Contents xi
65 The solution of simultaneous differential
equations using Laplace transforms
605
65.1 Introduction
605
65.2 Procedure to solve simultaneous
differential equations using Laplace
transforms
605
65.3 Worked problems on solving simultaneous
differential equations by using Laplace
transforms
605
Revision Test 18
610
66 Fourier series for periodic functions of
period 2π
611
66.1 Introduction
611
66.2 Periodic functions
611
66.3 Fourier series
611
66.4 Worked problems on Fourier series of
periodic functions of period 2π
612
67 Fourier series for a non-periodic function over
range 2π
617
67.1 Expansion of non-periodic functions
617
67.2 Worked problems on Fourier series of
non-periodic functions over a range of 2π 617
68 Even and odd functions and half-range
Fourier series
623
68.1 Even and odd functions
623
68.2 Fourier cosine and Fourier sine series
623
68.3 Half-range Fourier series
626
69 Fourier series over any range
630
69.1 Expansion of a periodic function of
period L
630
69.2 Half-range Fourier series for functions
defined over range L
634
70 A numerical method of harmonic analysis
637
70.1 Introduction
637
70.2 Harmonic analysis on data given in tabular
or graphical form
637
70.3 Complex waveform considerations
641
71 The complex or exponential form of a
Fourier series
644
71.1 Introduction
644
71.2 Exponential or complex notation
644
71.3 The complex coefficients
645
71.4 Symmetry relationships
649
71.5 The frequency spectrum
652
71.6 Phasors
653
Revision Test 19
658
Essential formulae
659
Index
675