## Advanced calculusPower series. Partial differentiation. Implicit functions. Applications to geometry. The definite integral. The gamma and beta functions. Line, surface, and space integrals. Vector notation. Differential equations of the first order. Differential equations of higher order. Bessel functions. Partial differential equations. Calculus of variations. Functions of a complex variable. Elliptic integrals. |

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### Contents

PRELIMINARY SECTION PAGE 1 Functions | 1 |

Continuity | 2 |

The derivative | 5 |

Copyright | |

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a)dx absolute value angle approaches a limit approaches zero arbitrary constants assume axis becomes Bessel equation circle coefficients complex numbers consider continuous function convergent series cosh cosine curvilinear coordinates defined definite integral determined dF dF differential equation direction dx dx dx dy dz dy dx elementary elliptic elliptic integral equa equal example expansion Find finite fixed formula given gives Hence independent variable infinite infinitesimal interval Jn(x Laplace's equation length line integral maximum negative normal obtained orthogonal osculating plane partial derivatives path perpendicular polar coordinates polynomial positive number power series prove quantity radius region of convergence result Rolle's theorem satisfy series converges Show singular singular solution sinh solution solved straight line substitute surface tangent plane tion vector w-plane whence