# [PDF] Modern Engineering Mathematics, 6th Edition Free Download

For first-year undergraduate modules in Engineering Mathematics.

Develop understanding and maths skills within an engineering context

Modern Engineering Mathematics, 6th Edition by Professors Glyn James and Phil Dyke, draws on the teaching experience and knowledge of three co-authors, Matthew Craven, John Searl and Yinghui Wei, to provide a comprehensive course textbook explaining the mathematics required for studying first-year engineering. No matter which field of engineering you will go on to study, this text provides a grounding of core mathematical concepts illustrated with a range of engineering applications. Its other hallmark features include its clear explanations and writing style, and the inclusion of hundreds of fully worked examples and exercises which demonstrate the methods and uses of mathematics in the real world. Woven into the text throughout, the authors put concepts into an engineering context, showing you the relevance of mathematical techniques and helping you to gain a fuller appreciation of how to apply them in your studies and future career.

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Table of Contents

## Table of contents :

Front Cover

Half Title Page

Title Page

Copyright Page

Contents

Preface

About the authors

Chapter 1 Number, Algebra and Geometry

1.1 Introduction

1.2 Number and arithmetic

1.2.1 Number line

1.2.2 Representation of numbers

1.2.3 Rules of arithmetic

1.2.4 Exercises (1–9)

1.2.5 Inequalities

1.2.6 Modulus and intervals

1.2.7 Exercises (10–14)

1.3 Algebra

1.3.1 Algebraic manipulation

1.3.2 Exercises (15–20)

1.3.3 Equations, inequalities and identities

1.3.4 Exercises (21–32)

1.3.5 Suffïx and sigma notation

1.3.6 Factorial notation and the binomial expansion

1.3.7 Exercises (33–35)

1.4 Geometry

1.4.1 Coordinates

1.4.2 Straight lines

1.4.3 Circles

1.4.4 Exercises (36–43)

1.4.5 Conics

1.4.6 Exercises (44–46)

1.5 Number and accuracy

1.5.1 Rounding, decimal places and significant figures

1.5.2 Estimating the effect of rounding errors

1.5.3 Exercises (47–56)

1.5.4 Computer arithmetic

1.5.5 Exercises (57–59)

1.6 Engineering applications

1.7 Review exercises (1–25)

Chapter 2 Functions

2.1 Introduction

2.2 Basic definitions

2.2.1 Concept of a function

2.2.2 Exercises (1–6)

2.2.3 Inverse functions

2.2.4 Composite functions

2.2.5 Exercises (7–13)

2.2.6 Odd, even and periodic functions

2.2.7 Exercises (14–16)

2.3 Linear and quadratic functions

2.3.1 Linear functions

2.3.2 Least squares fit of a linear function to experimental data

2.3.3 Exercises (17–23)

2.3.4 The quadratic function

2.3.5 Exercises (24–29)

2.4 Polynomial functions

2.4.1 Basic properties

2.4.2 Factorization

2.4.3 Nested multiplication and synthetic division

2.4.4 Roots of polynomial equations

2.4.5 Exercises (30–38)

2.5 Rational functions

2.5.1 Partial fractions

2.5.2 Exercises (39–42)

2.5.3 Asymptotes

2.5.4 Parametric representation

2.5.5 Exercises (43–47)

2.6 Circular functions

2.6.1 Trigonometric ratios

2.6.2 Exercises (48–54)

2.6.3 Circular functions

2.6.4 Trigonometric identities

2.6.5 Amplitude and phase

2.6.6 Exercises (55–66)

2.6.7 Inverse circular (trigonometric) functions

2.6.8 Polar coordinates

2.6.9 Exercises (67–71)

2.7 Exponential, logarithmic and hyperbolic functions

2.7.1 Exponential functions

2.7.2 Logarithmic functions

2.7.3 Exercises (72–80)

2.7.4 Hyperbolic functions

2.7.5 Inverse hyperbolic functions

2.7.6 Exercises (81–88)

2.8 Irrational functions

2.8.1 Algebraic functions

2.8.2 Implicit functions

2.8.3 Piecewise defined functions

2.8.4 Exercises (89–98)

2.9 Numerical evaluation of functions

2.9.1 Tabulated functions and interpolation

2.9.2 Exercises (99–104)

2.10 Engineering application: a design problem

2.11 Engineering application: an optimization problem

2.12 Review exercises (1–23)

Chapter 3 Complex Numbers

3.1 Introduction

3.2 Properties

3.2.1 The Argand diagram

3.2.2 The arithmetic of complex numbers

3.2.3 Complex conjugate

3.2.4 Modulus and argument

3.2.5 Exercises (1–18)

3.2.6 Polar form of a complex number

3.2.7 Euler’s formula

3.2.8 Exercises (19–27)

3.2.9 Relationship between circular and hyperbolic functions

3.2.10 Logarithm of a complex number

3.2.11 Exercises (28–33)

3.3 Powers of complex numbers

3.3.1 De Moivre’s theorem

3.3.2 Powers of trigonometric functions and multiple angles

3.3.3 Exercises (34–41)

3.4 Loci in the complex plane

3.4.1 Straight lines

3.4.2 Circles

3.4.3 More general loci

3.4.4 Exercises (42–50)

3.5 Functions of a complex variable

3.5.1 Exercises (51–56)

3.6 Engineering application: alternating currents in electrical networks

3.6.1 Exercises (57–58)

3.7 Review exercises (1–34)

Chapter 4 Vector Algebra

4.1 Introduction

4.2 Basic definitions and results

4.2.1 Cartesian coordinates

4.2.2 Scalars and vectors

4.2.3 Addition of vectors

4.2.4 Exercises (1–10)

4.2.5 Cartesian components and basic properties

4.2.6 Complex numbers as vectors

4.2.7 Exercises (11–26)

4.2.8 The scalar product

4.2.9 Exercises (27–40)

4.2.10 The vector product

4.2.11 Exercises (41–56)

4.2.12 Triple products

4.2.13 Exercises (57–65)

4.3 The vector treatment of the geometry of lines and planes

4.3.1 Vector equation of a line

4.3.2 Exercises (66–72)

4.3.3 Vector equation of a plane

4.3.4 Exercises (73–83)

4.4 Engineering application: spin-dryer suspension

4.4.1 Point-particle model

4.5 Engineering application: cable-stayed bridge

4.5.1 A simple stayed bridge

4.6 Review exercises (1–22)

Chapter 5 Matrix Algebra

5.1 Introduction

5.2 Basic concepts, definitions and properties

5.2.1 Definitions

5.2.2 Basic operations of matrices

5.2.3 Exercises (1–11)

5.2.4 Matrix multiplication

5.2.5 Exercises (12–18)

5.2.6 Properties of matrix multiplication

5.2.7 Exercises (19–33)

5.3 Determinants

5.3.1 Exercises (34–50)

5.4 The inverse matrix

5.4.1 Exercises (51–59)

5.5 Linear equations

5.5.1 Exercises (60–71)

5.5.2 The solution of linear equations: elimination methods

5.5.3 Exercises (72–78)

5.5.4 The solution of linear equations: iterative methods

5.5.5 Exercises (79–84)

5.6 Rank

5.6.1 Exercises (85–93)

5.7 The eigenvalue problem

5.7.1 The characteristic equation

5.7.2 Eigenvalues and eigenvectors

5.7.3 Exercises (94–95)

5.7.4 Repeated eigenvalues

5.7.5 Exercises (96–101)

5.7.6 Some useful properties of eigenvalues

5.7.7 Symmetric matrices

5.7.8 Exercises (102–106)

5.8 Engineering application: spring systems

5.8.1 A two-particle system

5.8.2 An n-particle system

5.9 Engineering application: steady heat transfer through composite materials

5.9.1 Introduction

5.9.2 Heat conduction

5.9.3 The three-layer situation

5.9.4 Many-layer situation

5.10 Review exercises (1–26)

Chapter 6 An Introduction to Discrete Mathematics

6.1 Introduction

6.2 Set theory

6.2.1 Definitions and notation

6.2.2 Union and intersection

6.2.3 Exercises (1–8)

6.2.4 Algebra of sets

6.2.5 Exercises (9–17)

6.3 Switching and logic circuits

6.3.1 Switching circuits

6.3.2 Algebra of switching circuits

6.3.3 Exercises (18–29)

6.3.4 Logic circuits

6.3.5 Exercises (30–31)

6.4 Propositional logic and methods of proof

6.4.1 Propositions

6.4.2 Compound propositions

6.4.3 Algebra of statements

6.4.4 Exercises (32–37)

6.4.5 Implications and proofs

6.4.6 Exercises (38–47)

6.5 Engineering application: decision support

6.6 Engineering application: control

6.7 Review exercises (1–23)

Chapter 7 Sequences, Series and Limits

7.1 Introduction

7.2 Sequences and series

7.2.1 Notation

7.2.2 Graphical representation of sequences

7.2.3 Exercises (1–13)

7.3 Finite sequences and series

7.3.1 Arithmetical sequences and series

7.3.2 Geometric sequences and series

7.3.3 Other finite series

7.3.4 Exercises (14–25)

7.4 Recurrence relations

7.4.1 First-order linear recurrence relations with constant coefficients

7.4.2 Exercises (26–28)

7.4.3 Second-order linear recurrence relations with constant coefficients

7.4.4 Exercises (29–35)

7.5 Limit of a sequence

7.5.1 Convergent sequences

7.5.2 Properties of convergent sequences

7.5.3 Computation of limits

7.5.4 Exercises (36–40)

7.6 Infinite series

7.6.1 Convergence of infinite series

7.6.2 Tests for convergence of positive series

7.6.3 The absolute convergence of general series

7.6.4 Exercises (41–49)

7.7 Power series

7.7.1 Convergence of power series

7.7.2 Special power series

7.7.3 Exercises (50–56)

7.8 Functions of a real variable

7.8.1 Limit of a function of a real variable

7.8.2 One-sided limits

7.8.3 Exercises (57–61)

7.9 Continuity of functions of a real variable

7.9.1 Properties of continuous functions

7.9.2 Continuous and discontinuous functions

7.9.3 Numerical location of zeros

7.9.4 Exercises (62–69)

7.10 Engineering application: insulator chain

7.11 Engineering application: approximating functions and Padé approximants

7.12 Review exercises (1–25)

Chapter 8 Differentiation and Integration

8.1 Introduction

8.2 Differentiation

8.2.1 Rates of change

8.2.2 Definition of a derivative

8.2.3 Interpretation as the slope of a tangent

8.2.4 Differentiable functions

8.2.5 Speed, velocity and acceleration

8.2.6 Exercises (1–7)

8.2.7 Mathematical modelling using derivatives

8.2.8 Exercises (8–18)

8.3 Techniques of differentiation

8.3.1 Basic rules of differentiation

8.3.2 Derivative of xr

8.3.3 Differentiation of polynomial functions

8.3.4 Differentiation of rational functions

8.3.5 Exercises (19–25)

8.3.6 Differentiation of composite functions

8.3.7 Differentiation of inverse functions

8.3.8 Exercises (26–33)

8.3.9 Differentiation of circular functions

8.3.10 Extended form of the chain rule

8.3.11 Exercises (34–37)

8.3.12 Differentiation of exponential and related functions

8.3.13 Exercises (38–46)

8.3.14 Parametric and implicit differentiation

8.3.15 Exercises (47–59)

8.4 Higher derivatives

8.4.1 The second derivative

8.4.2 Exercises (60–72)

8.4.3 Curvature of plane curves

8.4.4 Exercises (73–78)

8.5 Applications to optimization problems

8.5.1 Optimal values

8.5.2 Exercises (79–88)

8.6 Numerical differentiation

8.6.1 The chord approximation

8.6.2 Exercises (89–93)

8.7 Integration

8.7.1 Basic ideas and definitions

8.7.2 Mathematical modelling using integration

8.7.3 Exercises (94–102)

8.7.4 Definite and indefinite integrals

8.7.5 The Fundamental Theorem of Calculus

8.7.6 Exercise (103)

8.8 Techniques of integration

8.8.1 Integration as antiderivative

8.8.2 Integration of piecewise-continuous functions

8.8.3 Exercises (10–109)

8.8.4 Integration by parts

8.8.5 Exercises (110–111)

8.8.6 Integration using the general composite rule

8.8.7 Exercises (112–116)

8.8.8 Integration using partial fractions

8.8.9 Exercises (117–118)

8.8.10 Integration involving the circular and hyperbolic functions

8.8.11 Exercises (119–120)

8.8.12 Integration by substitution

8.8.13 Integration involving (ax2+bx+ c)

8.8.14 Exercises (121–126)

8.9 Applications of integration

8.9.1 Volume of a solid of revolution

8.9.2 Centroid of a plane area

8.9.3 Centre of gravity of a solid of revolution

8.9.4 Mean values

8.9.5 Root mean square values

8.9.6 Arclength and surface area

8.9.7 Moments of inertia

8.9.8 Exercises (127–136)

8.10 Numerical evaluation of integrals

8.10.1 The trapezium rule

8.10.2 Simpson’s rule

8.10.3 Exercises (137–142)

8.11 Engineering application: design of prismatic channels

8.12 Engineering application: harmonic analysis of periodic functions

8.13 Review exercises (1–39)

Chapter 9 Further Calculus

9.1 Introduction

9.2 Improper integrals

9.2.1 Integrand with an infinite discontinuity

9.2.2 Infinite integrals

9.2.3 Exercise (1)

9.3 Some theorems with applications to numerical methods

9.3.1 Rolle’s theorem and the first mean value theorems

9.3.2 Convergence of iterative schemes

9.3.3 Exercises (2–7)

9.4 Taylor’s theorem and related results

9.4.1 Taylor polynomials and Taylor’s theorem

9.4.2 Taylor and Maclaurin series

9.4.3 L’Hôpital’s rule

9.4.4 Exercises (8–20)

9.4.5 Interpolation revisited

9.4.6 Exercises (21–23)

9.4.7 The convergence of iterations revisited

9.4.8 Newton–Raphson procedure

9.4.9 Optimization revisited

9.4.10 Exercises (24–27)

9.4.11 Numerical integration

9.4.12 Exercises (28–31)

9.5 Calculus of vectors

9.5.1 Differentiation and integration of vectors

9.5.2 Exercises (32–36)

9.6 Functions of several variables

9.6.1 Representation of functions of two variables

9.6.2 Partial derivatives

9.6.3 Directional derivatives

9.6.4 Exercises (37–46)

9.6.5 The chain rule

9.6.6 Exercises (47–56)

9.6.7 Successive differentiation

9.6.8 Exercises (57–67)

9.6.9 The total differential and small errors

9.6.10 Exercises (68–75)

9.6.11 Exact differentials

9.6.12 Exercises (76–78)

9.7 Taylor’s theorem for functions of two variables

9.7.1 Taylor’s theorem

9.7.2 Optimization of unconstrained functions

9.7.3 Exercises (79–87)

9.7.4 Optimization of constrained functions

9.7.5 Exercises (88–93)

9.8 Engineering application: deflection of a built-in column

9.9 Engineering application: streamlines in fluid dynamics

9.10 Review exercises (1–35)

Chapter 10 Introduction to Ordinary Differential Equations

10.1 Introduction

10.2 Engineering examples

10.2.1 The take-off run of an aircraft

10.2.2 Domestic hot-water supply

10.2.3 Hydro-electric power generation

10.2.4 Simple electrical circuits

10.3 The classification of ordinary differential equations

10.3.1 Independent and dependent variables

10.3.2 The order of a differential equation

10.3.3 Linear and nonlinear differential equations

10.3.4 Homogeneous and nonhomogeneous equations

10.3.5 Exercises (1–2)

10.4 Solving differential equations

10.4.1 Solution by inspection

10.4.2 General and particular solutions

10.4.3 Boundary and initial conditions

10.4.4 Analytical and numerical solution

10.4.5 Exercises (3–6)

10.5 First-order ordinary differential equations

10.5.1 A geometrical perspective

10.5.2 Exercises (7–10)

10.5.3 Solution of separable differential equations

10.5.4 Exercises (11–17)

10.5.5 Solution of differential equations of form

10.5.6 Exercises (18–22)

10.5.7 Solution of exact differential equations

10.5.8 Exercises (23–30)

10.5.9 Solution of linear differential equations

10.5.10 Solution of the Bernoulli differential equations

10.5.11 Exercises (31–38)

10.6 Numerical solution of first-order ordinary differential equations

10.6.1 A simple solution method: Euler’s method

10.6.2 Analysing Euler’s method

10.6.3 Using numerical methods to solve engineering problems

10.6.4 Exercises (39–45)

10.7 Engineering application: analysis of damper performance

10.8 Linear differential equations

10.8.1 Differential operators

10.8.2 Linear differential equations

10.8.3 Exercises (46–54)

10.9 Linear constant-coefficient differential equations

10.9.1 Linear homogeneous constant-coefficient equations

10.9.2 Exercises (55–61)

10.9.3 Linear nonhomogeneous constant-coefficient equations

10.9.4 Exercises (62–65)

10.10 Engineering application: second-order linear constant-coefficient differential equations

10.10.1 Free oscillations of elastic systems

10.10.2 Free oscillations of damped elastic systems

10.10.3 Forced oscillations of elastic systems

10.10.4 Oscillations in electrical circuits

10.10.5 Exercises (66–73)

10.11 Numerical solution of second- and higher-order differential equations

10.11.1 Numerical solution of coupled first-order equations

10.11.2 State-space representation of higher-order systems

10.11.3 Exercises (74–79)

10.12 Qualitative analysis of second-order differential equations

10.12.1 Phase-plane plots

10.12.2 Exercises (80–81)

10.13 Review exercises (1–35)

Chapter 11 Introduction to Laplace Transforms

11.1 Introduction

11.2 The Laplace transform

11.2.1 Definition and notation

11.2.2 Transforms of simple functions

11.2.3 Existence of the Laplace transform

11.2.4 Properties of the Laplace transform

11.2.5 Table of Laplace transforms

11.2.6 Exercises (1–3)

11.2.7 The inverse transform

11.2.8 Evaluation of inverse transforms

11.2.9 Inversion using the first shift theorem

11.2.10 Exercise (4)

11.3 Solution of differential equations

11.3.1 Transforms of derivatives

11.3.2 Transforms of integrals

11.3.3 Ordinary differential equations

11.3.4 Exercise (5)

11.3.5 Simultaneous differential equations

11.3.6 Exercise (6)

11.4 Engineering applications: electrical circuits and mechanical vibrations

11.4.1 Electrical circuits

11.4.2 Mechanical vibrations

11.4.3 Exercises (7–12)

11.5 Review exercises (1–18)

Chapter 12 Introduction to Fourier Series

12.1 Introduction

12.2 Fourier series expansion

12.2.1 Periodic functions

12.2.2 Fourier’s theorem

12.2.3 The Fourier coefficients

12.2.4 Functions of period 2

12.2.5 Even and odd functions

12.2.6 Even and odd harmonics

12.2.7 Linearity property

12.2.8 Convergence of the Fourier series

12.2.9 Exercises (1–7)

12.2.10 Functions of period T

12.2.11 Exercises (8–13)

12.3 Functions defined over a finite interval

12.3.1 Full-range series

12.3.2 Half-range cosine and sine series

12.3.3 Exercises (14–23)

12.4 Differentiation and integration of Fourier series

12.4.1 Integration of a Fourier series

12.4.2 Differentiation of a Fourier series

12.4.3 Exercises (24–26)

12.5 Engineering application: analysis of a slider–crank mechanism

12.6 Review exercises (1–21)

Chapter 13 Data Handling and Probability Theory

13.1 Introduction

13.2 The raw material of statistics

13.2.1 Experiments and sampling

13.2.2 Data types

13.2.3 Graphs for qualitative data

13.2.4 Histograms of quantitative data

13.2.5 Alternative types of plot for quantitative data

13.2.6 Exercises (1–5)

13.3 Probabilities of random events

13.3.1 Interpretations of probability

13.3.2 Sample space and events

13.3.3 Axioms of probability

13.3.4 Conditional probability

13.3.5 Independence

13.3.6 Exercises (6–23)

13.4 Random variables

13.4.1 Introduction and definition

13.4.2 Discrete random variables

13.4.3 Continuous random variables

13.4.4 Properties of density and distribution functions

13.4.5 Exercises (24–31)

13.4.6 Measures of location and dispersion

13.4.7 Expected values

13.4.8 Independence of random variables

13.4.9 Scaling and adding random variables

13.4.10 Measures from sample data

13.4.11 Exercises (32–48)

13.5 Important practical distributions

13.5.1 The binomial distribution

13.5.2 The Poisson distribution

13.5.3 The normal distribution

13.5.4 The central limit theorem

13.5.5 Normal approximation to the binomial

13.5.6 Random variables for simulation

13.5.7 Exercises (49–65)

13.6 Engineering application: quality control

13.6.1 Attribute control charts

13.6.2 United States standard attribute charts

13.6.3 Exercises (66–67)

13.7 Engineering application: clustering of rare events

13.7.1 Introduction

13.7.2 Survey of near-misses between aircraft

13.7.3 Exercises (68–69)

13.8 Review exercises (1–13)

Appendix I Tables

Al.1 Some useful results

Al.2 Trigonometric identities

Al.3 Derivatives and integrals

Al.4 Some useful standard integrals

Answers to Exercises

Index

Back Cover

## Product information

ASIN : B08HL765LD

Publisher : Pearson; 6th edition (March 11, 2020)

Language : English

Paperback : 1176 pages

ISBN-10 : 1292253495

ISBN-13 : 978-1292253497

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