# General Mathematics

## Objectives

To provide the basis for some working knowledge of mathematical techniques (in the Linear Algebra and Analysis domains).

## General characterization

##### Code

10692

##### Credits

6.0

##### Responsible teacher

Paula Cristiana Costa Garcia Silva Patrício

##### Hours

Weekly - 5

Total - 72

##### Teaching language

Português

### Prerequisites

The student must be familiar with mathematics taught at pre-university level in Portugal (science area).

### Bibliography

Cap. 1: S. Lang. A first course in Calculus. Springer-Verlag, 1986, ISBN 0-387-96201-8

Cap. 2: M. Braun. Differential Equations and their applications (4th edition). Springer-Verlag, 1993, ISBN 0-387-97894-1

Cap. 3: H. Anton, C. Rorres. Elementary linear algebra Applications version (7th ed.). Wiley,1994, ISBN 0-471-30570-7

### Teaching method

In this course there are lectures (3 hours weekly) and practical classes (3 hours weekly).

Students have, in advance, at their disposal a guide with all the theoretical and practical notes for classes. The practical notes consist on two separate lists of problems, one to be almost entirely solved during classes, and the other one intended for the student’s autonomous work.

There is also some office hours where each student can individually talk to and/or seek help from any teacher of the discipline.

### Evaluation method

Conditions for evaluation admittance:

• for freshmen student - maximum of 3 unjustified absences to classes;

• for other students - maximum of 8 unjustified absences to classes.

Evaluation can be done through tests during classes period, or by final exam.

More details available in the portuguese version.

## Subject matter

1. Integration

- Primitives
- Integral calculus

2. Differential equations

- Separable equations
- First order linear equations
- Second order linear equations with constant coefficients

3. Matrices

- Operations with Matrices
- Systems of Linear Equations
- Determinants
- Eigenvalues and eigenvectors