Complex Functions Theory c-12

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155 pages
In this book you find the basic mathematics that is needed by engineers and university students .
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A propos de l'auteur

Leif Mejlbro was educated as a mathematician at the University of Copenhagen, where he wrote his thesis on Linear Partial Differential Operators and Distributions. Shortly after he obtained a position at the Technical University of Denmark, where he remained until h...


In this book you find the basic mathematics that is needed by engineers and university students . The author will help you to understand the meaning and function of mathematical concepts. The best way to learn it, is by doing it, the exercises in this book will help you do just that.

Topics as Elementary complex functions, calculus of residua and its application to e.g. integration are illustrated.

This book requires knowledge of Calculus 1 and Calculus 2.

  1. Special Functions
    1. The Gamma Function
    2. The Beta function
    3. The sine and cosine and exponential integrals
    4. The error function
    5. The Bessel functions
  2. Applications
    1. Linear ordinary differential equations
    2. Linear systems of ordinary differential equations
    3. Linear partial differential equations
    4. The Dirac measure
    5. The z transformation
  3. Extension of the inversion formula
    1. The inversion formula for analytic functions with branch cuts
    2. The inversion formula for functions with infinitely many singularities
  4. Appendices
    1. Trigonometric formulæ
    2. Integration of trigonometric polynomials
    3. Tables of some Laplace transforms and Fourier transforms
  5. Index