2024
Mathematics
Name: 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
Learning Goals
The aim of this course is to consolidate the basic formation in Mathematics and to provide new mathematical knowledge and skills. Regarding competences it is intended that students acquire ability to apply the mathematical knowledge to real life situations, autonomously and seriously.
Contents
Linear systems. Eliminations of Gauss. Matrices and vectors. Operations with matrices. Determinants. Inverse matrix. Cramer's Rule.
Functions, Limits, and Continuity. Inverse and composite functions. Limits of numerical successions. Continuous functions and their properties.
Differential Calculus and Applications. Derivatives of composite, implicit, and inverse functions. Logarithmic differentiation. Theorems of Fermat, Rolle, Lagrange and Cauchy. Rule of L'Hôpital. Taylor's formula. Numerical differentiation. Applications of derivatives.
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. Euler's method. First order separable and linear differential equations. Applications in the natural sciences.
Functions, Limits, and Continuity. Inverse and composite functions. Limits of numerical successions. Continuous functions and their properties.
Differential Calculus and Applications. Derivatives of composite, implicit, and inverse functions. Logarithmic differentiation. Theorems of Fermat, Rolle, Lagrange and Cauchy. Rule of L'Hôpital. Taylor's formula. Numerical differentiation. Applications of derivatives.
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. Euler's method. First order separable and linear differential equations. Applications in the natural sciences.
Teaching Methods
The teaching methodology consists of structured exposition using illustrative examples and applications. In 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 continuous assessment, consisting of three tests, or alternatively, the final assessment. Each test requires a minimum grade of 8 points, and the final grade is calculated as the arithmetic average of the three. A minimum grade of 10 points is required to pass.
The final assessment, during the regular period, consists of a written exam, which also requires a minimum grade of 10 points for passing.
Students who do not pass or who wish to improve their grade may take the exam during the resit period.
The final assessment, during the regular period, consists of a written exam, which also requires a minimum grade of 10 points for passing.
Students who do not pass or who wish to improve their grade may take the exam during the resit period.
Teaching Staff
Certificações
