Mathematical Analysis II

Recommended Prerequisites

Mathematical Analysis I and Linear Algebra and Analytic Geometry.

Teaching Methods

The teaching in this course assumes two formats: theoretical and example classes. During a theoretical class teaching is mostly expository. During an example class teaching consists of problem solving by the students under the guidance of the lecturer. A strong interaction between notions and their practical application is emphasised. 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 is available to students to help them on the tasks assigned by the lecturers.

Learning Outcomes

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

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

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

3. Solve problems involving applications of integration to mathematical modelling;

4. Solve a separable differential equation;         

5. Solve linear differential equations;

6. Solve systems of linear equations with constant coefficients. 

Work Placement(s)

No

Syllabus

I. Integral calculus in R2 and R3

I.1 Double integrals and applications

I.2 Triple integrals and applications

I.3 Change of variables in double and triple integrals 

I.4 Line integrals. Green's Theorem

I.5 Surface integrals. Stoke's and divergence theorems

II. Linear Differential Equations

II.1 First order differential equations: the separable case and the linear case

II.1 Annihilator, reduction of order, and variation of parameters methods

II2. Systems of linear differential equations with constant parameters.

Head Lecturer(s)

Maria Elisabete Felix Barreiro

Assessment Methods

Continuous assessment
2 or more midterm exams: 100.0%

Final assessment
Exam: 100.0%

Bibliography

[1] James Stewart: Cálculo, Volumes I e II., Cengage Learning, (tradução da 8ª edição norte-americana) 2017

[2] Gabriel E. Pires: Cálculo diferencial e integral em Rn. IST Press (Colecção Ensino da Ciência e da Tecnologia), 2012.

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

[4] Erwin Kreiszig: Advanced Engineering Mathematics, Willey (10ª edição: 2014). 

[5] Dennis G. Zill: Equações Diferenciais com aplicações em modelagem. Cengage Learning (tradução da 10ª edição norte-americana), 2016.