ISLA Santarém 505

Mathematics II

• ApresentaçãoPresentation

  The course develops reasoning skills and the study of real functions of one and several variables, introducing differential and integral calculus and their applications, in order to master derivation and integration techniques and understand the respective fundamental concepts.
• ProgramaProgramme

  1Real functions of a real variable 1.1Definition & properties 1.2Elementary functions & operations with function 1.3Polynomial functions 1.4Modulus function 1.5Composite function & inverse function 1.6Exponential & logarithmic functions 1.7Trigonometric function 1.8Limits & continuity of functions 2.Differential calculus in IR 2.1Derivative of a function at a point: definition & geometric interpretation 2.2Derivative function & derivation rules 2.3Derivatives of order greater than one 2.4Theorem of the derivative of composite function 2.5Cauchy's rule 2.6Optimization applications in the study of function monotonicity 3.Integral calculus in IR 3.1Primitive properties 3.2Primitization techniques 3.3Defined integral & properties 3.4Fundamental theorem of integral calculus & indefinite integral 3.5Applications integral calculus:calculating areas & solving differential equations 4Real functions with two or more real variables 4.1Generalities 4.2Partial derivatives 4.3Gradient vector 4.4Directional derivatives
• ObjectivosObjectives

  The objectives of this curricular unit are: O1. Develop students' reasoning ability; O2. Develop skills related to the study of real functions of one or more real variables; O3. Present concepts of differential calculus and integral calculus of functions and their applications. At the end of the course, students should be able to: C1. Master the techniques associated with differential and integral calculus of functions; C2. Master the basic principles of derivation, integration and their properties; C3. Understand the fundamental concepts of real functions of one or more real variables.
• BibliografiaBibliography

  Amaral, I. et al. (2018). Primitivas e Integrais. 7.ª Edição, Edições Sílabo. Faria, A. et al. (2021). Análise Matemática I - Resumo Teórico, Exercícios Resolvidos e Propostos. 1.ª Edição, Edições Sílabo. Guidorizzi, H. (2021). Um Curso de Cálculo - Volume 1. 6.ª Edição, 3.ª Impressão. LTC – Livros Técnicos e Científicos Editora Ltda. Martinho, C. et al. (2020). Primitivas e Integrais – Com Aplicações às Ciências Empresariais. 2.ª Edição Revista e Ampliada, Edições Sílabo. Stewart, J. (2017). Cálculo Volume 1 - Tradução da 8ª Edição Norte Americana. Cengage Learning.  Stewart, J. (2017). Cálculo Volume 2 - Tradução da 8ª Edição Norte Americana, 2017, Cengage Learning.  
• MetodologiaMethodology

  The methodology to be used will strike a balance between theoretical foundations and their practical application. Classes will address the concepts of different topics and then demonstrate their practical application through a series of exercises inside and outside the classroom, encouraging active and independent participation by students. The expository method will be used to introduce concepts and structure reasoning, and the interrogative method will be used to assess learning in the theoretical part of each chapter. In the practical part, the demonstrative method will be used to provide practical examples of the content, as well as active, participatory, and autonomous methods to connect with each student's experience. In summary: (1) Expository and Interrogative Methodology – participatory teaching, using motivation strategies whenever necessary, and (2) Active Pedagogical Methodologies such as Flipped Classroom, Gamification, and Problem/Project-Based Learning.  
• LínguaLanguage

  Português
• TipoType

  Semestral
• ECTS

  6
• NaturezaNature

  Mandatory
• EstágioInternship

  Não
• AvaliaçãoEvaluation

  Avaliação Curricular: O estudante realiza 2 fichas de exercícios em grupo e dois testes individuais. O estudante aprova se a classificação final for superior ou igual a 9.5 valores. A classificação final é calculada pela fórmula Classificação Final = 0.2*F1+0.3*T1+0.2*F2+0.3*T2, onde F1, F2, T1 e T2 denotam, respetivamente, as notas nas fichas de exercícios e nos testes individuais. 

  Avaliação Final: O estudante realiza o exame completo e aprova se obtiver classificação superior ou igual a 9.5 valores.