Calculus II
1
2019-2020
01001890
Basic Sciences
Portuguese
Face-to-face
SEMESTRIAL
6.0
Compulsory
1st Cycle Studies
Recommended Prerequisites
Calculus I.
Teaching Methods
The theoretical lectures are predominantly expository. It will prevail a strong interaction between concepts and their practical application, giving a central role to visualization and analysis of particular situations before making an approach to more abstract notions. The transformation of concepts into working tools will be achieved by encouraging personal work. In practical classes the students will solve exercises under the guidance of the instructor and they will be encouraged to solve problems independently. The formal lectures will be complemented by periods of individual attendance.
Learning Outcomes
Provide knowledge about differential calculus of real-valued functions of several variables and integral calculus of real-valued functions of two and three variables. Throughout the course, students must develop computational skills and acquire an understanding of the concepts that will enable them to evaluate the scope and limitations of the studied materials, as well as their applications.
Work Placement(s)
NoSyllabus
Real functions of several variables – differential calculus
• Limits and continuity
• Partial derivatives
• Differentiability
• Chain rule
• Directional derivatives. Gradient
• Implicit function theorem
• Maxima and minima. Lagrange Multipliers
Integral calculus in R2 and R3
• Double integrals and applications
• Triple integrals and applications
• Change of variables in double and triple integrals.
Head Lecturer(s)
Gonçalo Gutierres da Conceição
Assessment Methods
Continuous assessment
Midterm exam (0-100%); Test (0-50%); Problem solving report (0-50%): 100.0%
Final assessment
Exam: 100.0%
Bibliography
- J. Stewart, Cálculo , 4ª ed., Vol 1 e Vol.2, Pioneira, São Paulo, 2001.
- Earl W. Swokowski, Cálculo com geometria analítica Vol I e Vol II, São Paulo, McGraw-Hill, 1983.
- J. Campos Ferreira, Introdução à Análise Matemática, Fund. Calouste Gulbkenkian,1993.
- A. Breda e J. Costa, Cálculo com funções de várias variáveis, McGraw-Hill, Lisboa, 1996