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Presentation
Presentation
Master the main basic with complex numbers. Understand the concept of real number serie. To allow a greater knowledge about the concepts of limit, continuity, derivative, primitive and integral and the relation between these concepts. Acquisition of competences to use differential and integral calculus in solving diverse problems.
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Class from course
Class from course
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Degree | Semesters | ECTS
Degree | Semesters | ECTS
Bachelor | Semestral | 5
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Year | Nature | Language
Year | Nature | Language
1 | Mandatory | Português
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Code
Code
ULHT2710-2228
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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
Complex numbers.
Sequences of real numbers and infinite sums.
Real functions of real variable.
Composite function.
Reverse function.
Limits and continuity of functions.
Derived from a function.
Geometric interpretation.
Derivation rules.
Cauchy's Rule.
Complete study of functions.
Meaning of primitive.
Primitive techniques.
Definition of integral of Riemann.
Properties of integral.
Criteria for integrability.
The fundamental theorem of integral calculus.
The mean value theorem for definite integrals.
Differential and integral calculus in more than one real variable.
Taylor series
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Objectives
Objectives
Introduction of complex numbers and basic operations with them. Introduction to real series. Real functions of real variable. Composite function. Reverse function. Limits and continuity of functions. Derived from a function. Geometric interpretation. Derivation rules. Derivative of the compound function and the inverse function. Cauchy's Rule. Complete study of functions. Meaning of primitive. Primitivation Techniques. Definition of integral of Riemann. Properties of the integral. Criteria for integrability. Fundamental theorem of integral calculus. The mean value theorem for definite integrals. Application of differential and integral calculus to more than one real variable. Representation of functions using Taylor series.
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Teaching methodologies and assessment
Teaching methodologies and assessment
The presentation of the material is carried out in the active participation of the students. Concrete examples are presented and the students and invited to analyze the concepts involved in the examples. In the theoretical-practical classes, students analyze and solve problems involving the concepts presented in class. Students are encouraged to try various resolution strategies.
Continuous assessment: two frequencies to be carried out during the semester, the first with a weighting of 40% and the second of 50% (there is no minimum mark in each frequency) and a participation component with a weighting of 10%. Students who obtain an average of 9.5 or higher are considered approved. Both frequencies can be replaced by a single test at the end of the semester with a weight of 90% of the final grade.
Assessment by exam: Students who obtain a grade of 9.5 or higher in the exam will be approved.
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References
References
- Apostol, T.M. (2004). Cálculo, vol. 1, 2ª ed.; Reverté.
- Larson, R. and Hostetler, R. and Edwards, B. (2006). Cálculo, 8ªEd., McGraw-Hill.
- Howard Anton (1999). Calculus, 9th Edition, John Wiley & Sons.
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Office Hours
Office Hours
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Mobility
Mobility
No
