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 61066 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 62669 Fourier series over any range 630
69.1 Expansion of a periodic function of
periodL 630
69.2 Half-range Fourier series for functions
defined over rangeL 63470 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 653Revision Test 19 658Essential formulae 659
Index 675