Fourier Series and Systems of Differential...
Publisher: Bookboon.com
Published: 2013
ISBN-13: 9788776812423
Table of contents: title: Content; title: 1. Review of some important trigonometric formulæ; title: 1.1. Trigonometric formulæ; title: 1.2. Integration of trigonometric polynomials; title: 2. Fourier series; methods of calculation; title: 2.1. General; title: 2.2. Standard procedure; title: 2.3. Standard Fourier series; title: 2.4. The square function; title: 2.5. The identical function in ] - p ; p [; title: 2.6. The first sawtooth function; title: 2.7. The second sawtooth function; title: 2.8. Expansion of cosine in a sinus series over a half period; title: 2.9. Symmetric parabolic arc in [- p ; p]; title: 2.20. Hyperbolic cosine in [- p ; p]; title: 2.11. Exponential function over ] - p ; p ]; title: 3. A list of problems in the Theory of Fourier series; title: 3.1. A piecewise constant function; title: 3.2. Piecewise linear functions; title: 3.3. A piecewise polynomial of second degree; title: 3.4. A piecewise polynomial of third degree; title: 3.5. A piecewise polynomial of fourth degree; title: 3.6. Piecewise sinus; title: 3.7. Piecewise cosine; title: 3.8. Mixed sinus and cosine; title: 3.9. A piecewise polynomial times a trigonometric function; title: 3.10. The exponential function occurs; title: 3.11. The problem of the assumption of no vertical half tangent; title: 4. Systems of linear dierential equations; methods; title: 4.1. The Existence and Uniqueness Theorem; title: 4.2. Constant system matrix A; title: 4.3. Eigenvalue method, real eigenvalues, A a constant (2 x 2)-matrix; title: 4.4. The eigenvalue method, complex conjugated eigenvalues, comples calculations; title: 4.5. The eigenvalue method, complex conjugated eigenvalues, real calculations; title: 4.6. Direct determination of the exponential matrix exp(At); title: 4.7. The fumbling method; title: 4.8. Solution of an inhomogeneous linear system of dierential equations; title: 5. The eigenvalue problem of dierential equations; title: 5.1. Constant coecients; title: 5.2. Special case; the guessing method; title: 5.3. The initial value problem; title: 5.4. The boundary value problem; title: 5.5. The eigenvalue problem; title: 5.6. Examples; title: 6. Formulæ; title: 6.1. Squares etc.; title: 6.2. Powers etc.; title: 6.3. Differentiation; title: 6.4. Special derivatives; title: 6.5. Integration; title: 6.6. Special antiderivatives; title: 6.7. Trigonometric formulæ; title: 6.8. Hyperbolic formulæ; title: 6.9. Complex transformation formulæ; title: 6.10. Taylor expansions; title: 6.11. Magnitudes of functions