Advanced Engineering Mathematics (6th Edition)


Download Advanced Engineering Mathematics (6th Edition) written by K.A. Stroud, Dexter Booth in PDF format. This book is under the category Engineering and bearing the isbn/isbn13 number 1352010259; 1352010267/9781352010251/ 9781352010268. You may reffer the table below for additional details of the book.


An extended-standing; fashionable; complete textbook encompassing all of the arithmetic required on higher-degree engineering arithmetic undergraduate programs. Its distinctive strategy takes you thru all of the arithmetic you want in a step-by-step vogue with numerous examples and workouts. Advanced Engineering Mathematics; sixth Edition; (PDF) calls for that you simply get entangled with it by asking you to finish steps that you must have the ability to handle from prior examples or information you could have acquired; whereas correctly introducing new steps. By working with the writers by means of the examples; you turn out to be skillful as you go. By the time you come to attempting examples by yourself; confidence is excessive.

NOTE: The product solely consists of the ebook; Advanced Engineering Mathematics 6e in PDF. No access codes are included.

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K.A. Stroud, Dexter Booth


Red Globe Press; 6th edition










1352010259; 1352010267


9781352010251/ 9781352010268

Table of contents

Table of contents :
Summary of contents
Preface to the first edition
Preface to the sixth edition
New to this edition
Hints on using the book
Useful background information
Programme 1 Numerical solutions of equations and interpolation
Learning outcomes
The Fundamental Theorem of Algebra
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
Numerical solution of equations by iteration
Using a spreadsheet
Relative addresses
Newton–Raphson iterative method
Tabular display of results
Modified Newton–Raphson method
And now . . .
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
Learning outcomes
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 transforms
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
Learning outcomes
Heaviside unit step function
Unit step at the origin
Effect of the unit step function
Laplace transform of u(t – c)
Laplace transform of u(t – c).f(t – c ) (the second shift theorem)
Differential equations involving the unit step function
The convolution theorem
Review summary 3
Can you?
Checklist 3
Test exercise 3
Further problems 3
Programme 4 Laplace transforms 3
Learning outcomes
Laplace transforms of periodic functions
Periodic functions
Inverse transforms
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
Review summary 4
Can you?
Checklist 4
Test exercise 4
Further problems 4
Programme 5 Difference equations and the Z transform
Learning outcomes
Difference equations
Solving difference equations
Solution by inspection
The particular solution
The Z transform
Table of Z transforms
Properties of Z transforms
First shift theorem (shifting to the left)
Second shift theorem (shifting to the right)
Final value theorem
The initial value theorem
The derivative of the transform
Inverse transforms
Solving difference equations
Review summary 5
Can you?
Checklist 5
Test exercise 5
Further problems 5
Programme 6 Introduction to invariant linear systems
Learning outcomes
Invariant linear 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
Responses of a continuous system
Impulse response
Arbitrary input
Exponential response
The transfer function H(s)
Differential equations
Responses of a discrete system
The discrete unit impulse
Arbitrary input
Exponential response
Transfer function
Difference equations
Review summary 6
Can you?
Checklist 6
Test exercise 6
Further problems
Programme 7 Fourier series 1
Learning outcomes
Periodic functions
Graphs of y = Asin nx
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
Learning outcomes
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 1/2 a0
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
Learning outcomes
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 Dirac delta (refer to Programme 4, Frames 29ff)
The triangle function
Alternative forms
Properties of the Fourier transform
Time shifting
Frequency shifting
Time scaling
The Heaviside unit step function
The convolution theorem
Fourier cosine and sine transforms
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 1
Learning outcomes
Higher derivatives
Leibnitz theorem – nth derivative of a product of two 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
Learning outcomes
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
Learning outcomes
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
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
Learning outcomes
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
Learning outcomes
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
Learning outcomes
Eigenvalues of 2 x 2 matrices
Characteristic equation
Sum and product of eigenvalues
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
Learning outcomes
Differential equations
Family of solutions
Direction fields
A specific solution
Family of solutions
Autonomous differential equations
Equilibrium solutions
The phase line
Semi-stable solution
Non-autonomous equations
Review summary 16
Can you?
Checklist 16
Test exercise 16
Further problems 16
Programme 17 Phase plane analysis
Learning outcomes
Phase plane analysis
Mass-spring system
Phase plane analysis
Eigenvalues and the phase plane
Imaginary eigenvalues
Two complex eigenvalues
Behaviour around the critical point
Two real and negative eigenvalues
Behaviour around the critical point
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
Learning outcomes
Multiple critical points
Problems with linearization
Review summary
Can you?
Checklist 18
Test exercise 18
Further problems 18
Programme 19 Dynamical systems
Learning outcomes
Dynamical systems
Predator-prey problems
Competition within a single population
Two non-interacting populations
Two interacting populations
Second-order differential equations
Undamped pendulum: small oscillations
Undamped pendulum: no approximation
Damped pendulum
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
Learning outcomes
Small increments
Taylor’s theorem for one independent variable
Taylor0s theorem for two independent variables
Small increments
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
Learning outcomes
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
Revision summary 21
Can you?
Checklist 21
Test exercise 21
Further problems 21
Programme 22 Numerical solutions of partial differential equations
Learning outcomes
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–Nicolson procedure
Dimensional analysis
Review summary 22
Can you?
Checklist 22
Test exercise 22
Further problems 22
Programme 23 Multiple integration 1
Learning outcomes
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
Learning outcomes
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
Learning outcomes
Gamma and beta functions
The gamma function
The beta function
Reduction formulas
Relationship 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
Learning outcomes
Triple products
Scalar triple product 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 function)
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
Learning outcomes
Line integrals
Scalar field
Vector field
Volume integrals
Surface integrals
Scalar fields
Vector fields
Conservative vector fields
Divergence theorem
Stokes’ theorem
Direction of unit normal vectors to a surface S
Green’s theorem
Review summary 27
Can you?
Checklist 27
Test exercise 27
Further problems 27
Programme 28 Vector analysis 3
Learning outcomes
Curvilinear coordinates
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 dV 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
Learning outcomes
Functions of a complex variable
Complex mapping
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
Learning outcomes
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
Text exercise 30
Further problems 30
Programme 31 Complex analysis 3
Learning outcomes
Maclaurin series
Radius of convergence
Singular points
Removable singularities
Circle of convergence
Taylor’s series
Laurent’s series
Calculating residues
Integrals of real functions
Integrals of the form
Review summary 31
Can you?
Checklist 31
Test exercise 31
Further problems 31
Programme 32 Optimization and linear programming
Learning outcomes
Linear programming (or linear optimization)
Linear inequalities
Graphical representation of linear inequalities
Solver parameters
Nonlinear programming
Review summary 32
Can you?
Checklist 32
Test exercise 32
Further problems 32
1 Green’s theorem
Proof of Green’s theorem
2 Proof that sec
3 Vector triple products
4 Divergence theorem (Gauss’ theorem)
5 Stokes’ theorem
Proof of Stokes’ theorem
Test exercise 1 (page 42)
Further problems 1 (page 43)
Test exercise 2 (page 90)
Further problems 2 (page 91)
Test exercise 3 (page 121)
Further problems 3 (page 122)
Test exercise 4 (page 154)
Further problems 4 (page 155)
Test exercise 5 (page 191)
Further problems 5 (page 191)
Test exercise 6 (page 236)
Further problems 6 (page 237)
Test exercise 7 (page 266)
Further problems 7 (page 267)
Test exercise 8 (page 297)
Further problems 8 (page 298)
Test exercise 9 (page 334)
Further problems 9 (page 335)
Test exercise 10 (page 357)
Further problems 10 (page 357)
Test exercise 11 (page 376)
Further problems 11 (page 376)
Test exercise 12 (page 394)
Further problems 12 (page 395)
Text exercise 13 (page 434)
Further problems 13 (page 435)
Test exercise 14 (page 478)
Further problems 14 (page 479)
Test exercise 15 (page 510)
Further problems 15 (page 510)
Test exercise 16 (page 536)
Further problems 16 (page 536)
Test exercise 17 (page 577)
Further problems 17 (page 578)
Test exercise 18 (page 600)
Further problems 18 (page 600)
Test exercise 19 (page 635)
Further problems 19 (page 635)
Test exercise 20 (page 680)
Further problems 20 (page 680)
Test exercise 21 (page 717)
Further problems 21 (page 718)
Test exercise 22 (page 761)
Further problems 22 (page 762)
Test exercise 23 (page 815)
Further problems 23 (page 816)
Test exercise 24 (page 858)
Further problems 24 (page 858)
Test exercise 25 (page 895)
Further problems 25 (page 895)
Text exercise 26 (page 941)
Further problems 26 (page 941)
Test exercise 27 (page 991)
Further problems 27 (page 992)
Test exercise 28 (page 1019)
Further problems 28 (page 1019)
Test exercise 29 (page 1058)
Further problems 29 (page 1059)
Test exercise 30 (page 1106)
Further problems 30 (page 1107)
Test exercise 31 (page 1136)
Further problems 31 (page 1137)
Test exercise 32 (page 1160)
Further problems 32 (page 1161)

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