Higher Engineering Mathematics, Sixth Edition

Index

Adding alternating waveforms, 265
Adjoint of matrix, 239
Algebra, 1–12
Algebraic method of successive
approximations, 81–84
substitution, integration,392–395
Amplitude, 140, 143
Angle between two vectors, 276
of any magnitude, 135–137
of depression, 106–108
of elevation, 106–108
Angular velocity, 129
Applications of complex numbers, 221
differentiation, 299
rates of change, 299–300
small changes, 312–313
tangents and normals, 311–312
turning points, 303–307
velocity and acceleration,
300–303
integration, 375
areas, 375–376
centroids, 380–381
mean value, 377–378
r.m.s. value, 377–378
second moment of area, 383–391
volumes, 378–379
Arc, 122
length, 124
Area of circle, 124
sector, 125
triangle, 108–111
irregular figures, 203–205
under curve, 375–376
Argand diagram, 214
Argument, 219
Arithmetic mean, 541
progression, 51
Astroid, 315
Asymptotes, 190–196
Auxiliary equation, 477
Average, 541
value of waveform, 206–210

Base, 87
Bessel functions, 508
Bessel’s equation, 506–511

Binary addition, 89

numbers, 87–90

Binomial distribution, 556–559

expression, 58

series/theorem, 59–66

practical problems, 64–66

Bisection method, 77–81

Bits, 87

Boundary conditions, 445, 516

Brackets, 2

Calculus, 287

Cardioid, 315

Cartesian complex numbers, 213–218

co-ordinates, 117–120

Catenary, 43

Centre of area, 380

gravity, 380

mass, 380

Centripetal acceleration, 131

force, 130–132

Centroids, 380–381

Chain rule, 295

Change of limits, 395–396

Chord, 122

Circle, 122, 179

area, 124

equation of, 127–129, 179

Circumference, 122

Class interval, 534

Coefficient of correlation, 570–571

Cofactor, 237

Combination of periodic functions,

265–274

Common difference, 51

logarithms, 20

ratio, 54

Complementary function, 483

Complex numbers, 213–224

applications of, 221–224

Cartesian form, 213

coefficients, 645–649

conjugate, 216

equations, 217–218

exponential form, 228–230

form of Fourier series, 644–649

polar form, 218–221

powers of, 225–226

roots of, 226–228

Complex wave, 146–151

considerations, 641–643

Compound angles, 163–176

Computer numbering systems, 87

Conditional probability, 548

Continuous data, 529

function, 186, 611

Contour map, 359

Conversion ofasinωt+bcosωtinto

Rsin(ωt+α), 165–169

Correlation, linear, 570–574

Cosecant, 98

Cosh, 41

series, 49–50

Coshθsubstitution,406–408

Coshec, 41

Cosine, 98

curves, 138–143

rule, 108, 268–270

wave production, 137–138

Cotangent, 99

Coth, 41

Cramer’s rule, 247–248

Cross product, 280

Cubic equations, 9, 178

Cumulative frequency distribution, 535

Curve sketching, 196–202

Cycloid, 315

Deciles, 546–547

Decimal numbers, 87

Definite integrals, 372–374

Degree of differential equation, 445

De Moivre’s theorem, 225–230

Dependent event, 548

Depression, angle of, 106–108

Derivatives, 288

Laplace transforms of, 589

Determinant, 235, 237–239

to solve simultaneous equations,

241–244

Determination of law, 37

Diameter, 122