Syllabus |
1.1. Limited sets. Maximum, mínimum, supremum infimum. 1.2 topological notions. 1.2 Generalities on functions 2. Real functions of a real variable: limits and continuity 2.1 Examples of functions: exponential and logarithmic; trigonometric and respective inverses; hyperbolic functions 2.2 Limits 2.3 Continuous Functions 3. Differential calculus in R 3.1 Definition of derivative and examples 3.2 Derivation rules 3.3 Theorems of Rolle, Lagrange, and Cauchy 3.4 Higher order derivatives and Taylor formula 3.5 Applications to the computation of limits 3.6 Extremes, concavity asymptotes 4. Integral calculus in R 4.1 Integral of Riemann 4.2 Fundamental Theorem of Integral Calculus 4.3 Immediate Primitives 4.4 primitives of rational functions 4.5 Primitive by parts and by substitution; 4.6 Geometric Applications of the integral calculus
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Main Bibliography |
Main bibliography:
– James Stewart, Cálculo, volume I, 7.ª Edição, Cengage Learning, 2013
Secondary Bibliography:
- 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 – Swokowski, E. W., Cálculo com Geometria Analítica, Vol. 1 e 2, McGrawHill, 1983
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