Introduction to Applied Mathematics

Code:

M1027

Acronym:

M1027

Level:

100

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2017/2018 - 2S

Active?	Yes
Web Page:	https://moodle.up.pt/course/view.php?id=189
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	109	Official Study Plan	1	-	6	56	162

Teaching language

Suitable for English-speaking students

Objectives

Application of mathematical concepts, namely the ones studied in other first-year courses, to the analytical and numerical treatment of mathematical models in Physics, Biology, Ecology, Economics, Medicine and other fields of knowledge.

Learning outcomes and competences

The student should be able to translate the proposed problems in mathematical language, classify them, propose an adequate model and test such model. 

Whenever possible, the student should solve the problem analytically as well as obtaining a graphic representation of it. He should also be capable of using the Maxima software for graphic representation and simulation of solutions to the problem. 

Working method

Presencial

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

Requirements: Real Analysis I, Linear Algebra and Analytic Geometry I.
Co-requirements: Real Analysis II.

Program

Discrete mathematical modeling with classical examples of application: 

a) modeling in one dimension: discrete dynamical system and its variation, resolution of linear and affine model; fixed points, phase portrait and graph; models in Economics, Biology and Social Sciences; 

b) modeling in dimensions two and three: discrete dynamical system and its variation, resolution of the dynamical system in the linear case; fixed points, phase portrait (in dimension two) and graph; models in Ecology and Epidemiology.

Continuous mathematical modeling with classical examples of application: 

a) first order autonomous differential equation (o.d.e.): resolution in the linear and affine case as well cases where an explicit solution can be obtained; continuous model in Pharmacy, Physics and Biology; 

b) phase portrait of an autonomous o.d.e.: equilibria, monotonicity intervals, concavity; graph of the solutions by analysis of the phase portrait.

Adapting a model to a set of points: transformation into an affine model, graph method and least square method to determine an affine model. 

 

 

Mandatory literature

Giordano Frank R.; A first course in mathematical modeling. ISBN: 978-0-495-55877-4

Teaching methods and learning activities

Theoretical classes: exposition of the theory and indication of problems to be treated in practical classes. 
Practical classes: resolution of concrete problems with use of computer and adequate software for the resolution of problems in class time.

Software

Maxima

Evaluation Type

Distributed evaluation without final exam

Assessment Components

designation	Weight (%)
Participação presencial	0,00
Teste	100,00
Total:	100,00

Eligibility for exams

Participation in at least 75% of practical classes.

Calculation formula of final grade

1. The final grade will be the sum of the points obtained in three partial components: 
T1 - theoretical assessment: 7 points, minimum 2.5 points. 
T2 - theoretical assessment: 7 points, minimum 2.5 points. 
P - practical assessment using computer (will take place on one of days scheduled for replacement of classes): 6 points, minimum 2 points. 

2. In the second call the theoretical and practical assessment will take place on the day of the exam. The theoretical component has maximum grade 14, minimum 5 points. The practical component is worth 6 points, minimum 2 points. The final grade will be the sum of the two components.

3. Exception: if the sum of the points obtained in the three components is greater than 17, then a (eventually oral) complementary assessment may be required, to take place in a date to fix with the student. The final grade can be 17, 18, 19 or 20.

 

 

 

Special assessment (TE, DA, ...)

Students that, due to special conditions, are exempted from distributed assessment will have an exam under the conditions described for the second call.

Classification improvement

The improvement of final grade will consist of an exam following the same structure of the second call.