Calculus II

Recommended Prerequisites

Calculus I and Linear Algebra and Analytic Geometry.    

Teaching Methods

The teaching in this course will assume two formats: theoretical and example classes. During a theoretical class teaching is mostly expository. During an example class teaching will consist of problem solving by the students under the guidance of the lecturer. A strong interaction between notions and their practical application is emphasized. In this task, the visualization and the analysis of concrete examples takes on a central role and prepares the way for the abstract definitions. Tutorial support will be available to students to help them on the tasks assigned by the lecturers.

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. The student who successfully completes this course will be able to:

1. Detected non-continuous real functions of two variables at a given point;         

2. Compute the directions of greatest growth of a real function of two variables;

3. Solve a constrained extrema problem;           

4. Compute areas of plane regions and surface graphs using double integration;

5. Compute volumes uding double and triple integrals, as well as the center of mass of a solid (with arbitrary density function);

6. Solve problems involving applications of integration to mathematical modelling.                

Work Placement(s)

No

Syllabus

I. Real functions of several variables

I.1 Limits and continuity

I.2 Partial derivatives

I.3 Differentiability

I.4 Chain rule

I.5 Directional derivatives.

I.6 Maxima and minima. Lagrange Multipliers

 

II. Integral calculus in R2 and R3

II.1 Double integrals and applications

II.2 Triple integrals and applications

II.3 Change of variables in double and triple integrals.   

Head Lecturer(s)

Maria João Rodrigues Ferreira

Assessment Methods

Continuous assessment
2 or more midterm exams: 100.0%

Final assessment
Exam: 100.0%

Bibliography

Stewart, J. Cálculo, Volumes I e II., Cengage Learning, (tradução da 8ª edição norte-americana) 2017

Pires, G. Cálculo diferencial e integral em Rn. IST Press (Colecção Ensino da Ciência e da Tecnologia), 2012.

Breda, A.; Nunes da Costa, J.: Cálculo com funções de várias variáveis. McGraw-Hill, Lisboa, 1996.

Baptista, M.O. Matemática - Integrais Duplos, Triplos, de Linha e de Superfície. Edições Sílabo. (2ª Edição: 2001)

Kreiszig, E. Advanced Engineering Mathematics, Willey (10ª edição: 2014).