Advanced engineering mathematics / K.A. Stroud ; with Dexter J. Booth.

Format:

Book

Author/Creator:

Stroud, K. A., author.

Booth, Dexter J., author.

Language:

English

Subjects (All):

Engineering mathematics--Programmed instruction.

Engineering mathematics.

Genre:

Textbooks.

Programmed instructional materials.

Physical Description:

xxvi, 1222 pages ; 25 cm

Edition:

Sixth edition.

Place of Publication:

London : Red Globe Press, 2020.

Contents:

Machine generated contents note: Programme 1 Numerical solutions of equations and interpolation

Learning outcomes

Introduction

The Fundamental Theorem of Algebra

Relations between the coefficients and the roots of a polynomial equation

Cubic equations

Transforming a cubic to reduced form

Tartaglia's solution for a real root

Numerical methods

Bisection

Numerical solution of equations by iteration

Using a spreadsheet

Relative addresses

Newton-Raphson iterative method

Tabular display of results

Modified Newton-Raphson method

Interpolation

Linear interpolation

Graphical interpolation

Gregory-Newton interpolation formula using forward finite differences

Central differences

Gregory-Newton backward differences

Lagrange interpolation

Review summary 1

Can you? checklist 1

Test exercise 1

Further problems 1

Programme 2 Laplace transforms 1

Laplace transforms

Differentiating and integrating a transform

Theorem 1 The first shift theorem

Theorem 2 Multiplying by t and tn

Theorem 3 Dividing by t

Inverse transforms

Rules of partial fractions

The `cover up' rule

Table of inverse transformations

Solution of differential equations by Laplace transforms

Transforms of derivatives

Solution of first-order differential equations

Solution of second-order differential equations

Simultaneous differential equations

Review summary 2

Can you? checklist 2

Test exercise 2

Further problems 2

Programme 3 Laplace transforms 2

Heaviside unit step function

Unit step at the origin

Effect of the unit step function

Laplace transform of u(t

c)

c)·f(t

c) (the second shift theorem)

Differential equations involving the unit step function

Convolution

The convolution theorem

Review summary 3

Can you? checklist 3

Test exercise 3

Further problems 3

Programme 4 Laplace transforms 3

Laplace transform of periodic functions

Periodic functions

Inverse transformations

The Dirac delta

the unit impulse

Graphical representation

Laplace transform of δ(t

a)

The derivative of the unit step function

Differential equations involving the unit impulse

Harmonic oscillators

Damped motion

Forced harmonic motion with damping

Resonance

Review summary 4

Can you? checklist 4

Test exercise 4

Further problems 4

Programme 5 Difference equations and the Z transform

Sequences

Difference equations

Solving difference equations

Solution by inspection

The particular solution

The Z transform

Table of Z transforms

Properties of Z transforms

Linearity

First shift theorem (shifting to the left)

Second shift theorem (shifting to the right)

Scaling

Final value theorem

The initial value theorem

The derivative of the transform

Sampling

Review summary 5

Can you? checklist 5

Test exercise 5

Further problems 5

Programme 6 Introduction to invariant liner systems

Invariant linear systems

Systems

Input-response relationships

Linear systems

Time-invariance of a continuous system

Shift-invariance of a discrete system

Differential equations

The general nth-order equation

Zero-input response and zero-state response

Zero-input, zero response

Time-in variance

Responses of a continuous system

Impulse response

Arbitrary input

Exponential response

The transfer function H(s)

Responses of a discrete system

The discrete unit impulse

Transfer function

Review summary 6

Can you? checklist 6

Test exercise 6

Further problems 6

Programme 7 Fourier series 1

Graphs of y = A sin nx

Harmonics

Non-sinusoidal periodic functions

Analytic description of a periodic function

Integrals of periodic functions

Orthogonal functions

Fourier series

Dirichlet conditions

Effect of harmonics

Gibbs' phenomenon

Sum of a Fourier series at a point of discontinuity

Review summary 7

Can you? checklist 7

Test exercise 7

Further problems 7

Programme 8 Fourier series 2

Odd and even functions and half-range series

Odd and even functions

Products of odd and even functions

Half-range series

Series containing only odd harmonics or only even harmonics

Significance of the constant term 1/2a0

Functions with periods other than 2π

Functions with period T

Fourier coefficients

Half-range series with arbitrary period

Review summary 8

Can you? checklist 8

Test exercise 8

Further problems 8

Programme 9 Introduction to the Fourier transform

Complex Fourier series

Complex exponentials

Complex spectra

The two domains

Continuous spectra

Fourier's integral theorem

Some special functions and their transforms

Even functions

Odd functions

Top-hat function

The triangle function

Alternative forms

Properties of the Fourier transform

Time shifting

Frequency shifting

Time scaling

Symmetry

Differentiation

The Heaviside unit step function

Fourier cosine and sine transformations

Table of transforms

Review summary 9

Can you? checklist 9

Test exercise 9

Further problems 9

Programme 10 Power series solutions of ordinary differential equations

Higher derivatives

Leibnitz theorem

nth derivative of a product of functions

Choice of function for u and v

Power series solutions

Leibnitz-Maclaurin method

Cauchy-Euler equi-dimensional equations

Review summary 10

Can you? checklist 10

Test exercise 10

Further problems 10

Programme 11 Power series solutions of ordinary differential equations 2

Solution of differential equations by the method of Frobenius

The indicial equation

Review summary 11

Can you? checklist 11

Test exercise 11

Further problems 11

Programme 12 Power series solutions of ordinary differential equations 3

Bessel's equation

Gamma and Bessel functions

Graphs of Bessel functions J0(x) and J1(x)

Legendre's equation

Legendre polynomials

Rodrigue's formula and the generating function

Sturm-Liouville systems

Orthogonality

Legendre's equation revisited

Polynomials as a finite series of Legendre polynomials

Review summary 12

Can you? checklist 12

Test exercise 12

Further problems 12

Programme 13 Numerical solutions of ordinary differential equations

Taylor's series

Function increment

First-order differential equations

Euler's method

The exact value and the errors

Graphical interpretation of Euler's method

The Euler-Cauchy method

or the improved Euler method

Euler-Cauchy calculations

Runge-Kutta method

Second-order differential equations

Euler second-order method

Runge-Kutta method for second-order differential equations

Predictor-corrector methods

Review summary 13

Can you? checklist 13

Test exercise 13

Further problems 13

Programme 14 Matrix algebra

Singular and non-singular matrices

Rank of a matrix

Elementary operations and equivalent matrices

Consistency of a set of linear equations

Uniqueness of solutions

Solution of sets of linear equations

Inverse method

Row transformation method

Gaussian elimination method

Triangular decomposition method

Using an electronic spreadsheet

Comparison of methods

Matrix transformation

Rotation of axes

Review summary 14

Can you? checklist 14

Test exercise 14

Further problems 14

Programme 15 Systems of ordinary differential equations

Eigenvalues of 2 [×] 2 matrices

Characteristic equation

Sum and product of eigenvalues

Eigenvectors

Systems of linear, first-order ordinary differential equations

Repeated eigenvalues

Diagonalization of a matrix

Modal matrix

Spectral matrix

Systems of linear, second-order differential equations

Review summary 15

Can you? checklist 15

Test exercise 15

Further problems 15

Programme 16 Direction fields

Family of solutions

Direction fields

DFIELD

A specific solution

Autonomous differential equations

Equilibrium solutions

The phase line

Non-autonomous equations

Review summary 16

Can you? checklist 16

Test exercise 16

Further problems 16

Programme 17 Phase plane analysis

Phase plane analysis

Mass-spring system

PPLANE

Contents note continued: Phase plane analysis

Eigenvalues and the phase plane

Imaginary eigenvalues

Two complex eigenvalues

Behaviour around the critical point

Two real and negative eigenvalues

Two real and positive eigenvalues

Two real eigenvalues of different signs

Two identical eigenvalues

Star node

Singular coefficient matrix

The inhomogeneous case

Critical point moved to the origin

Review summary 17

Can you? checklist 17

Test exercise 17

Further problems 17

Programme 18 Nonlinear systems

Multiple critical points

Linearization

Problems with linearization

Review summary 18

Can you? checklist 18

Test exercise 18

Further problems 18

Programme 19 Dynamical systems

Dynamical systems

Predator-prey problems

Competition within a single population

Two non-interacting populations

Two interacting populations

Undamped pendulum: small oscillations

Undamped pendulum: no approximation

Damped pendulum

Bifurcation

First-order equations

Second-order equations

Limit cycles

The Van der Pol equation

Review summary 19

Can you? checklist 19

Test exercise 19

Further problems 19

Programme 20 Partial differentiation

Small increments

Taylor's theorem for one independent variable

Taylor's theorem for two independent variables

Rates of change

Implicit functions

Change of variables

Inverse functions

General case

Stationary values of a function

Maximum and minimum values

Saddle point

Lagrange undetermined multipliers

Functions with three independent variables

Review summary 20

Can you? checklist 20

Test exercise 20

Further problems 20

Programme 21 Partial differential equations

Partial differential equations

Solution by direct integration

Initial conditions and boundary conditions

The wave equation

Solution of the wave equation

Solution by separating the variables

The heat conduction equation for a uniform finite bar

Solutions of the heat conduction equation

Laplace's equation

Solution of the Laplace equation

Laplace's equation in plane polar coordinates

The problem

Separating the variables

The n = 0 case

Review summary 21

Can you? checklist 21

Test exercise 21

Further problems 21

Programme 22 Numerical solutions of partial differential equations

Numerical approximation to derivatives

Functions of two real variables

Grid values

Computational molecules

Summary of procedures

Derivative boundary conditions

Second-order partial differential equations

Elliptic equations

Hyperbolic equations

Parabolic equations

Second partial derivatives

Time-dependent equations

The Crank-Nicholson procedure

Dimensional analysis

Review summary 22

Can you? checklist 22

Test exercise 22

Further problems 22

Programme 23 Multiple integration 1

Differentials

Exact differential

Integration of exact differentials

Area enclosed by a closed curve

Line integrals

Alternative form of a line integral

Properties of line integrals

Regions enclosed by closed curves

Line integrals round a closed curve

Line integral with respect to arc length

Parametric equations

Dependence of the line integral on the path of integration

Exact differentials in three independent variables

Green's theorem

Review summary 23

Can you? checklist 23

Test exercise 23

Further problems 23

Programme 24 Multiple integration 2

Double integrals

Surface integrals

Three dimensional coordinate systems

Cartesian coordinates

Cylindrical coordinates

Spherical coordinates

Element of volume in the three coordinate systems

Volume integrals

Change of variables in multiple integrals

Curvilinear coordinates

Transformation in three dimensions

Review summary 24

Can you? checklist 24

Test exercise 24

Further problems 24

Programme 25 Integral functions

Gamma and beta functions

The gamma function

The beta function

Reduction formulas

Relation between the gamma and beta functions

Application of gamma and beta functions

Duplication formula for gamma functions

The error function

The graph of erf(x)

The complementary error function erfc(x)

Elliptic functions

Standard forms of elliptic functions

Complete elliptic functions

Alternative forms of elliptic functions

Review summary 25

Can you? checklist 25

Test exercise 25

Further problems 25

Programme 26 Vector analysis 1

Triple products

Scalar triple products of three vectors

Properties of scalar triple products

Coplanar vectors

Vector triple products of three vectors

Differentiation of vectors

Differentiation of sums and products of vectors

Unit tangent vectors

Partial differentiation of vectors

Integration of vector functions

Scalar and vector fields

Grad (gradient of a scalar field)

Directional derivatives

Unit normal vectors

Grad of sums and products of scalars

Div (divergence of a vector function)

Curl (curl of a vector function)

Summary of grad, div and curl

Multiple operations

Review summary 26

Can you? checklist 26

Test exercise 26

Further problems 26

Programme 27 Vector analysis 2

Scalar field

Vector field

Scalar fields

Vector fields

Conservative vector fields

Divergence theorem (Gauss' theorem)

Stokes' theorem

Direction of unit normal vectors to a surface S

Review summary 27

Can you? checklist 27

Test exercise 27

Further problems 27

Programme 28 Vector analysis 3

Orthogonal curvilinear coordinates

Orthogonal coordinate systems in space

Scale factors

Scale factors for coordinate systems

General curvilinear coordinate system (u, v, w)

Transformation equations

Element of arc ds and element of volume d V in orthogonal curvilinear coordinates

Grad, div and curl in orthogonal curvilinear coordinates

Particular orthogonal systems

Review summary 28

Can you? checklist 28

Test exercise 28

Further problems 28

Programme 29 Complex analysis 1

Functions of a complex variable

Complex mapping

Mapping of a straight line in the z-plane onto the w-plane under the transformation w = f (z)

Types of transformation of the form w = az + b

Nonlinear transformations

Mapping of regions

Review summary 29

Can you? checklist 29

Test exercise 29

Further problems 29

Programme 30 Complex analysis 2

Differentiation of a complex function

Regular function

Cauchy-Riemann equations

Harmonic functions

Complex integration

Contour integration

line integrals in the z-plane

Cauchy's theorem

Deformation of contours at singularities

Conformal transformation (conformal mapping)

Conditions for conformal transformation

Critical points

Schwarz-Christoffel transformation

Open polygons

Review summary 30

Can you? checklist 30

Test exercise 30

Further problems 30

Programme 31 Complex analysis 3

Maclaurin series

Radius of convergence

Singular points

Poles

Removable singularities

Circle of convergence

Laurent's series

Residues

Calculating residues

Integrals of real functions

Integrals of the form [∫]2π0 F(cosθ, sinθ) dθ

Integrals of the form [∫][∞]-[∞] F(x) dx

Integrals of the form [∫][∞]-[∞] F(x)sinxcosx dx

Review summary 31

Can you? checklist 31

Test exercise 31

Further problems 31

Programme 32 Optimization and linear programming

Optimization

Linear programming (or linear optimization)

Linear inequalities

Graphical representation of linear inequalities

Solver

Solver parameters

Applications

Nonlinear programming

Review summary 32

Can you? checklist 32

Test exercise 32

Further problems 32.

Notes:

Includes index.

ISBN:

9781352010251

1352010259

OCLC:

1145418263

Publisher Number:

99987477372