Assignments

(see the "Formula for the Calcultation of the Final Score")

Special assessment (TE, DA, ...)

Any type of special student evaluation may take one of the following forms: exclusively an oral examination; an oral examination plus a written examination, the student being required to pass both of them; only a written examination. The option for one of them is of sole responsibility of the professors in charge of the course unit.

Classification improvement

(see the "Formula for the Calcultation of the Final Score")

Observations

The students can contact either of the professors of thisd unit:
Fernando Jorge Moreira fjm@fc.up.pt