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Anton & Rorres' Elementary Linear Algebra, (As per syllabus of GTU)

Dr. Kailas K. Kanani, Dr. Gaurang V. Ghodasara

ISBN: 9788126533442

740 pages

INR 649

Description

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.

 

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 Null space

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 R2

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