文档介绍：Leif Mejlbro
Calculus 4b
Fourier series and Systems of Differential
Equations and Eigenvalue problems
Guidelines for Solutions of Problems
Studentensupport
Calculus 4b – Fourier series and Systems of Differential Equations and
Eigenvalue problems – Guidelines for Solutions of Problems
© 2007 Leif Mejlbro & Studentensupport
Kostenloser Download unter
ISBN 978-87-7681-242-3
Studentensupport
Calculus 4b Contents
Contents
Preface 6
1 Review of some important trigonometric formulæ 7
Trigonometric formulæ 7
Integration of trigonometric polynomials 7
2 Fourier series; methods of calculation 11
General 11
Standard procedure 14
Standard Fourier series 18
The square function 18
The identical function in ] - π; π[ 19
The fi rst sawtooth function 19
The second sawtooth function 21
Expansion of cosine in a sinus series over a half period 22
Symmetric parabolic arc in [- π; π] 23
Hyperbolic cosine in [- π; π] 23
Exponential function over ] - π; π] 25
3 A list of problems in the Theory of Fourier series 27
A piecewise constant function 27
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