## Mathematical methods for scientists and engineers |

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### Contents

Elements of Function Theory | 1 |

Differential Calculus | 14 |

Integral Calculus | 46 |

Copyright | |

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### Common terms and phrases

analytic function angle asymptotic Bessel functions bounded calculus circle coefficients complex numbers complex variable components compute Consequently constant continuous function contour convenient converges coordinates covariant curve defined denoted determinant differential equation domain dx dy element elliptic integrals evaluated example exists expressed in terms formula Fourier Fourier series func function f(x gamma function given Green's theorem independent infinite integral equation integral representation integrand interval inverse Laguerre polynomials Legendre limit line integral mapping function mathematical matrix method multiply obtained orthogonal orthonormal set Paperbound partial derivatives path polygon polynomials positive number potential power series prob quadratic form radius radius of convergence random variables readily real axis region relation result Riemann satisfy shown in Fig solution surface tangent tensor of order theorem theory tion traverses vanish vector velocity written xy plane zero