Engineering Mathematics PDF by K A Stroud

ENGINEERING MATHEMATICS BY K A STROUD pdf

Download Engineering Mathematics PDF by K A StroudEngineering Mathematics: A groundbreaking and comprehensive reference with over 500,000 copies sold since it first debuted in 1970, the new fifth edition of Engineering Mathematics has been thoroughly revised and expanded. An interactive Personal Tutor CD-ROM is included with every book. Buy from Amazon



Providing a broad mathematical survey, this innovative volume covers a full range of topics from the very basic to the advanced. Whether you’re an engineer looking for a useful on-the-job reference or want to improve your mathematical skills, or you are a student who needs an in-depth self-study guide, Engineering Mathematics is sure to come in handy time and time again.

Features Engineering Mathematics PDF by K A Stroud

  • Offers a unique programmed approach that takes users through the mathematics in a step-by-step fashion with a wealth of worked examples and exercises.
  • Contains Quizzes, Learning Outcomes and Can You? Checklists that guide readers through each topic and focus understanding.
  • Updated throughout for the latest calculators and Excel spreadsheets.
  • Ideal as reference or a self-learning manual.

Extra Bonus! Visit Personal Tutor Online at http://www.palgrave.com/stroud, the companion website maintained by this book’s British publisher, where you’ll find hundreds of interactive practice questions and engineering applications questions putting the mathematics in context


PREFACE – Engineering Mathematics PDF by K A Stroud

The purpose of this book is to provide a complete year’s course in
mathematics for those studying in the engineering, technical and
scientific fields. The material has been specially written for courses lead-
ing to

(i) Part I of B.Sc. Engineering Degrees,

(ii) Higher National Diploma and Higher National Certificate in techno-
logical subjects, and for other courses of a comparable level. While formal
proofs are included where necessary to promote understanding, the
emphasis throughout is on providing the student with sound mathematical
skills and with a working knowledge and appreciation of the basic con-
cepts involved. The programmed structure ensures that the book is highly
suited for general class use and for individual self-study, and also provides
a ready means for remedial work or subsequent revision.

The book is the outcome of some eight years’ work undertaken in the
development of programmed learning techniques in the Department of
Mathematics at the Lanchester College of Technology, Coventry. For the
past four years, the whole of the mathematics of the first year of various
Engineering Degree courses has been presented in programmed form, in
conjunction with seminar and tutorial periods. The results obtained have
proved to be highly satisfactory, and further extension and development
of these learning techniques are being pursued. Engineering Mathematics PDF

Each programme has been extensively validated before being produced
in its final form and has consistently reached a success level above 80/80,
i.e. at least 80% of the students have obtained at least 80% of the possible
marks in carefully structured criterion tests. In a research programme,
carried out against control groups receiving the normal lectures, students
working from programmes have attained significantly higher mean scores
than those in the control groups and the spread of marks has been con-
siderably reduced. The general pattern has also been reflected in the results
of the sessional examinations.

The advantages of working at one’s own rate, the intensity of the
student involvement, and the immediate assessment of responses, are well
known to those already acquainted with programmed learning activities.
Programmed learning in the first year of a student’s course at a college or
university provides the additional advantage of bridging the gap between
the rather highly organised aspect of school life and the freer environment
and which puts greater emphasis on personal responsibility for his own pro-
gress which faces every student on entry to the realms of higher education.

Acknowledgement and thanks are due to all those who have assisted
in any way in the development of the work, including those who have
been actively engaged in validation processes. I especially wish to
record my sincere lhanks for the continued encouragement and support
which I received from my present Head of Department at the College,

Mr. J. E. Sellars, M.Sc, A.F.R.Ae.S., F.I.M.A., and also from
Mr. R. Wooldridge, M.C., B.Sc, F.I.M.A., formerly Head of Department,
now Principal of Derby College of Technology. Acknowledgement is also
made of the many sources, too numerous to list, from which the selected
examples quoted in the programmes have been gleaned over the years.
Their inclusion contributes in no small way to the success of the work.

K. A. Stroud

Table Of Content

Preface v

Hints on using the book xii

Useful background information xiii

Programme 1 : Complex Numbers, Part 1

Introduction: The symbol j; powers ofj; complex numbers 1

Multiplication of complex numbers

Equal complex numbers

Graphical representation of a complex number

Graphical addition of complex numbers

Polar form of a complex number

Exponential form of a complex number

Test exercise I

Further problems I

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Programme 2: Complex Numbers, Part 2

Introduction 37

Loci problems
Test exercise II
Further problems II

Programme 3: Hyperbolic Functions

Introduction 73

Graphs of hyperbolic functions

Evaluation of hyperbolic functions

Inverse hyperbolic functions

Log form of the inverse hyperbolic functions

Hyperbolic identities

Trig, identities and hyperbolic identities

Relationship between trigonometric & hyperbolic functions

Test exercise III

Further problems HI

Programme 4: Determinants

Determinants \q\

Determinants of the third order

Evaluation of a third order determinant

Simultaneous equations in three unknowns

Consistency of a set of equations

Properties of determinants

vii

Test exercise IV
Further problems IV

Programme 5: Vectors

Introduction: Scalar and vector quantities 141

Vector representation

Two equal vectors

Types of vectors

Addition of vectors

Components of a given vector

Components of a vector in terms of unit vectors

Vectors in space

Direction cosines

Scalar product of two vectors

Vector product of two vectors

Angle between two vectors

Direction ratios

Summary

Test exercise V

Further problems V

^/Programme 6: Differentiation

Standard differential coefficients 1 7 1

Functions of a function

Logarithmic differentiation

Implicit functions

Parametric equations

Test exercise VI

Further problems VI

Programme 7: Differentiation Applications, Part 1

Equation of a straight line 195

Centre of curvature
Test exercise VII
Further problems VII

Programme 8: Differentiation Applications, Part 2

^-Inverse trigonometrical functions 223

Differentiation of inverse trig, functions

^Differentiation coefficients of inverse hyperbolic functions
— • Maximum and minimum values (turning points J
Test exercise VIII
Further problems VIII

Programme 9: Partial Differentiation, Part 1

Partial differentiation 25 1

Small increments
Test exercise IX
Further problems IX

Programme 10: Partial Differentiation, Part 2

Partial differentiation 277

Rates of change problems
Change of variables
Test exercise X
Further problems X

Programme 1 1 : Series, Part 1

Series 297

Arithmetic and geometric means

Series of powers of natural numbers

Infinite series: limiting values

Convergent and divergent series

Tests for convergence; absolute convergence

Test exercise XI

Further problems XI

Programme 1 2: Series, Part 2

— Power series, Maclaurin ‘s series 327

Standard series
The binomial series
Approximate values
Limiting values
Test exercise XII
Further problems XII

^Programme 13: Integration, Part 1

Introduction 357

Standard integrals

Functions of a linear function

Integrals of the form

Integration of products – integration by parts

Integration by partial fractions

Integration of trigonometrical functions .

Test exercise XIII

Further problems XIII

Programme 14: Integration, Part 2

Test exercise XIV 389

Further problems XIV

Programme 15: Reduction Formulae

Test exercise XV 419

Further problems XV

1/^Programme 16: Integration Applications, Part 1

x^Parametric equations 435

\^Mean values
*-^k.m.s. values

Summary sheet

Test exercise XVI

Further problems XVI

Programme 17: Integration Applications, Part 2

Introduction 457

Volumes of solids of revolution
Centroid of a plane figure
Centre of gravity of a solid of revolution
Lengths of curves

Lengths of curves – parametric equations
Surfaces of revolution

Surfaces of revolution – parametric equations
Rules of Pappus
Revision summary
Test exercise XVII
Further problems XVII

Programme 18: Integration Applications, Part 3

Moments of inertia 483

Radius of gyration

Parallel axes theorem

Perpendicular axes theorem

Useful standard results

Second moment of area

Composite figures

Centres of pressure

Depth of centre of pressure

Test exercise XVIII

Further problems XVIII

^-”Programme 19: Approximate Integration

t- Introduction 517

j. Approximate integration
1 Method 1 — by series

s/ftethod 2 – Simpson ‘s rule
\ftoof of Simpson ‘s rule

Test exercise XIX

Further problems XIX

Programme 20: Polar Co-ordinates Systems

Introduction to polar co-ordinates 539

Polar curves
Standard polar curves
Test exercise XX
Further problems XX

Programme 21: Multiple Integrals

Summation in two directions 565

Double integrals: triple integrals

Applications

Alternative notation

Determination of volumes by multiple integrals

Test exercise XXI

Further problems XXI

Programme 22: First Order Differential Equations

Introduction 593

Formation of differential equations

Solution of differential equations

Method 1 – by direct integration

Method 2 – by separating the variables

Method 3 — homogeneous equations: by substituting y = vx

Method 4 – linear equations: use of integrating factor

Test exercise XXII

Further problems XXII

Programme 23: Second Order Differential Equations with Constant
Coefficients

Test exercise XXIII 637

Further problems XXIII

Programme 24: Operator D Methods

The operator D 70 1

Inverse operator 7/D

Solution of differential equations by operator D methods

Special cases

Test exercise XXIV

Further problems XXIV

Answers 707

Index 744

xi

HINTS ON USING THE BOOK – Engineering Mathematics PDF by K A Stroud

This book contains twenty-four lessons, each of which has been
written in such a way as to make learning more effective and more
interesting. It is almost like having a personal tutor, for you proceed at
your own rate of learning and any difficulties you may have are cleared
before you have the chance to practise incorrect ideas or techniques.

You will find that each programme is divided into sections called
frames, each of which normally occupies half a page. When you start a
programme, begin at frame 1. Read each frame carefully and carry out
any instructions or exercise which you are asked to do. In almost every
frame, you are required to make a response of some kind, testing your
understanding of the information in the frame, and you can immediately
compare your answer with the correct answer given in the next frame. To
obtain the greatest benefit, you are strongly advised to cover up the
following frame until you have made your response. When a series of dots
occurs, you are expected to supply the missing word, phrase, or number.
At every stage, you will be guided along the right path. There is no need
to hurry: read the frames carefully and follow the directions exactly. In
this way, you must learn. Engineering Mathematics PDF

At the end of each programme, you will find a short Test Exercise.
This is set directly on what you have learned in the lesson: the questions
are straightforward and contain no tricks. To provide you with the
necessary practice, a set of Further Problems is also included: do as many
of these problems as you can. Remember that in mathematics, as in many
other situations, practice makes perfect — or more nearly so.

Even if you feel you have done some of the topics before, work
steadily through each programme: it will serve as useful revision and fill
in any gaps in your knowledge that you may have.

Related – Engineering Mathematics PDF by K A Stroud

Author

K. A.Stroud was formerly Principal Lecturer in the Department of Mathematics at Coventry University, UK. He is also the author of Foundation Mathematics and Advanced Engineering Mathematics, companion volumes to this book.

Dexter J. Booth was formerly Principal Lecturer in the School of Computing and Engineering at the University of Huddersfield, UK. He is the author of several mathematics textbooks and is co-author of Foundation Mathematics and Advanced Engineering Mathematics.

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