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# Introduction to Vector Analysis

by Harry F. Davis and Arthur David Snider

Introduction to Vector Analysis, 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

1. Chapter 1: Vector Algebra
1. 1.1 Definitions
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
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
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: Historical Notes
7. Appendix B: Two Theorems of Advanced Calculus
8. Appendix C: 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: The Vector Equations of Electromagnetism
1. D.1 Electrostatics
10. Appendix E: Constrained Optimization