Higher Engineering Mathematics, Sixth Edition

676 Index

Differential coefficient, 288

Differential equations, 445

a

d^2 y

dx^2

+b

dy

dx

+cy=0 type,

477–482

a

d^2 y

dx^2

+b

dy

dx

+cy=f(x)type,

483–492

dy

dx

=f(x)type, 445–447

dy

dx

=f(y)type, 447–449

dy

dx

=f(x)·f(y)type, 449–451

dy

dx

+Py=Qtype, 456–460

degree of, 445

first order, separation of variables,

444

homogeneous first order, 452–455

numerical methods, 461

partial, 515

power series method, 493

simultaneous, using Laplace

transforms, 605–609

using Laplace transforms, 600–604

Differentiation, 68, 287

applications, 299–314

from first principles, 288

function of a function, 295–296, 320

implicit, 320–324

inverse hyperbolic function,

341–344

trigonometric function, 334–339

logarithmic, 325–329

methods of, 287–298

of common functions, 289–292

of hyperbolic functions, 331–332

of parametric equations, 315–319

partial, 345

first order, 345–348

second order, 348–350

product, 292–293

quotient, 293–295

successive, 296–298

Direction cosines, 278

Discontinuous function, 186

Discrete data, 529

Dividend, 7

Divisor, 7

D-operator form, 477

Dot product, 276

Double angles, 45, 169–170

Elastic string, 519

Elevation, angle of, 106–108

Ellipse,179, 199, 315

Equations, 3

Bessel’s, 506–511

circle, 126

complex, 217–218

heat conduction, 518, 523–525

hyperbolic, 47–48

indicial, 24–25, 501, 503, 507

Laplace, 515, 517, 518, 525–527

Legendre’s, 511–513

Newton-Raphson, 84

normal, 575

of circle, 127–129, 179

quadratic, 5–6

simple, 3

simultaneous, 4–5, 241–247

solving by iterative methods, 77–86

tangents, 311–312

transmission, 518

trigonometric, 154–158

wave, 518–523

Euler-Cauchy method, 466

Euler’s formula, 653

Euler’s method, 461–470

Even function, 42, 186–188, 623

Expectation, 548

Exponential form of complex number,

228–230

Fourier series, 644

Exponential function, 27–39

graphs of, 29–31

power series, 28–29

Extrapolation, 576

Factorisation, 2

Factor theorem, 8–10

Family of curves, 444

Final value theorem, 591–592

First moment of area, 383

Formulae, 4

Fourier coefficients, 612

Fourier series, 146

cosine, 623–626

exponential form, 645

half-range,626–629, 634

non-periodic over range 2π,

617–622

over any range, 630–636

periodic of period 2π, 611–616

sine, 623–626

Frequency, 143, 529

curve, 562

distribution, 534, 538

domain, 652

polygon, 535, 538

relative, 529

spectrum, 652–653

Frobenius method, 500–506

Functional notation, 288

Function of a function, 295–296, 320

Functions of two variables, 357–366

Fundamental, 612

Gamma function, 508

Gaussian elimination, 248–249

General solution of a differential

equation, 445, 447

Geometric progression, 54–57

Gradient of a curve, 287–288

Graphs of exponential functions, 29–31

hyperbolic functions, 43–44

logarithmic function, 25–26

trigonometric functions, 134

Grouped data, 534–539, 545

Growth and decay laws, 34–37

Half range Fourier series, 624–629,

634

Half-wave rectifier, 148

Harmonic analysis, 146, 637–643

Harmonic synthesis, 146–151

Heat conduction equation, 518,

523–525

Hexadecimal number, 92–95

Higher order differentials, 493–495

Histogram, 535, 538, 543

of probabilities,558, 560

Homogeneous, 452, 477

Homogeneous first order differential

equations, 452–460

Horizontal bar chart, 530

component, 254, 270

Hyperbola, 180

rectangular, 180, 199, 315

Hyperbolic functions, 41–50, 159

differentiation of, 331–332

graphs of, 43–44

inverse, 334–344

solving equations, 47–48

Hyperbolic identities,45–47, 160–161

logarithms, 20, 31–34, 325

Hypotenuse, 97

Identities

hyperbolic, 45–47, 160–161

trigonometric, 45, 152–154

i,j,knotation, 263