RESIDUE.MTH: SOLVING PROBLEMS OF

INTEGRATION USING THE RESIDUE THEOREM

Montreal International Symposium on Technology and its Integration into Mathematics Education

“TIME-2004”

Montreal, Canada, July 15-18, 2004

Yolanda Padilla Domínguez

Dpt. Applied Mathematic

University of Málaga

Pedro Rodríguez Cielos

Dpt. Applied Mathematic

University of Málaga

José Luis Galán García

Dpt. Applied Mathematic

University of Málaga

Mª Ángeles Galán García

Dpt. Computing Science

Umeå University (Sweden)

INTRODUCTION The use of computer as a tool to support

teaching has been extended in University, especially in practical subjects

The choice of the program to be used is one of the most important matters

For the practical exercises with computer we develop in Engineering, among the great amount of mathematical software available, we have chosen Derive mainly due to its easiness of use in front of other mathematical software

INTRODUCTION The elaboration of application files is very useful

when solving specific problems because we can solve these problems easier than using the standard functions of Derive

In this paper we present the file RESIDUE.MTH, created for being used in subjects that deal with complex variable, aimed at Engineering students. Such file contains a series of macros that allow to solve some typical problems related to applications of the Residue Theorem

Content of RESIDUE.MTH

Compute of residues

Complex integrals using the residue theorem

Improper integrals of a rational function

Improper integrals of the form p(x)/q(x)sin(kx) or p(x)/q(x)cos(kx)

The macros contained in the file can be grouped within the following blocks:

We prefer to use large names for macros instead of using shorthands because we think it is easier for pupils to remember the full name and, on the other hand, the large name of the macro allows to guess what it solves

RESIDUE.MTH: SOLVING PROBLEMS OF

INTEGRATION USING THE RESIDUE THEOREM

Montreal International Symposium on Technology and its Integration into Mathematics Education

“TIME-2004”

Montreal, Canada, July 15-18, 2004

Yolanda Padilla Domínguez

Dpt. Applied Mathematic

University of Málaga

Pedro Rodríguez Cielos

Dpt. Applied Mathematic

University of Málaga

José Luis Galán García

Dpt. Applied Mathematic

University of Málaga

Mª Ángeles Galán García

Dpt. Computing Science

Umeå University (Sweden)