Fourier Series and Systems of Differential...
Publisher: Bookboon
Published: 2013
ISBN-13: 9788776812423
Table of contents: title: Review of some important trigonometric formulæ; title: Trigonometric formulæ; title: Integration of trigonometric polynomials; title: Fourier series; methods of calculation; title: General; title: Standard procedure; title: Standard Fourier series; title: The square function; title: The identical function in ] - p ; p [; title: The first sawtooth function; title: The second sawtooth function; title: Expansion of cosine in a sinus series over a half period; title: Symmetric parabolic arc in [- p ; p]; title: Hyperbolic cosine in [- p ; p]; title: Exponential function over ] - p ; p ]; title: A list of problems in the Theory of Fourier series; title: A piecewise constant function; title: Piecewise linear functions; title: A piecewise polynomial of second degree; title: A piecewise polynomial of third degree; title: A piecewise polynomial of fourth degree; title: Piecewise sinus; title: Piecewise cosine; title: Mixed sinus and cosine; title: A piecewise polynomial times a trigonometric function; title: The exponential function occurs; title: The problem of the assumption of no vertical half tangent; title: Systems of linear dierential equations; methods; title: The Existence and Uniqueness Theorem; title: Constant system matrix A; title: Eigenvalue method, real eigenvalues, A a constant (2 x 2)-matrix; title: The eigenvalue method, complex conjugated eigenvalues, comples calculations; title: The eigenvalue method, complex conjugated eigenvalues, real calculations; title: Direct determination of the exponential matrix exp(At); title: The fumbling method; title: Solution of an inhomogeneous linear system of dierential equations; title: The eigenvalue problem of dierential equations; title: Constant coecients; title: Special case; the guessing method; title: The initial value problem; title: The boundary value problem; title: The eigenvalue problem; title: Examples; 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