Comprehensive Mathematics for Computer Scientists 2: Calculus and ODEs, Splines, Probability, Fourier and Wavelet Theory, Fractals and Neural Networks, Categories and Lambda Calculus

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Springer Science & Business Media, Mar 30, 2006 - Computers - 355 pages
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This second volume of a comprehensive tour through mathematical core subjects for computer scientists completes the ?rst volume in two - gards: Part III ?rst adds topology, di?erential, and integral calculus to the t- ics of sets, graphs, algebra, formal logic, machines, and linear geometry, of volume 1. With this spectrum of fundamentals in mathematical e- cation, young professionals should be able to successfully attack more involved subjects, which may be relevant to the computational sciences. In a second regard, the end of part III and part IV add a selection of more advanced topics. In view of the overwhelming variety of mathematical approaches in the computational sciences, any selection, even the most empirical, requires a methodological justi?cation. Our primary criterion has been the search for harmonization and optimization of thematic - versity and logical coherence. This is why we have, for instance, bundled such seemingly distant subjects as recursive constructions, ordinary d- ferential equations, and fractals under the unifying perspective of c- traction theory.
 

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Contents

Topology and Calculus
3
Differentiability
37
Inverse and Implicit Functions 59
58
Integration
73
The Fundamental Theorem of Calculus and Fubinis Theorem
87
Vector Fields 97
96
Fixpoints
105
Main Theorem of ODEs
113
Splines 161
160
Fourier Theory
183
Wavelets
215
Fractals 231
230
Neural Networks
253
Probability Theory 279
278
Lambda Calculus
313
A Further Reading 335
334

Third Advanced Topic
125
Categories
139

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