Front Cover -- Elementary Vector Calculus and its Applications with MATLAB Programming -- Contents -- Preface -- List of Figures -- 1 Basic Concept of Vectors and Scalars -- 1.1 Introduction and Importance -- 1.2 Representation of Vectors -- 1.3 Position Vector and Vector Components -- 1.4 Modulus or Absolute Value of a Vector -- 1.5 Zero Vector and Unit Vector -- 1.6 Unit Vectors in the Direction of Axes -- 1.7 Representation of a Vector in terms of Unit Vectors -- 1.8 Addition and Subtraction of Vectors -- 1.9 Product of a Vector with a Scalar -- 1.10 Direction of a Vector -- 1.11 Collinear and Coplanar Vectors -- 1.11.1 Collinear Vectors -- 1.11.2 Coplanar Vectors -- 1.12 Geometric Representation of a Vector Sum -- 1.12.1 Law of Parallelogram of Vectors -- 1.12.2 Law of Triangle of Vectors -- 1.12.3 Properties of Addition of Vectors -- 1.12.4 Properties of Scalar Product -- 1.12.5 Expression of Any Vector in Terms of the Vectors Associated with its Initial Point and Terminal Point -- 1.12.6 Expression of Any Vector in Terms of Position Vectors -- 1.13 Direction Cosines of a Vector -- 1.14 Exercise -- 2 Scalar and Vector Products -- 2.1 Scalar Product, or Dot Product, or Inner Product -- 2.2 The Measure of Angle Between two Vectors and Projections -- 2.2.1 Properties of a Dot Product -- 2.3 Vector Product or Cross Product or Outer Product of Two Vectors -- 2.4 Geometric Interpretation of a Vector Product -- 2.4.1 Properties of a Vector Product -- 2.5 Application of Scalar and Vector Products -- 2.5.1 Work Done by a Force -- 2.5.2 Moment of a Force About a Point -- 2.6 Exercise -- 3 Vector Differential Calculus -- 3.1 Introduction -- 3.2 Vector and Scalar Functions and Fields -- 3.2.1 Scalar Function and Field -- 3.2.2 Vector Function and Field -- 3.2.3 Level Surfaces -- 3.3 Curve and Arc Length -- 3.3.1 Parametric Representation of Curves.

3.3.2 Curves with Tangent Vector -- 3.3.2.1 Tangent Vector -- 3.3.2.2 Important Concepts -- 3.3.3 Arc Length -- 3.3.3.1 Unit Tangent Vector -- 3.4 Curvature and Torsion -- 3.4.1 Formulas for Curvature and Torsion -- 3.5 Vector Differentiation -- 3.6 Gradient of a Scalar Field and Directional Derivative -- 3.6.1 Gradient of a Scalar Field -- 3.6.1.1 Properties of Gradient -- 3.6.2 Directional Derivative -- 3.6.2.1 Properties of Gradient -- 3.6.3 Equations of Tangent and Normal to the Level Curves -- 3.6.4 Equation of the Tangent Planes and Normal Lines to the Surfaces -- 3.7 Divergence and Curl of a Vector Field -- 3.7.1 Divergence of a Vector Field -- 3.7.1.1 Physical Interpretation of Divergence -- 3.7.2 Curl of a Vector Field -- 3.7.2.1 Physical Interpretation of Curl -- 3.7.3 Formulae for grad, div, curl Involving Operator -- 3.7.3.1 Formulae for grad, div, curl Involving Operator Once -- 3.7.3.2 Formulae for grad, div, curl Involving Operator Twice -- 3.8 Exercise -- 4 Vector Integral Calculus -- 4.1 Introduction -- 4.2 Line Integrals -- 4.2.1 Circulation -- 4.2.2 Work Done by a Force -- 4.3 Path Independence of Line Integrals -- 4.3.1 Theorem: Independent of Path -- 4.4 Surface Integrals -- 4.4.1 Flux -- 4.4.2 Evaluation of Surface Integral -- 4.4.2.1 Component form of Surface Integral -- 4.5 Volume Integrals -- 4.5.1 Component Form of Volume Integral -- 4.6 Exercise -- 5 Theorem, Stokes Theorem, and Gauss' Theorem -- 5.1 Green's Theorem (in the Plane) -- 5.1.1 Area of the Plane Region -- 5.2 Stokes' Theorem -- 5.3 Gauss' Divergence Theorem -- 5.4 Exercise -- 6 MATLAB Programming -- 6.1 Basic of MATLAB Programming -- 6.1.1 Basic of MATLAB Programming -- 6.1.1.1 Introductory MATLAB programmes -- 6.1.1.2 Representation of a Vector in MATLAB -- 6.1.1.3 Representation of a Matrix in MATLAB.

6.2 Some Miscellaneous Examples using MATLAB Programming -- References -- Index -- About the Authors -- Back Cover.