Calculus II

Code	14894
Year	1
Semester	S2
ECTS Credits	6
Workload	TP(60H)
Scientific area	Mathematics
Entry requirements	There is no entry requirement.
Mode of delivery	Presential classes
Work placements	Not applicable
Learning outcomes	With this Curricular Unit it is intended that students acquire basic knowledge of Differential and Integral Calculus of functions of several variables. At the end of this UC the student should be able to: 1) Calculate limits of functions of several variables; 2) Study the continuity of functions of several variables; 3) Derive functions of several variables; 4) Apply the derivatives to the calculation of maximums and minimums; 5) Integrate functions of several variables; 6) Use integral calculus to determine areas and volumes. 7) Formulate and solve problems using the differential and integral calculus of functions with several variables
Syllabus	1 Real Functions of Several Variables 1.1 Introduction 1.1.1 Algebraic notions 1.1.2 Sets in R^2 and R^3 1.2 Topological notions in R^n 1.3 Functions, Scalar and Vector Fields 1.4 Limits 1.5 Continuity 1.6 1st Order Partial Derivatives 1.7 Differentiability 1.8 Tangent Plane. Linearization 1.9 Directional Derivative 1.10 Higher Order Derivatives. Schwarz's theorem 1.11 Derivative of the Composite Function. Implicit Function 1.12 Free and Conditioned Extremes 2 Integral Calculus in R^n 2.1 Double Integral 2.2 Triple Integral 2.3 Change of variable
Main Bibliography	Alberto Simões, Apontamentos de Cálculo II, UBI. Stewart, James, "Cálculo", Volume II, 5ª edição Thomson Learning, 2001. Lang, S., "Calculus of Several Variables", Undergraduate Texts in Mathematics, Third Edition, Springer-Verlag,1987. Apostol,T.M., "Calculus",Volume II, John Wiley & Sons, 1968. J. Marsden e A. Tromba, Vector Calculus, W H Freeman & Co., 2003. Jaime Carvalho e Silva, Princípios de Análise Matemática Aplicada, Mc Graw Hill, 1999. Cálculo diferencial e integral, vol. I e vol. II, N. Piskounov, Lopes da Silva, 1987. Robert A. Adams, Calculus: A Complete Course, Addison-Wesley, 2006. H. Anton, I. Bivens e S. Davis, Calculus, (Eight Edition), John Wiley & Sons, 2006.
Teaching Methodologies and Assessment Criteria	During the teaching-learning period, the evaluation will be periodic and will consist of 2 tests to be carried out on April 28 and June 9, each with a quotation of 10 values. A student will pass if the sum of the test scores has a rating greater than or equal to 9.5. Whenever the final classification is greater than or equal to 17 values, a defense will be held, in any case a minimum grade of 16 values ??will be assured. If, in the event of a defense, the student does not appear, he/she will have a final grade equal to 16 values. All students are admitted to the exam.
Language	Portuguese. Tutorial support is available in English.