Mathematic

Code:

M1029

Acronym:

M1029

Level:

100

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2023/2024 - 1S

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

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:AP	41	Official Study Plan	1	-	6	56	162

Teaching language

Portuguese

Objectives

The aim of this course is that the student:
- masters basic concepts and results of Euclidean plane geometry, including isometries;
- masters basic techniques of differential and recognizes some of its applications;
- masters some basic concepts of probability and statistics;
specially those necessary for geographic information course units.

Learning outcomes and competences

Acquisition of basic skills in Euclidean plane geometry, pre-calculus and differential calculus, and probability and statistics.

Working method

Presencial

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

Mathematics contents up to the 9th year of schooling.

Program

1) Statics and numerical methods:
Sum symbol; average, variance, standard deviation; Least squares line; Correlation coefficient.

2) Trigonometry:
Oriented angles; Trigonometric circle; Measure of an angle. Parametric equation of a circle. Sine,cossine and tangent of an angle.

3) Geometry: 
Coordinate axes and point coordinates;  Distance between two points; Circle and sphere equations.
Planar symmetry (translations, reflections, homothety);
Vectors: Scalar product of vectors; Angle defined by two vectors; Perpendicularity among vectors, lines and planes.
Equations for lines and planes (implicit and parametric); Slope of a line on a plane; Slopes of perpendicular lines; Parallelism among vectors and planes.

4) Functions:
Graphs; Image of a set; Injective, surjective and bijective functions; Composion; Inverse function. Trigonometric functions: Sine, cossine and tangent; Properties: periodicity, parity, zeros and local extremes; Graphs; Inverse functions.

5) Continuity and differentiation of real valued functions of one real variable:
Intuitive approach to limits and continuity of functions; Sum, difference, product and quotient of functions and composion of functions. Continuity of polynomial, rational, trigonometric,  exponential and logarithm functions.

6) Derivative of a function at a given point; Geometric interpretation; Derivative of sums, differences, products and quotients of functions; Derivative of composed and inverse functions; Derivative of polynomial, rational, trigonometric,  exponential and logarithm functions.
Derivative rules and reference functions; tangent line to graphs.

 

Mandatory literature

Martins Maria Eugénia Graça; Introdução às probabilidades e estatística. ISBN: 972-674-270-6
Stewart James; Cálculo. ISBN: 85-221-0479-4 (Vol. I)

Complementary Bibliography

Crilly Tony; 50 ideias de matemática que precisa mesmo de saber. ISBN: 978-972-20-4708-1
Rosen Joe; Symmetry discovered. ISBN: 0-521-20695-2
Anton Howard; Calculus. ISBN: 0-471-48273-0

Teaching methods and learning activities

Presentation of topics in lectures, including the relevant examples.
Exercises presented in the course's homepage, solved in example classes.

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

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.

The first test is for 6 points and the other are for 7 points. For approval in the tests the student should obtain a total of at least 9,50 points.

During the exam period there is an additional test divided in 3 parts, each corresponding to a test, so that each student can improve the classification obtained in a test or tests.

 A minimum of 9.5 in the exam is required for approval.

 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

Written exam.

Observations

The jury may ask a student to do an extra test in case of doubt about his/her tests or exam.


Jury:
Paula Alexandra de Ameida Bastos Carvalho Lomp
Maria do Rosário Machado Lema Sinde Pinto