Mathematical Laboratory

Code:

M1025

Acronym:

M1025

Level:

100

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2021/2022 - 1S

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

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:M	94	Official Study Plan	1	-	3	28	81

Teaching language

Portuguese

Objectives

Use of Geogebra Software and an algebraic manipulation program (Maxima) to treat analysis problems, algebra and geometry. Particular attention is given to the consolidation, through the development and analysis of algorithms and geometric interpretation, of the concepts and problems covered in the courses Linear Algebra and Analytic Geometry I (M1010), Real Analysis I (M1011) and topics of Elementary Mathematics (M1024).

 

Learning outcomes and competences

It is intended that at the end of the course, the student is capable of using Geogebra and a manipulation algebraic language (Maxima), dealing with problem of analysis, algebra and geometry, solving them, graphing and interpreting their solutions.

 

Working method

Presencial

Program

Introduction to Maxima:graphic interface; variables; functions; programming structure; graphic sketch.

Real functions of a real variable: sketch of the graph and interpretation; definition of the derivative function,  tangent line of a curve at a point; calculation and geometric interpretation of limits; integral calculus and geometric interpretation; determination of maximum and minimum of functions. Limits of sequences. Approximate calculation of series sums. Polynomial approximation of functions.

Systems of linear equations: numerical resolution, graphical representation and interpretation of the solution; implementation in Maxima of  Gauss Elimination Method and geometric interpretation. Spaces and vector subspaces: geometric representation and interpretation of linear combinations, subspaces generated by linear combinations of elements of a set, the sum of linear subspaces, bases. Linear maps: representation of the images of R2 and R3 subsets; invariant subsets and subspaces; calculation and geometric interpretation of the determinant and properties of a matrix of a linear application. Calculation and geometric interpretation of the internal product and norm of vectors, and the vector product in RR^3.

The study of revolution curves and solids may also be addressed.

Mandatory literature

F. J. Moreira;; Apontamentos de apoio ao Maxima, 2015/16
http://maxima.sourceforge.net/documentation.html; Documentação do Software Maxima, Website, 2012
M.J. Costa; Slides de Laboratório de Matemática, M1025
M.G. Chaves ; Slides de Análise Real I M1011
Paula Lomp; Álgebra Linear e Geometria Anaítica I M1010
https://wiki.geogebra.org/pt/Manual; Manual Geogebra,

Complementary Bibliography

Zachary Hannan;; wxMaxima for Calculus I ; (free download at https://wxmaximafor.wordpress.com)
Adams Robert A.; Calculus. ISBN: 0-321-27000-2
Zachary Hannan;; wxMaxima for Calculus II ; (free download at https://wxmaximafor.wordpress.com)

Teaching methods and learning activities

Laboratory classes: resolution, by the teacher and the students, of exercises proposed in exercise sheets and / or proposed in class. Availability of slides to support classes; in particular supporting Maxima and solving some of the proposed exercises. Support to students in clarifying doubts in the contents and /or in solving exercises.

Software

Maxima
Geogebra (https://www.geogebra.org/)

keywords

Physical sciences > 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	53,00
Frequência das aulas	28,00
Total:	81,00

Eligibility for exams

No restrictions.

Calculation formula of final grade

Approval for the course can be obtained.

1) by performing two tests; in this case, it is mandatory a) to obtain a classification greater than or equal to 7.0 values in each one of them, and b) arithmetic mean of the classifications obtained in the two tests greater than or equal to 10 values. In this case, the student's final grade is: 0.5x(T1+T2) where, T1=first test grade and T2=second test grade.

Each of the tests may consist of a computer test with a written or oral component. The second test necessarily has a computer component.

Only students who have obtained a grade greater than or equal to 7 points in the 1st test can take the 2nd test.

 

2) by taking a final exam (regular or recourse period).

The exam will necessarily consist of a computer test, which may contain a written or oral component. 

Students who have passed the course by taking the tests, and have not obtained the desired result, may take the exam in the normal period. In this case, students will have to choose, at the time of delivery of the exam, to waive or not the classification obtained in the assessment by tests (checking the desired option on the exam).

 

Students with a classification higher than or equal to 17.5 points (obtained in tests or in the exam of any of the seasons) may have to carry out a work in Maxima or a computer test with a written or oral component, to obtain a grade greater than or equal to 18 values.

Examinations or Special Assignments

The exams required under special conditions will consist of a computer test with a written or oral component which can be preceded by an oral or writen or computer eliminatory exam.

 

Special assessment (TE, DA, ...)

The exams required under special conditions will consist of a computer test with a written or oral component which can be preceded by an oral eliminatory exam.