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# Calculus I

 Code 15962 Year 1 Semester S1 ECTS Credits 6 Workload TP(60H) Scientific area Mathematics Entry requirements - Learning outcomes With this Curricular Unit it is intended that students acquire basic knowledge of Differential and Integral Calculus of real functions of real variable. At the end of this Curricular Unit the student should be able to:1) Compute limits of real functions of real variable;2) Study the continuity of real functions of real variable;3) Compute derivatives of real functions of real variable;4) Apply the derivatives to the computation of maxima and minima of real functions of real variable;5) Compute primitives and integrals of real functions of real variable;6) Use integral calculus to determine areas and volumes of surfaces generated by revolution, as well as length of plain curves. Syllabus 1.1. Limited sets. Maximum, mínimum, supremum infimum.1.2 topological notions.1.2 Generalities on functions2. Real functions of a real variable: limits and continuity2.1 Examples of functions: exponential and logarithmic; trigonometric and respective inverses; hyperbolic functions2.2 Limits2.3 Continuous Functions3. Differential calculus in R3.1 Definition of derivative and examples3.2 Derivation rules3.3 Theorems of Rolle, Lagrange, and Cauchy3.4 Higher order derivatives and Taylor formula3.5 Applications to the computation of limits3.6 Extremes, concavity asymptotes4. Integral calculus in R4.1 Integral of Riemann4.2 Fundamental Theorem of Integral Calculus4.3 Immediate Primitives4.4 primitives of rational functions4.5 Primitive by parts and by substitution;4.6 Geometric Applications of the integral calculus Main Bibliography – James Stewart, Cálculo, volume I, 7.ª Edição, Cengage Learning, 2013Bibliografia Secundária: - Apostol, T.M., Cálculo, Vol. 1, Reverté, 1993- H. Anton, I. Bivens, S. Davis, Cálculo, volume I, 8.ª Edição, Bookman, 2007– Demidovitch, B., Problemas e exercícios de Análise Matemática, McGrawHill, 1977 - João Paulo Santos, Cálculo numa Variável Real, IST Press, 2012– Mann, W. R., Taylor, A. E., Advanced Calculus, John Wiley and Sons, 1983– Sarrico, C., Análise Matemática – Leituras e exercícios, Gradiva, 3.ª Edição, 1999 Teaching Methodologies and Assessment Criteria The classes will be theoretical-practical. The teacher presents the concepts and the results and illustrates the theory with examples and applications. The student is encouraged to participate in classes, interacting with the teacher and sometimes solving exercises and problems. Autonomous work, consisting mainly in solving the exercises, is encouraged. Language Portuguese. Tutorial support is available in English.

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Industrial Chemistry
Last updated on: 2024-01-10

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