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RESIDUE.MTH: SOLVING PROBLEMS OF INTEGRATION USING THE RESIDUE THEOREM

RESIDUE.MTH: SOLVING PROBLEMS OF INTEGRATION USING THE RESIDUE THEOREM. Montreal International Symposium on Technology and its Integration in to Mathematics Education “TIME-2004” Montreal, Canada, July 15-18, 2004. José Luis Galán García Dpt. Applied Mathematic University of Málaga.

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RESIDUE.MTH: SOLVING PROBLEMS OF INTEGRATION USING THE RESIDUE THEOREM

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  1. 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 José Luis Galán García Dpt. Applied Mathematic University of Málaga Mª Ángeles Galán García Dpt. Computing Science Umeå University (Sweden) Yolanda Padilla Domínguez Dpt. Applied Mathematic University of Málaga Pedro Rodríguez Cielos Dpt. Applied Mathematic University of Málaga

  2. 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

  3. 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

  4. Content of RESIDUE.MTH The macros contained in the file can be grouped within the following blocks: • 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)

  5. 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

  6. 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 José Luis Galán García Dpt. Applied Mathematic University of Málaga Mª Ángeles Galán García Dpt. Computing Science Umeå University (Sweden) Yolanda Padilla Domínguez Dpt. Applied Mathematic University of Málaga Pedro Rodríguez Cielos Dpt. Applied Mathematic University of Málaga

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