عنوان

Vectors in Physics and Engineering.

(Number (ISBN

135140556X

(Number (ISBN

9781351405560

Erroneous ISBN

9781138442672

Title Proper

Vectors in Physics and Engineering.

General Material Designation

[Book]

Place of Publication, Distribution, etc.

Milton :

Name of Publisher, Distributor, etc.

Routledge,

Date of Publication, Distribution, etc.

2019.

Date of Publication, Distribution, etc.

©1996.

Specific Material Designation and Extent of Item

1 online resource (299 pages)

Text of Note

Cover -- Half Title -- Title Page -- Copyright Page -- Contents -- Preface -- 1 Vector algebra I: Scaling and adding vectors -- 1.1 INTRODUCTION TO SCALARS,NUMBERS AND VECTORS -- 1.1.1 Scalars and numbers -- 1.1.2 Introducing vectors -- 1.1.3 Displacements and arrows -- 1.1.4 Vector notation -- 1.2 SCALING VECTORS AND UNIT VECTORS -- 1.2.1 Scaling a vector or multiplication of a vector by a number -- 1.2.2 Unit vectors -- 1.3 VECTOR ADDITION-THE TRIANGLE ADDITION RULE -- 1.4 LINEAR COMBINATIONS OF VECTORS -- 1.5 CARTESIAN VECTORS -- 1.5.1 Cartesian coordinates of a point -- a review -- 1.5.2 Cartesian unit vectors and cartesian components of a vector -- 1.6 MAGNITUDES AND DIRECTIONS OF CARTESIAN VECTORS -- 1.7 SCALING AND ADDING CARTESIAN VECTORS -- 1.8 VECTORS IN SCIENCE AND ENGINEERING -- 1.8.1 Definition of a vector and evidence for vector behaviour -- 1.8.2 Vector problems in science and engineering -- 2 Vector algebra II: Scalar products and vector products -- 2.1 THE SCALAR PRODUCT -- 2.1.1 Definition of the scalar product and projections -- 2.1.2 The scalar product in vector algebra -- 2.2 CARTESIAN FORM OF THE SCALAR PRODUCT -- 2.3 THE ANGLE BETWEEN TWO VECTORS -- 2.4 THE VECTOR PRODUCT -- 2.4.1 Definition of the vector product -- 2.4.2 The vector product in vector algebra -- 2.5 CARTESIAN FORM OF THE VECTOR PRODUCT -- 2.6 TRIPLE PRODUCTS OF VECTORS -- 2.6.1 The scalar triple product -- 2.6.2 The vector triple product -- 2.7 SCALAR AND VECTOR PRODUCTS IN SCIENCE AND ENGINEERING -- 2.7.1 Background summary: Forces, torque and equilibrium -- 2.7.2 Background summary: Work and energy -- 2.7.3 Background summary: Energy and torque on dipoles in electric and magnetic fields -- 3 Time-dependent vectors -- 3.1 INTRODUCING VECTOR FUNCTIONS -- 3.1.1 Scalar functions -- a review -- 3.1.2 Vector functions of time.

Text of Note

3.2 DIFFERENTIATING VECTOR FUNCTIONS -- DEFINITIONS OF VELOCITY AND ACCELERATION -- 3.2.1 Differentiation of a scalar function -- a review -- 3.2.2 Differentiation of a vector function -- 3.2.3 Definitions of velocity and acceleration -- 3.3 RULES OF DIFFERENTIATION OF VECTOR FUNCTIONS -- 3.4 ROTATIONAL MOTION-THE ANGULAR VELOCITY VECTOR -- 3.5 ROTATING VECTORS OF CONSTANT MAGNITUDE -- 3.6 APPLICATION TO RELATIVE MOTION AND INERTIAL FORCES -- 3.6.1 Relative translational motion and inertial forces -- 3.6.2 Relative rotational motion and inertial forces -- 4 Scalar and vector fields -- 4.1 PICTORIAL REPRESENTATIONS OF FIELDS -- 4.1.1 Scalar field contours -- 4.1.2 Vector field lines -- 4.2 SCALAR FIELD FUNCTIONS -- 4.2.1 Specifying scalar field functions -- 4.2.2 Cartesian scalar fields -- 4.2.3 Graphs and contours -- 4.3 VECTOR FIELD FUNCTIONS -- 4.3.1 Specifying vector field functions -- 4.3.2 Cartesian vector fields -- 4.3.3 Equation of a field line -- 4.4 POLAR COORDINATE SYSTEMS -- 4.4.1 Symmetries and coordinate systems -- 4.4.2 Cylindrical polar coordinate systems -- 4.4.3 Spherical polar coordinate systems -- 4.5 INTRODUCING FLUX AND CIRCULATION -- 4.5.1 Flux of a vector field -- 4.5.2 Circulation of a vector field -- 5 Differentiating fields -- 5.1 DIRECTIONAL DERIVATIVES AND PARTIAL DERIVATIVES -- 5.2 GRADIENT OF A SCALAR FIELD -- 5.2.1 Introducing gradient -- 5.2.2 Calculating gradients -- 5.2.3 Gradient and physical law -- 5.3 DIVERGENCE OF A VECTOR FIELD -- 5.3.1 Introducing divergence -- 5.3.2 Calculating divergence -- 5.3.3 Divergence and physical law -- 5.4 CURL OF A VECTOR FIELD -- 5.4.1 Introducing curl -- 5.4.2 Calculating curl -- 5.4.3 Curl and physical law -- 5.5 THE VECTOR DIFFERENTIAL OPERATOR "DEL -- 5.5.1 Introducing differential operators -- 5.5.2 The "del" operator -- 5.5.3 The Laplacian operator.

Text of Note

5.5.4 Vector-field identities -- 6 Integrating fields -- 6.1 DEFINITE INTEGRALS-A REVIEW -- 6.2 LINE INTEGRALS -- 6.2.1 Defining the scalar line integral -- 6.2.2 Evaluating simple line integrals -- 6.3 LINE INTEGRALS ALONG PARAMETERISED CURVES -- 6.3.1 Parameterisation of a curve -- 6.3.2 A systematic technique for evaluating line integrals -- 6.4 CONSERVATIVE FIELDS -- 6.5 SURFACE INTEGRALS -- 6.5.1 Introducing surface integrals -- 6.5.2 Expressing surface integrals as double integrals and evaluating them -- 6.6 STOKES'S THEOREM -- 6.6.1 An integral form of curl -- 6.6.2 Deriving Stokes's theorem -- 6.6.3 Using Stokes's theorem -- 6.7 VOLUME INTEGRALS -- 6.8 GAUSS'S THEOREM (THE DIVERGENCE THEOREM) -- Appendix A: SI units and physical constants -- Appendix B: Mathematical conventions and useful results -- Answers to selected Problems -- Index.

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8

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Title

Vectors in Physics and Engineering

International Standard Book Number

9781138442672

Durrant, Alan.

Date of Transaction

20200822180024.0

Cataloguing Rules (Descriptive Conventions))

rda

Electronic name

[Book]

Y