Mathematics I

Code:

M1014

Acronym:

M1014

Level:

100

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2024/2025 - 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	48	162
L:CC	0	study plan from 2021/22	2	-	6	48	162
L:EG	0	The study plan from 2019	1	-	6	48	162
L:F	0	Official Study Plan	3	-	6	48	162
L:G	0	study plan from 2017/18	3	-	6	48	162
L:Q	0	study plan from 2016/17	1	-	6	48	162
			3

Teaching language

Portuguese

Objectives

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

Learning outcomes and competences

Familiarity with basic techniques of matrices, differential and integral calculus, differential equations, and some of their applications.

Working method

Presencial

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

Basic mathematical knowledge acquired in the secondary education system.

Program

1. 
   

    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 and stationary state vector.
   4. Least squares method.
   
   II. Calculus
   1. Polynomial, exponential, logarithmic, and trigonometric functions(review). Inverse trigonometric functions, their derivatives; l'Hôpital's rule.
   2. Primitivation by substitution, change of variable, and by parts; primitivation of rational functions.
   3. Area and definite integral; Fundamental Theorem of Calculus; area of regions bounded by curves; improper integrals.
   4. First-order differential equations: separable or linear.
   5. Examples of modeling by differential equations.

   
   

 

Mandatory literature

Anton Howard; Álgebra linear com aplicações. ISBN: 978-85-7307-847-3
Adams Robert A.; Calculus. ISBN: 0-201-82823-5

Teaching methods and learning activities

Contact hours are divided into theoretical and practical classes. In the first ones, the contents of the course are presented using examples to illustrate them and to guide the students. In the practical classes exercises are solved. Support materials are available on the course webpage (Moodle). In addition to the classes, there are periods of attendance per week where students have the opportunity to clarify their questions.

keywords

Physical sciences > Mathematics > Applied mathematics

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	106,00
Frequência das aulas	56,00
Total:	162,00

Eligibility for exams

Not applicable.

Calculation formula of final grade

Exam.

Special assessment (TE, DA, ...)

Exam.

Classification improvement

Exam-

Observations

Any extudent can be called to an extra test (oral or written) to clarify any doubts that may have arisen.