Schaum’s Outlines Vector Analysis, 2nd Edition, is a comprehensive and accessible study guide for students studying vector analysis. This book is designed for undergraduate students in mathematics, physics, engineering, and other related disciplines, and provides a solid foundation in the concepts and techniques of vector analysis.
The 2nd edition of Schaums Outlines Vector Analysis has been updated to reflect the latest advancements in the field and includes a wealth of new and improved examples and exercises. The author, Murray R Spiegel, is known for his clear and concise writing style, which makes the material easy to understand and follow.
TABLE OF CONTENTS
CHAPTER 1 VECTORS AND SCALARS
- Introduction
- Vector Algebra
- Unit Vectors
- Rectangular Unit
- Vectors i, j, k
- Linear Dependence and Linear Independence
- Scalar Field
- Vector Field
- Vector Space Rn
CHAPTER 2 THE DOT AND CROSS PRODUCT
- Introduction
- Dot or Scalar Product
- Cross Product
- Triple Products
- Reciprocal Sets of Vectors
CHAPTER 3 VECTOR DIFFERENTIATION
- Introduction
- Ordinary Derivatives of Vector-Valued Functions
- Continuity and Differentiability
- Partial Derivative of Vectors
- Differential Geometry
CHAPTER 4 GRADIENT, DIVERGENCE, CURL
- Introduction
- Gradient
- Divergence
- Curl
- Formulas Involving
- Invariance
CHAPTER 5 VECTOR INTEGRATION
- Introduction
- Ordinary Integrals of Vector-Valued Functions
- Line Integrals
- Surface Integrals
- Volume Integrals
CHAPTER 6 DIVERGENCE THEOREM, STOKES’ THEOREM, AND RELATED INTEGRAL THEOREMS
- Introduction
- Main Theorems
- Related Integral Theorems
CHAPTER 7 CURVILINEAR COORDINATES
- Introduction
- Transformation of Coordinates
- Orthogonal Curvilinear Coordinates
- Unit Vectors in Curvilinear Systems
- Arc Length
- and Volume Elements
- Gradient, Divergence, Curl
- Special Orthogonal Coordinate Systems
One of the strengths of Schaums Outlines Vector Analysis is its concise and straightforward presentation of the material, which helps students quickly grasp the key concepts and techniques of vector analysis. Additionally, the book includes numerous solved problems, which provide opportunities for students to practice what they have learned and apply the concepts covered in the book to new problems.
Whether you are a student looking to improve your understanding of vector analysis or a professional seeking to refresh your knowledge of the subject, Schaums Outlines Vector Analysis, 2nd Edition, is an excellent resource that is sure to meet your needs. With its comprehensive coverage of the subject and its clear and concise presentation, this study guide is sure to provide a valuable resource for anyone interested in learning about vector analysis.
