About the Book

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