Complex Analysis with MATHEMATICA®
eBook - PDF

Complex Analysis with MATHEMATICA®

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

Complex Analysis with MATHEMATICA®

About this book

Complex Analysis with Mathematica offers a way of learning and teaching a subject that lies at the heart of many areas of pure and applied mathematics, physics, engineering and even art. This book offers teachers and students an opportunity to learn about complex numbers in a state-of-the-art computational environment. The innovative approach also offers insights into many areas too often neglected in a student treatment, including complex chaos and mathematical art. Thus readers can also use the book for self-study and for enrichment. The use of Mathematica enables the author to cover several topics that are often absent from a traditional treatment. Students are also led, optionally, into cubic or quartic equations, investigations of symmetric chaos and advanced conformal mapping. A CD is included which contains a live version of the book: in particular all the Mathematica code enables the user to run computer experiments.

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Yes, you can access Complex Analysis with MATHEMATICA® by William T. Shaw in PDF and/or ePUB format, as well as other popular books in Mathematics & Mathematical Analysis. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Cover
  2. Complex Analysis with Mathematica
  3. Title
  4. Copyright
  5. Dedication
  6. Contents
  7. Preface
  8. 1 Why you need complex numbers
  9. 2 Complex algebra and geometry
  10. 3 Cubics, quartics and visualization of complex roots
  11. 4 Newton–Raphson iteration and complex fractals
  12. 5 A complex view of the real logistic map
  13. 6 The Mandelbrot set
  14. 7 Symmetric chaos in the complex plane
  15. 8 Complex functions
  16. 9 Sequences, series and power series
  17. 10 Complex differentiation
  18. 11 Paths and complex integration
  19. 12 Cauchy's theorem
  20. 13 Cauchy's integral formula and its remarkable consequences
  21. 14 Laurent series, zeroes, singularities and residues
  22. 15 Residue calculus: integration, summation and the argument principle
  23. 16 Conformal mapping I: simple mappings and Möbius transforms
  24. 17 Fourier transforms
  25. 18 Laplace transforms
  26. 19 Elementary applications to two-dimensional physics
  27. 20 Numerical transform techniques
  28. 21 Conformal mapping II: the Schwarz–Christoffel mapping
  29. 22 Tiling the Euclidean and hyperbolic planes
  30. 23 Physics in three and four dimensions I
  31. 24 Physics in three and four dimensions II
  32. Bibliography
  33. Index