Mathematical Analysis II

Recommended Prerequisites

Mathematical Analysis 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

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

1. Compute limits of sequences and series;

2. Determine the convergence interval of a power series;

3. Compute the Taylor polynomial and the Taylor series of a function.

4. Compute the Fourier series of a periodic function.

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

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

7. Solve a constrained extrema problem.                             

Work Placement(s)

No

Syllabus

I. Series

I.1 Sequences and number series

I.2 Convergence criteria

I.3 Power series (Taylor formula and Tayor series)

I.4 Fourier Series

 

II. Real functions of several variables

II.1 Limits and continuity

II.2 Partial derivatives

II.3 Differentiability

II.4 Chain rule

II.5 Directional derivatives.

II.6 Maxima and minima. Lagrange Multipliers.   

Head Lecturer(s)

Susana Margarida Pereira da Silva Domingues de Moura

Assessment Methods

Continuous assessment
2 or more midterm exams: 100.0%

Final assessment
Course assessment can also be made by exam as an alternative to the midterm exams assessment: 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] Ana d'Azevedo Breda, Joana Nunes da Costa: Cálculo com funções de várias variáveis. McGraw-Hill, Lisboa (1996).

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

[5] Spiegel, M. (1977) –  Análise de Fourier, Colecção Schaum.