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Elementary Vector Calculus and Its Applications with MATLAB Programming.

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Sir Isaac Newton, one of the greatest scientists and mathematicians of all time, introduced the notion of a vector to define the existence of gravitational forces, the motion of the planets around the sun, and the motion of the moon around the earth. Vector calculus is a fundamental scientific tool...

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Bibliographic Details
Online Access: Full Text (via Taylor & Francis)
Main Author: Shah, Nita H.
Other Authors: Panchal, Jitendra
Format: eBook
Language:English
Published: Milton : River Publishers, 2023.
Series:River Publishers Series in Mathematical, Statistical and Computational Modelling for Engineering Ser.
Subjects:
MATLAB.
Vector analysis.
Table of Contents:
  • Cover
  • Half Title
  • Series Page
  • Title Page
  • Copyright Page
  • Table of Contents
  • Preface
  • List of Figures
  • Chapter 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
  • Chapter 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
  • Chapter 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.

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