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Presentation
Presentation
Mathematics II belongs to the compulsory group of curricular units of the cycle of studies and seeks to provide students with fundamental knowledge of mathematics, complementary to those given by the previous course units Algebra and Mathematics I, of the first semester. The course focuses on the themes of integral calculus and differential equations.
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Class from course
Class from course
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Degree | Semesters | ECTS
Degree | Semesters | ECTS
Bachelor | Semestral | 7
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Year | Nature | Language
Year | Nature | Language
1 | Mandatory | Português
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Code
Code
ULP928-505
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Prerequisites and corequisites
Prerequisites and corequisites
Not applicable
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Professional Internship
Professional Internship
Não
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Syllabus
Syllabus
Chap.1 Integral calculus. 1. Integral calculus in |R. 1.1. Definition and Properties. Primitive and Undefined integrals. 1.2. Immediate primitives. 1.3. Integration methodologies and their application. 1.4. Integration of certain classes of functions. 1.5. Defined integral: Definition and properties. Geometric meaning. Calculation and applications. 1.6. Integral calculus in | Rn. Fundamental concepts and calculation of multiple integrals. Chap.2 Ordinary Differential Equations. 2.1. Definitions. 2.2. General solutions and particular solutions. Boundary conditions. 2.3. Integration of ordinary differential equations of 1st and 2nd order.
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Objectives
Objectives
Introduce fundamental concepts and practices of mathematical calculation and analysis that enable the student to: Understand the concepts of primitivation and know how to perform the integration of real functions of a real variable by immediate primitivation, substitution and parts. Understand the concept and know how to calculate a definite integral and interpret its result geometrically. Know how to perform typical applications of the definite integral. Calculate multiple integrals. Solve differential equations of 1st. and 2nd. including the determination of particular solutions.
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Teaching methodologies and assessment
Teaching methodologies and assessment
B-Learning teaching model, with a hybrid of synchronous remote classes (7 weeks) and face-to-face classes (8 weeks). Use of Moodle as learning support platform. Problem Based Learnig (PBL). Assessment model includes valuing class participation and weekly work outside of class (small homework assignments), to encourage continued dedication to the course. Support for students outside of class.
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References
References
Piskounov, N. Cálculo Integral e Diferencial (Vol.I e II). Editora Lopes da Silva (there are other editions). Demidovitch, B. Problemas e Exercícios de Análise Matemática. Escolar Editora (there are other editions). Textos didáticos / Teaching texts: Artur Fernandes Costa (2020). Alguns elementos sobre Cálculo Integral em |R - Integrais Indefinidos e Definidos (33 p.). Artur Fernandes Costa (2020). Alguns elementos sobre Cálculo Integral em |Rn - Integrais Múltiplos (16 p.). Artur Fernandes Costa (2013). Equações diferenciais 1 (manuscrito, 22 p.). Artur Fernandes Costa (2013). Equações diferenciais 2 (manuscrito, 21 p.). Outros fornecidos ao longo das aulas pelos docentes / Others provided during classes by teachers.
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Office Hours
Office Hours
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Mobility
Mobility
No
