082-Engineering-Mathematics-Anthony-Croft-Robert-Davison-Martin-Hargreaves-James-Flint-Edisi-5-2017

Contents xi
Chapter17 Numericalintegration 496
17.1 Introduction 496
17.2 Trapezium rule 496
17.3 Simpson’s rule 500
Review exercises 17 505
Chapter18 Taylorpolynomials,TaylorseriesandMaclaurinseries 507
18.1 Introduction 507
18.2 Linearizationusing first-order Taylor polynomials 508
18.3 Second-order Taylor polynomials 513
18.4 Taylor polynomials of the nth order 517
18.5 Taylor’s formula and the remainder term 521
18.6 Taylor and Maclaurinseries 524
Review exercises 18 532
Chapter19 OrdinarydifferentialequationsI 534
19.1 Introduction 534
19.2 Basic definitions 535
19.3 First-order equations: simple equationsand separation
of variables 540
19.4 First-order linear equations:use of an integratingfactor 547
19.5 Second-order linear equations 558
19.6 Constant coefficient equations 560
19.7 Series solution of differentialequations 584
19.8 Bessel’s equationand Bessel functions 587
Review exercises 19 601
Chapter20 OrdinarydifferentialequationsII 603
20.1 Introduction 603
20.2 Analogue simulation 603
20.3 Higher order equations 606
20.4 State-space models 609
20.5 Numerical methods 615
20.6 Euler’s method 616
20.7 Improved Euler method 620
20.8 Runge–Kuttamethod of order 4 623
Review exercises 20 626
Chapter21 TheLaplacetransform 627
21.1 Introduction 627
21.2 Definitionof the Laplace transform 628