Curricular Unit:Code:
Mathematics997MATE
Year:Level:Course:Credits:
1UndergraduateQuality, Environment and Safety Management4 ects
Learning Period:Language of Instruction:Total Hours:
Winter SemesterPortuguese/English52
Learning Outcomes of the Curricular Unit:
The main objective of the curricular unit Mathematics in this academic degree is to provide the students basic mathematical knowledge and mathematical tools, which will promote logical and methodological thinking, and will enable the equation and resolution of applied problems.
At the end of the course the student will possess the following skills:
- Ability to interpret and mathematically equate real problems, using the concepts of functions, derivatives and integrals;
- Ability to select and adequately apply mathematical tools for solving these problems, including matrices and determinants;
- Ability to interpret and critically analyze the results obtained.
Syllabus:
1. Matrices and Determinants
1.1. Matrices. Matrix Operations. Row Operations. Systems of Equations. Matrix Inverse
1.2. Determinants. Cramer’s Rule.
2. Functions
2.1. Basic Concepts. Domain and Zeros
2.2. Polynomial, Rational, Exponential, Logarithmic
2.3. Derivatives. Derivative’s Techniques.
2.4. Applications of the Derivative
3. Integration
3.1. Indefinite Integrals
3.2. Definite Integrals. The Fundamental Theorem of Calculus
3.3. Applications of calculus: 1st order linear differential equations with separated variables
Demonstration of the Syllabus Coherence with the Curricular Unit's Objectives:
The syllabus presented covers the essential areas of knowledge and consistently achieves the objectives set out, since all the topics included in the program - differentiability, integrals and primitives, matrices and determinants - cover the main aspects of the study that will enable students to select and properly apply mathematical tools in applied problem solving.
Teaching Methodologies (Including Evaluation):
The teaching methodologies are mainly expositive, interrogative and demonstrative, both during classes and tutorial orientation sessions. Emphasis is given to the interpretation and mathematically equation of real problems, and to the proper selection and application of mathematical tools in problem solving. Problems and exercises are proposed, for resolution in classroom and individual study hours. Particular attention is given to the physical interpretation of the studied phenomena, trying to make a solid connection between theory and practice.
The evaluation is continuous, and includes the following items:
- Individual written tests;
- Practical application of knowledge in individual or group assignments
- Student performance, taking into account class attendance, the resolution of exercises outside classes, the attitude and active participation in class and in tutorial orientation.
Demonstration of the Coherence between the Teaching Methodologies and the Learning Outcomes:
The proposed methodologies are consistent with the objectives set for the course since they were planned in order to enhance physical interpretation of the studied phenomena, trying to make a solid connection between theory and practice. It is expected, therefore to help students to develop the ability to apply such techniques in solving applied problems.
Reading:
[1] Anton, H; Bivens, I.C.; Davis, S. Calculus: Early Transcendentals, 11th Edition, Wiley, 2019.
[2] Anton, H. Elementary Linear Algebra, 11th Edition, Wiley, 2019
[3] Ferreira, M.A.M.; Amaral, I.; Álgebra Linear – Matrizes e Determinantes – Vol. 1. 8ª edição. Edições Sílabo. 2018
[4] Ferreira, M.A.M.; Amaral, I.; Cálculo Diferencial em Rn. 5ª edição. Edições Sílabo. 2002
[5] Ferreira, M.A.M.; Amaral, I.; Primitivas e Integrais. 7ª edição. Edições Sílabo. 2018
Lecturer (* Responsible):
Alzira Dinis (madinis@ufp.edu.pt)