2023
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
Presentation
The objective is to consolidate basic training in Mathematics and provide new mathematical tools to model and analyze phenomena in the area of Natural Sciences, Life and Health, including matrix calculus, differentiation and integration of functions, solving differential equations.
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 on structured exposure using examples and applications to illustrate the theoretical concepts, using as resource the blackboard and transparencies, in solving chosen exercises with attendance to the individual student's needs. During the semester, a session given by a professional practitioner is foreseen in order to frame the usefulness and applicability of the contents of this curricular unit in future professional activity of students.
Students can choose the continuous assessment composed by three mandatory tests or, alternatively, evaluation by the final exam. The grades of all tests must not be less than 8 points. The final grade is calculated as the average of the tests grades. Students who have not received approval by continuous assessment can take the final exam and repeat it, if necessary, on the day of the appeal exam.
Students can choose the continuous assessment composed by three mandatory tests or, alternatively, evaluation by the final exam. The grades of all tests must not be less than 8 points. The final grade is calculated as the average of the tests grades. Students who have not received approval by continuous assessment can take the final exam and repeat it, if necessary, on the day of the appeal exam.
Teaching Staff
