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Presentation
Presentation
Introduction and exploration of basic concepts of Mathematics.
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Class from course
Class from course
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Degree | Semesters | ECTS
Degree | Semesters | ECTS
Bachelor | Semestral | 6
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Year | Nature | Language
Year | Nature | Language
1 | Mandatory | Português
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Code
Code
ULP452-6
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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
Revisions on set of numbers and geometry in the plane.
Succession.
Limited succession monotonous, convergent. Arithmetic and geometric progressions.
Real functions of a real variable.
Function graphs. Properties of the main functions. Limits. Complete study of functions.
Differential calculus in IR.
Definition and intuitive notion of derivative. Derivation rules. Derivatives of the main functions. Derivative of composite and inverse functions. Derivatives of higher than first order. Applications: maximum, minimum research and inflection points. Cauchy rules and L'Hôpital.
Differential calculus in IRn.
Domains. Partial derivatives. Gradient. Derived directional. Total differential. Derivatives of composite functions and implicit functions. Search free and conditioned extremes.
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Objectives
Objectives
It is intended that the students revisit and deepen their knowledge of property and of operations of successions and real functions of real variable, as well as differentiation and its applications. Based on this knowledge, the objective is that the student learns to operate and differentiate in IRn.
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Teaching methodologies and assessment
Teaching methodologies and assessment
Whenever appropriate, the methodologies to support the teaching-learning process are student – centred as well as in the development of their autonomy. In this context, students will often be encouraged to carry out a set of practical exercises.
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References
References
Demidovitch, B. (2010) Problemas e Exercícios de Análise Matemática, McGraw-Hill.
Azenha, A. & Jerónimo, M. A. (1995). Elementos de cálculo diferencial e integral em IR e IRn. Brasil: Mc-Graw Hill.
Apostol, T. M (2004). Calculus (volume 2). Editorial Reverté.
N. Piskounov, Cálculo Integral e Diferencial (Vol.I e II), Editora Lopes da Silva, 1974.
Larson, R., e Edwards, B. (2018). Calculus of a single variable (11th edition). Cengage Learning.
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Office Hours
Office Hours
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Mobility
Mobility
No
