Anton & Rorres' Elementary Linear Algebra  (English, Undefined, Kanani Kailas K.)

This book is an adaptation of the ninth edition of the best-selling title in linear algebra, Elementary Linear Algebra by Howard Anton and Chris Rorres. Noted for its expository style and clarity of presentation, this text presents an elementary treatment of the subject and addresses the changing needs of a new generation of students. The aim is to present the fundamentals of linear algebra in the clearest possible way - pedagogy being the main consideration.

Four new chapters have been included to cover the prescribed syllabus. The book includes numerous solved and unsolved problems. A section 'Technology Exercises' is also included for further exploration of the chapter's contents.

About The Author

Dr. Kailas K. Kanani is a PhD and is working as Assistant Professor in Mathematics, L. E. College, Morbi, Gujarat. She has 10 years of teaching experience. Dr. Kanani has 16 publications in different national and international journals/proceedings to her credit.

Dr. Gaurang V. Ghodasara is a PhD and is Assistant Professor in Mathematics, L. E. College, Morbi, Gujarat. He has 7 years of experience in this field. Dr. Ghodasara has 7 publications in different national and international journals/proceedings to his credit.

Table of Contents

Chapter 1A Parameterization of Curves, Arc Length and Surface Area
1A.1 Parameterization of Plane Curve
1A.2 Length of an Arc
1A.3 Length of an Arc in Polar Coordinates
1A.4 Parameterization of Surfaces
1A.5 Surface of Solid of Revolution
Chapter 1B Vector Algebra
1B.1 Unit Vector
1B.2 Components of a Vector
1B.3 Position Vector
1B.4 Product of Two Vectors
1B.5 Product of Three Vectors
Chapter 1C Vector Differential Calculus
1C.1 Vector Function
1C.2 Differentiation of a Vector Function
1C.3 General Rules for Differentiation of Vector Function
1C.4 Geometrical Interpretation of
1C.5 Velocity and Acceleration
1C.6 Scalar and Vector Point Functions
1C.7 Vector Differential Operator
1C.8 Gradient of a Scalar Function
1C.9 Geometrical Interpretation of Gradient
1C.10 Direction Derivative
1C.11 Properties of Gradient
1C.12 Divergence of a Vector Point Function
1C.13 Physical Interpretation of Divergence
1C.14 Curl of Vector Point Function
1C.15 Physical Interpretation of Curl
1C.16 Properties of Divergence and Curl
1C.17 Repeated Operations by ?
1C.18 Conservative Vector Field and Scalar Potential
Chapter 1D Vector Integral Calculus
1D.1 Integration of Vector Functions
1D.2 Line Integral
1D.3 Surface Integral
1D.4 Volume Integral
1D.5 Green's Theorem in the Plane
1D.6 Stokes Theorem
1D.7 Gauss Theorem of Divergence
Chapter 1 Systems of Linear Equations and Matrices
1.1 Introduction to Systems of Linear Equations
1.2 Gaussian Elimination
1.3 Matrices and Matrix Operations
1.4 Inverses; Rules of Matrix Arithmetic
1.5 Elementary Matrices and a Method for Finding A-1
1.6 Further Results on Systems of Equations and Invertibility
1.7 Diagonal, Triangular, and Symmetric Matrices
Chapter 2 Determinants
2.1 Determinants by Cofactor Expansion
2.2 Evaluating Determinants by Row Reduction
2.3 Properties of the Determinant Function
2.4 A Combinatorial Approach to Determinants
Chapter 3 Vectors in 2-Space and 3-Space
3.1 Introduction to Vectors (Geometric)
3.2 Norm of a Vector; Vector Arithmetic
3.3 Dot Product; Projections
3.4 Cross Product
3.5 Lines and Planes in 3-Space
Chapter 4 Euclidean Vector Spaces
4.1 Euclidean n-Space
4.2 Linear Transformations from Rn to Rm
4.3 Properties of Linear Transformations from Rn to Rm
4.4 Linear Transformations and Polynomials
Chapter 5 General Vector Spaces
5.1 Real Vector Spaces
5.2 Subspaces
5.3 Linear Independence
5.4 Basis and Dimension
5.5 Row Space, Column Space, and Nullspace
5.6 Rank and Nullity
Chapter 6 Inner Product Spaces
6.1 Inner Products
6.2 Angle and Orthogonality in Inner Product Spaces
6.3 Orthonormal Bases; Gram-Schmidt Process; QR-Decomposition
6.4 Best Approximation; Least Squares
6.5 Change of Basis
6.6 Orthogonal Matrices
Chapter 7 Eigenvalues, Eigenvectors
7.1 Eigenvalues and Eigenvectors
7.2 Diagonalization
7.3 Orthogonal Diagonalization
Chapter 8 Linear Transformations
8.1 General Linear Transformations
8.2 Kernel and Range
8.3 Inverse Linear Transformations
8.4 Matrices of General Linear Transformations
8.5 Similarity
8.6 Isomorphism
Chapter 9 Additional Topics
9.1 Application to Differential Equations
9.2 Geometry of Linear Operators on R?
9.3 Least Squares Fitting to Data
9.4 Approximation Problems; Fourier Series
9.5 Quadratic Forms
9.6 Diagonalizing Quadratic Forms; Conic Sections
9.7 Quadric Surfaces
9.8 Comparison of Procedures for Solving Linear Systems
9.9 LU-Decompositions
Answers to Exercises