Real Functions in One Variable
Publisher: Bookboon
Published: 2013
ISBN-13: 9788776811174
Table of contents: title: Sisältö; title: Complex Numbers; title: Introduction; title: Definition; title: Rectangular description in the Euclidean plane; title: Description of complex numbers in polar coordinates; title: Algebraic operations in rectangular coordinates; title: The complex exponential function; title: Algebraic operations in polar coordinates; title: Roots in polynomials; title: The Elementary Functions; title: Introduction; title: Inverse functions; title: Logarithms and exponentials; title: Power functions; title: Trigonometric functions; title: Hyperbolic functions; title: Area functions; title: Arcus functions; title: Magnitude of functions; title: Differentiation; title: Introduction; title: Definition and geometrical interpretation; title: A catalogue of known derivatives; title: The simple rules of calculation; title: Differentiation of composite functions; title: Differentiation of an implicit given function; title: Differentiation of an inverse function; title: Integration; title: Introduction; title: A catalogue of standard antiderivatives; title: Simple rules of integration; title: Integration by substitution; title: Complex decomposition of fractions of polynomials; title: Integration of a fraction of two polynomials; title: Integration of trigonometric polynomials; title: Simple Differential Equations; title: Introduction; title: Differential equations which can be solved by separation; title: The linear differential equation of first order; title: Linear differential equations of constant coefficients; title: Euler’s differential equation; title: Linear differential equations of second order with variable coefficients; title: Approximations of Functions; title: Introduction; title: e - functions; title: Taylor’s formula; title: Taylor expansions of standard functions; title: Limits; title: Asymptotes; title: Approximations of integrals; title: Miscellaneous applications; title: Formulæ; title: Squares etc.; title: Powers etc.; title: Differentiation; title: Special derivatives; title: Integration; title: Special antiderivatives; title: Trigonometric formulæ; title: Hyperbolic formulæ; title: Complex transformation formulæ; title: Taylor expansions; title: Magnitudes of functions