Cálculo II

Mathematics and Calculus I.

In theoretical classes, a theoretical exposition of each subject is made, which is complemented in the theoretical-practical classes by the study of practical examples and by solving exercises to apply the knowledge acquired. The practical-laboratory classes are taught, if possible, in a computer room to deal with the subjects using MATLAB software – the use of software will allow a deepening of the concepts and a better understanding by the student, allowing solving  more complexes problems.

Understand and apply the basic concepts of differentiation and integration of functions with several variables. Find the derivatives and integrals of functions with several variables. Understand and apply the basic concepts of vector analysis. Recognize the importance of the material taught in the area of biomedical engineering. Use the MATLAB software in the numerical treatment of the subjects and compare, with criticism, the results obtained by computational means with the ones obtained analytically. Base problem solving on mathematics. Select appropriately the available information (from monographs, textbooks, internet, …). Expose the problems’ solution in a clear and simple way. Show interest and autonomy in teamwork.

1. Ordinary differential equations
1.1. Introdution and motivation
1.2. First order differential equations
1.3. First order linear equation
1.4. Bernoulli’s equation
1.5. Separable variable equation
1.6. Zero degree homogeneous equation
2. Functions with several variables and their derivatives
2.1. Conics and quadrics
2.2. Domain
2.3. Level curves and graphic
2.4. Limits and continuity
2.5. Partial derivatives
2.6. Differentiability
2.7. Directional derivative and the gradient vector
2.8. Maximum and minimum values
2.9. Using the MATLAB in the treatment of functions with two variables.
3. Multiple Integrals
3.1. Double Integrals: Definition; Properties; Geometric meaning; Evaluation and Applications
3.2. Triple Integrals: Definition; Properties; Geometric meaning; Evaluation and Applications.
4. Vector Analysis
4.1. Parametric coordinates
4.2. Line integrals and applications
4.3. Vector fields
4.4. Rotational and divergent.

NAO

•  Howard Anton. (1999). Cálculo um novo horizonte (Volume 2). Bookman.
• João R. Cardoso. (2013). Apontamentos de apoio às aulas de Cálculo II. DFM, ISEC.
• João R. Cardoso. (2013). Atividades de apoio às aulas de MATLAB. DFM, ISEC.
• Rodrigues, R. (2020). Notas teóricas e exercícios de Análise Matemática. DFM, ISEC
• Finney, Weir e Giordano. (2003). Cálculo (Volume 2). Addison Wesley.
• Larson, Hostetler, Edwards. (2006). Cálculo (Volume 2). 8ªEd. McGrawHill.
• James Stewart. (2008). Calculus – Early Transcendentals. 6ªEd. Thomson