Introduction to Vector Analysis

by Harry F. Davis and Arthur David Snider

Introduction to Vector Analysis This book, in its seventh edition, has always enjoyed a reputation for expository excellence. The text is both a learning manual as well as a reference manual. It is based on a dual geometric-analytic approach to each topic of discussion. The concepts and theorems are first visualized and understood heuristically, and then are reduced to an algebra-calculus framework for computation or mathematical scrutiny. The text is unique in its presentation of the Laplacian and the vector potential and can be used at several levels. The first four chapters constitute a compact one-semester introduction to the subject. Chapter five and the appendices address deeper topics in differential geometry, potential theory, physics, and engineering.

Formats:Textbook, Student Solutions Manual

Product ISBN
Textbook 978-0-697-16099-7
Student Solutions Manual 978-1-932628-31-9

Table of Contents

  1. Chapter 1: Vector Algebra
    1. 1.1 Definitions
    2. 1.2 Addition and Subtraction
    3. 1.3 Multiplication of Vectors by Numbers
    4. 1.4 Cartesian Coordinates
    5. 1.5 Space Vectors
    6. 1.6 Types of Vectors
    7. 1.7 Some Problems in Geometry
    8. 1.8 Equations of a Line
    9. 1.9 Scalar Products
    10. 1.10 Equations of a Plane
    11. 1.11 Orientation
    12. 1.12 Vector Products
    13. 1.13 Triple Scalar Products
    14. 1.14 Vector Identities
    15. 1.15 Optional Reading: Tensor Notation
  2. Chapter 2: Vector Functions of a Single Variable
    1. 2.1 Differentiation
    2. 2.2 Space Curves, Velocities, and Tangents
    3. 2.3 Acceleration and Curvature
    4. 2.4 Planar Motion in Polar Coordinates
    5. 2.5 Optional Reading: Tensor Notation
  3. Chapter 3: Scalar and Vector Fields
    1. 3.1 Scalar Fields: Isotomic Surfaces: Gradients
    2. 3.2 Vector Fields and Flow Lines
    3. 3.3 Divergence
    4. 3.4 Curl
    5. 3.5 Del Notation
    6. 3.6 The Laplacian
    7. 3.7 Optional Reading: Dyadics: Taylor Polynomials
    8. 3.8 Vector Identities
    9. 3.9 Optional Reading: Tensor Notation
    10. 3.10 Cylindrical and Spherical Coordinates
    11. 3.11 Optional Reading: Orthogonal Curvilinear Coordinates
  4. Chapter 4: Lines, Surface, and Volume Integrals
    1. 4.1 Line Integrals
    2. 4.2 Domains: Simply Connected Domains
    3. 4.3 Conservative Fields: The Potential Function
    4. 4.4 Conservative Fields: Irrotational Fields
    5. 4.5 Optional Reading: Vector Potentials and Solendoidal Fields
    6. 4.6 Oriented Surfaces
    7. 4.7 Surface Integrals
    8. 4.8 Volume Integrals
    9. 4.9 Introduction to the Divergence Theorem and Stokes' Theorem
    10. 4.10 Optional Reading: Introduction to the Transport Theorems
  5. Chapter 5: Advanced Topics
    1. 5.1 The Divergence Theorem
    2. 5.2 Green's Formuals: Laplaces's and Poisson's Equations
    3. 5.3 The Fundamental Theorem of Vector Analysis
    4. 5.4 The Point-Slope Form
    5. 5.5 Stoke's Theorem
    6. 5.6 The Transport Theorems
    7. 5.7 Matrix Techniques in Vector Analysis
    8. 5.8 Linear Orthogonal Transformations
    9. 5.9 Systems of Linear Equations: Solutions by Addition
    10. 5.10 Applications: Distance-Rate-Time, Number Problems, Amounts, and Costs
    11. 5.11 Applications: Interest and Mixture
  6. Appendix A
    1. Historical Notes
  7. Appendix B
    1. Two Theorems of Advanced Calculus
  8. Appendix C
    1. The Vector Equations of Classical Mechanics
      1. C.1 Mechanics of Particles and Systems of Particles
      2. C.2 Mechanics of Rigid Bodies
  9. Appendix D
    1. The Vector Equations of Electromagnetism
      1. D.1 Electrostatics
  10. Appendix E
    1. Constrained Optimization
  11. Selected Answers and Notes
  12. Index