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Linear algebra with applications

Author: Gareth Williams
Publisher: Sudbury, Mass. : Jones and Bartlett Publishers, ©2008.
Edition/Format:   Print book : English : 6th edView all editions and formats
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Genre/Form: Textbooks
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Gareth Williams
ISBN: 9780763746315 0763746312 9780763757533 0763757535
OCLC Number: 145378809
Notes: Includes index.
Description: xvi, 544 pages : color illustrations ; 28 cm
Contents: Part 1 Linear Equations, Vectors, and Matrices --
1: Linear Equations and Vectors --
1.1 Matrices and Systems of Linear Equations --
1.2 Gauss-Jordan Elimination --
1.3 The Vector Space Rn --
1.4 Basis and Dimension --
1.5 Dot Product, Norm, Angle, and Distance --
(Option: This section may be covered just before section 4.6) --
1.6* Curve Fitting, Electrical Networks, and Traffic Flow --
Chapter1 Review Exercises --
2 Matrices and Linear Transformations --
2.1 Addition, Scalar Multiplication, and Multiplication of Matrices --
2.2 Properties of Matrix Operations --
2.3 Symmetric Matrices and Seriation in Archaeology --
2.4 The Inverse of a Matrix and Cryptography --
2.5 Matrix Transformations, Rotations, and Dilations --
2.6 Linear Transformations, Graphics, and Fractals --
2.7* The Leontief Input-Output Model in Economics --
2.8* Markov Chains, Population Movements, and Genetics --
2.9* A Communication Model and Group Relationships in Sociology --
Chapter 2 Review Exercises --
3 Determinants and Eigenvectors --
3.1 Introduction to Determinants --
3.2 Properties of Determinants --
3.3 Determinants, Matrix Inverses, and Systems of Linear Equations --
3.4 Eigenvalues and Eigenspaces --
3.5* Google, Demography, and Weather Prediction --
(Option: Section 5.3 on Diagonalization of Matrices can be covered here.) --
Chapter 3 Review Exercises --
Part 2: Vector Spaces --
4 General Vector Spaces --
4.1 General Vector Spaces and Subspaces --
4.2 Linear Combinations --
4.3 Linear Dependence and Independence --
4.4 Properties of Bases --
4.5 Rank --
4.6 Orthonormal Vectors and Projections --
4.7 Kernel, Range and The Rank/Nullity Theorem --
4.8 One-to-One Transformations and Inverse Transformations --
4.9* Transformations and Systems of Linear Equations --
Chapter 5: Review Exercises --
5 Coordinate Representations --
5.1 Coordinate Vectors --
5.2 Matrix Representations of Linear Transformations --
5.3 Diagonalization of Matrices 5.4* Quadratic Forms, Difference Equations, and Normal Modes --
Chapter 6 Review Exercises --
6 Inner Product Spaces --
6.1 Inner Product Spaces --
6.2* Non-Euclidean Geometry and Special Relativity --
6.3* Approximation of Functions and Coding Theory --
6.4* Least Squares Curves --
Chapter 7 Review Exercises --
Part 3 Numerical Linear Algebr --
7 Numerical Methods --
7.1* Gaussian Elimination --
7.2* The Method of LU Decomposition --
7.3* Practical Difficulties in Solving Systems of Equations --
7.4* Iterative Methods for Solving Systems of Linear Equations --
7.5* Eigenvalues by Iteration and Connectivity of Networks --
Chapter 8 Review Exercises --
8: Linear Programming --
8.1* A Geometrical Introduction to Linear Programming --
8.2* The Simplex Method --
8.3* Geometrical Explanation of the Simplex Method --
Chapter 9 Review Exercises --
Appendixes --
A Cross Product --
B Equations of Lines in Three-Space --
C Graphing Calculator Manual --
C1 Reduced Echelon Form of a Matrix (Sections 1.1, 1.2) --
C2 Matrix Operations (Sections 2.1, 2.2) --
C3 Powers of a Matrix (Section 2.2) --
C4 Transpose of a Matrix (Section 2.3) --
C5 Inverse of a Matrix (Section 2.4) --
C6 Determinant of a Matrix (Section 3.1) --
C7 Summary of Formats for Row Operations (Sections 1.1, 1.2) --
D MATLAB Manual --
D1 Entering and Displaying a Matrix (Section 1.1) --
D2 Solving Systems of Linear Equations (Sections 1.1, 1.2, 1.6) --
D3 Dot Product, Norm, Angle, Distance, (Section 1.4) --
D4 Matrix Operations, Submatrices, Rows and Columns (Sections 2.1 --
2.3) --
D5 Computational Considerations (Section 2.2) --
D6 Inverse of a Matrix (Section 2.4) --
D7 Solving Systems of Equations using Matrix Inverse (Section 2.4) --
D8 Cryptography (Section 2.4) --
D9 Transformations defined by Matrices (Section 2.5, 2.6) --
D10 Fractals (Section 2.6) --
D11 Leontief I/O Model (Section 2.7) --
D12 Markov Chains (Sections 2.8, 3.5) --
D13 Digraphs (Section 2.9) --
D14 Determinants (Sections 3.1, 3.2, 3.3) --
D15 Cramer's Rule (Section 3.3) --
D16 Eigenvalues, Eigenvectors, and Applications (Sections 3.4, 3.5) --
D17 Linear Combinations, Dependence, Basis, Rank (Sections 1.3, 4.2 --
4.5) --
D18 Projection, Gram --
Schmidt Orthogonalization (Section 4.6) --
D19 Kernel and Range (Section 4.7) --
D20 Inner Product, Non-Euclidean Geometry (Sections 6.1, 6.2) --
D21 Space-Time Travel (Section 6.2) --
D22 Pseudoinverse and Least Squares Curves (Section 6.4) --
D23 LU Decomposition (Section 7.2) --
D24 Condition Number of a Matrix (Section 7.3) --
D25 Jacobi and Gauss-Seidel Iterative Methods (Section 7.4) --
D26 The Simplex Method in Linear Programming (Section 8.2) --
D27 Cross Product (Appendix A) --
D28 MATLAB Commands, Functions and M-files --
D29 The Linear Algebra with Applications Toolbox M-Files --
Answers to Selected Exercises --
Index.
Responsibility: Gareth Williams.
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