Mathematics

Code: MAT11377L

6 ECTS

Duration: 15 weeks/156 hours

Scientific Area: Mathematics

Teaching languages: Portuguese

Languages of tutoring support: Portuguese

Regime de Frequência: Presencial

Sustainable Development Goals

4. Educação de qualidade - Assegurar a educação inclusiva, e equitativa e de qualidade, e promover oportunidades de aprendizagem ao longo da vida para todos.

Learning Goals

The objective of this curricular unit is to consolidate basic training in Mathematics and provide new mathematical tools suited to the needs of the undergraduate degree.
In terms of skills, the aim is for students to acquire the ability to apply mathematical knowledge to real-life situations in an autonomous and critical manner.

- Systems of Linear Equations. Eliminations of Gauss. Matrices and vectors. Operations with matrices. Determinants. Inverse matrix. Cramer's Rule.
- Functions, Limits, and Continuity. Inverse and composite functions. Continuous functions and their properties.
- Differential Calculus and Applications. Derivatives of composite, implicit, and inverse functions. Theorems of Fermat, Rolle, Cauchy and Lagrange. Rule of L'Hôpital. Taylor's formula. Newton's method for solving nonlinear equations and finding extrema of functions. Numerical differentiation.
- Integral Calculus and Applications. Primitives. Methods of primitivation: by substitution and by parts. Primitives of rational functions. Integral. The fundamental theorem of integral calculus. Numerical integration. Applications of integrals. Improper integrals. Power series.
- Ordinary Differential Equations. First order separable and linear differential equations. Euler's method. Applications in the natural sciences.

Teaching Methods

The teaching methodology used consists of structured exposition using illustrative examples and applications. In the theoretical?practical classes, the methodology consists of solving exercises appropriate to the subject matter, with individual guidance for each student. During the semester, a session is planned, led by someone from the students' professional practice, in order to contextualize the usefulness and applicability of the course content in their future professional activity.

Assessment

Students may choose between continuous assessment consisting of 3 tests or, alternatively, a final exam. Test scores must not be lower than 8 points. The final grade is the average of the test scores. Students who do not pass the continuous assessment may take the final exam during the regular period and retake it, if necessary, during the resit period.