Calculus II

Objectives

The Integral Calculus, due to its numerous applications, is one of the key chapters in any degree in Mathematics, Engineering or Computer Science. These applications from the evaluation of areas, through the calculation of volumes of solids, lengths of curves etc., are the key to solve many of the problems that arise daily.

The Differential Calculus for functions of several variables plays a very important role in mathematics. Beyond its informative function, providing students with basic knowledge, it also has a formative function. Introduces the student to the accuracy of mathematical argumentation, construction of proofs, and their applications to various areas. In applications, it is undoubtedly the calculation of extremes of a function, subject to several conditions, that the differential calculus reaches its peak on this curricular unit.

Program

Integral Calculus: Primitives and integrals (by parts and substitution). Primitives of rational functions. Applying integrals to evaluate areas, volumes of solids and lengths of curves Numerical integration.

Introduction to Differential Equations: Differential equation of variables separable. Homogeneous and nonhomogeneous differential equations. The logistic equation.

Differential calculus for functions with several variables: Domains, limit and continuity. Partial derivatives. Chain rule. Directional derivative and gradient. Tangent planes. Second-derivative test for extrema of functions of two variables. Extrema with constraints: Lagrange´s multipliers.

Teaching Methodologies

The topics of this course are presented in lectures, both using the blackboard and computer presentations. Practical classes aim at solving exercises, promoting teacher/student interaction.

Course materials are made available through the Moodle e-learning platform, boosting up asynchronous activities.

Bibliography

Nilo Kühlkamp , Cálculo I, Ed. da UFSC, 2006.

Earl W. Swokowski , Cálculo com geometria analítica, McGraw-Hill, 1983.

Wilfred Kaplan, Cálculo avançado, Edgard Blücher, 1975.

Barroso, Leônidas Conceição, Cálculo numérico com aplicaçöes, Ed. Harbra, Säo Paulo, 1987.

Apostol,T., Calculus, Vol 1, John Wiley and Sons, New York, 1976.

Swokowski, E. W., Cálculo com Geometria Analítica, McGraw-Hill, 1983.

Demidovitch B. ,Problemas e Exercícios de Matemática, Mir, 1986.

Piskounov, N. Cálculo Diferencial e Integral, Vol.I e II, Lopes da Silva Editora, 1988.

Howard Anton, Cálculo um novo horizonte, vol. 1, 6ª Edição, Kookman, 2000.

James Stewart, Cálculo, vol. 1, 5ª Edição, Thomson, 2008.

Apontamentos dos docentes/Teachers' notes.