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A BRIEF ON TENSOR ANALYSIS (UNDERGRADUATE TEXTS IN By James G. Simmonds *VG+*
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- Buy It NowA BRIEF ON TENSOR ANALYSIS (UNDERGRADUATE TEXTS IN By James G. Simmonds *VG+*
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Item specifics
- Condition
- Book Title
- A Brief on Tensor Analysis (Undergraduate Texts in Mathematics)
- Item Height
- 9.21 inches
- ISBN-10
- 038794088X
- ISBN
- 9780387940885
- Subject Area
- Mathematics
- Publication Name
- Brief on Tensor Analysis
- Publisher
- Springer New York
- Item Length
- 9.3 in
- Subject
- Calculus, Mathematical Analysis
- Publication Year
- 1993
- Series
- Undergraduate Texts in Mathematics Ser.
- Type
- Textbook
- Format
- Hardcover
- Language
- English
- Item Weight
- 28.6 Oz
- Item Width
- 6.1 in
- Number of Pages
- Xiv, 114 Pages
About this product
Product Identifiers
Publisher
Springer New York
ISBN-10
038794088X
ISBN-13
9780387940885
eBay Product ID (ePID)
5038293279
Product Key Features
Number of Pages
Xiv, 114 Pages
Language
English
Publication Name
Brief on Tensor Analysis
Subject
Calculus, Mathematical Analysis
Publication Year
1993
Type
Textbook
Subject Area
Mathematics
Series
Undergraduate Texts in Mathematics Ser.
Format
Hardcover
Dimensions
Item Weight
28.6 Oz
Item Length
9.3 in
Item Width
6.1 in
Additional Product Features
Edition Number
2
Intended Audience
Scholarly & Professional
TitleLeading
A
Number of Volumes
1 vol.
Illustrated
Yes
Edition Description
Reprint,Revised edition
Table Of Content
I Introduction: Vectors and Tensors.- Three-Dimensional Euclidean Space.- Directed Line Segments.- Addition of Two Vectors.- Multiplication of a Vector v by a Scalar '.- Things That Vectors May Represent.- Cartesian Coordinates.- The Dot Product.- Cartesian Base Vectors.- The Interpretation of Vector Addition.- The Cross Product.- Alternative Interpretation of the Dot and Cross Product. Tensors.- Definitions.- The Cartesian Components of a Second Order Tensor.- The Cartesian Basis for Second Order Tensors.- Exercises.- II General Bases and Tensor Notation.- General Bases.- The Jacobian of a Basis Is Nonzero.- The Summation Convention.- Computing the Dot Product in a General Basis.- Reciprocal Base Vectors.- The Roof (Contravariant) and Cellar (Covariant) Components of a Vector.- Simplification of the Component Form of the Dot Product in a General Basis.- Computing the Cross Product in a General Basis.- A Second Order Tensor Has Four Sets of Components in General.- Change of Basis.- Exercises.- III Newton's Law and Tensor Calculus.- Rigid Bodies.- New Conservation Laws.- Nomenclature.- Newton's Law in Cartesian Components.- Newton's Law in Plane Polar Coordinates.- The Physical Components of a Vector.- The Christoffel Symbols.- General Three-Dimensional Coordinates.- Newton's Law in General Coordinates.- Computation of the Christoffel Symbols.- An Alternative Formula for Computing the Christoffel Symbols.- A Change of Coordinates.- Transformation of the Christoffel Symbols.- Exercises.- IV The Gradient, the Del Operator, Covariant Differentiation, and the Divergence Theorem.- The Gradient.- Linear and Nonlinear Eigenvalue Problems.- The Del Operator.- The Divergence, Curl, and Gradient of a Vector Field.- The Invariance of ? · v, ? × v, and ?v.- The Covariant Derivative.- The Component Forms of ? · v, ? × v, and ?v.- The Kinematics of Continuum Mechanics.- The Divergence Theorem.- Differential Geometry.- Exercises.
Synopsis
This new edition is intended for third and fourth year undergraduates in Engineering, Physics, Mathematics, and the Applied Sciences, and can serve as a springboard for further work in Continuum Mechanics or General Relativity. Starting from a basic knowledge of calculus and matrix algebra, together with fundamental ideas from mechanics and geometry, the text gradually develops the tools for formulating and manipulating the field equations of Continuum Mechanics. The mathematics of tensor analysis is introduced in well-separated stages: the concept of a tensor as an operator; the representation of a tensor in terms of its Cartesian components; the components of a tensor relative to a general basis, tensor notation, and finally, tensor, There are three changes in the second edition. First, with the help of readers and colleagues-thanks to all-I have corrected typographical errors and made minor changes in substance and style. Second, I have added a fewmore Exercises,especially at the end ofChapter4.Third, I have appended a section on Differential Geometry, the essential mathematical tool in the study of two-dimensional structural shells and four-dimensional general relativity. JAMES G. SIMMONDS vii Preface to the First Edition When I was an undergraduate, working as a co-op student at North Ameri can Aviation, I tried to learn something about tensors. In the Aeronautical Engineering Department at MIT, I had just finished an introductory course in classical mechanics that so impressed me that to this day I cannot watch a plane in flight-especially in a turn-without imaging it bristling with vec tors. Near the end of the course the professor showed that, if an airplane is treated as a rigid body, there arises a mysterious collection of rather simple looking integrals called the components of the moment of inertia tensor., There are three changes in the second edition. First, with the help of readers and colleagues-thanks to all-I have corrected typographical errors and made minor changes in substance and style. Second, I have added a fewmore Exercises, especially at the end ofChapter4.Third, I have appended a section on Differential Geometry, the essential mathematical tool in the study of two-dimensional structural shells and four-dimensional general relativity. JAMES G. SIMMONDS vii Preface to the First Edition When I was an undergraduate, working as a co-op student at North Ameri- can Aviation, I tried to learn something about tensors. In the Aeronautical Engineering Department at MIT, I had just finished an introductory course in classical mechanics that so impressed me that to this day I cannot watch a plane in flight-especially in a turn-without imaging it bristling with vec- tors. Near the end of the course the professor showed that, if an airplane is treated as a rigid body, there arises a mysterious collection of rather simple- looking integrals called the components of the moment of inertia tensor.
LC Classification Number
QA299.6-433
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