Visual Linear Algebra
John Wiley & Sons Inc
9780471682998 (ISBN)
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Visual Linear Algebra is a new kind of textbook—a blend of interactive computer tutorials and traditional text. The computer tutorials provide a lively learning environment in which students are introduced to concepts and methods and where they develop their intuition. The traditional sections provide the backbone whose core is the development of theory and where students’ understanding is solidified. Although the design of Visual Linear Algebra is novel, the goals for the book are quite traditional. Foremost among these is to provide a rich set of materials that help students achieve a thorough understanding of the core topics of linear algebra and genuine competence in using them.
Chapter 1 Systems of Linear Equations 1
1.1 Solving Linear Systems 2
1.2 Geometric Perspectives on Linear Systems 18
1.3A Solving Linear Systems Using Maple 26
1.3B Solving Linear Systems Using Mathematics 36
1.4 Curve Fitting and Temperature Distribution-Application 45
Chapter 2 Vectors 56
2.1 Geometry of Vectors 57
2.2 Linear Combinations of Vectors 71
2.3 Decomposing the Solution of a Linear System 84
2.4 Linear Independence of Vectors 92
2.5 Theory of Vector Concepts 106
Chapter 3 Matrix Algebra 113
3.1 Product of a Matrix and a Vector 114
3.2 Matrix Multiplication 125
3.3 Rules of Matrix Algebra 140
3.4 Markov Chains-Application 147
3.5 Inverse of a Matrix 161
3.6 Theory of Matrix Inverses 175
3.7 Cryptology-Application 180
Chapter 4 Linear Transformations 193
4.1 Introduction to Matrix Transformations 194
4.2 Geometry of Matrix Transformations of the Plane 198
4.3 Geometry of Matrix Transformations of 3-Space 220
4.4 Linear Transformations 232
4.5 Computer Graphics-Applications 237
Chapter 5 Vector Spaces 255
5.1 Subspaces of Rᴺ 256
5.2 Basis and Dimension 262
5.3 Theory of Basis and Dimension 272
5.4 Subspaces Associated with a Matrix 275
5.5 Theory of Subspaces Associated with a Matrix 285
5.6 Loops and Spanning Trees-Application 289
5.7 Abstract Vector Spaces 297
Chapter 6 Determinants 306
6.1 Determinants and Cofactors 307
6.2 Properties of Determinants 311
6.3 Theory of Determination 322
Chapter 7 Eigenvalues and Eigenvectors 328
7.1 Introduction to Eigenvalues and Eigenvectors 329
7.2 The Characteristics Polynomial 343
7.3 Discrete Dynamical Systems-Application 356
7.4 Diagonalization and Similar Matrices 373
7.5 Theory of Eigenvalues and Eigenvectors 389
7.6 Systems of Linear Differential Equations-Application 395
7.7 Complex Numbers and Complex Vectors 407
7.8 Complex Eigenvalue and Eigenvectors 411
Chapter 8 Orthogonality 431
8.1 Dot Product and Orthogonal Vectors 432
8.2 Orthogonal Projections in R² and R³ 437
8.3 Orthogonal Projections and Orthogonal Bases in Rᴺ 447
8.4 Theory of Orthogonality 456
8.5 Least-Squares Solution-Application 463
8.6 Weighted Least-Squares and Inner Products on Rᴺ 475
8.7 Approximation of Functions and Integral Inner Products 483
8.8 Inner Product Spaces 496
Appendix A Glossary of Linear Algebra Definitions 503
Appendix B Linear Algebra Theorems 510
Appendix C Advice for Using Maple with Visual Linear Algebra 519
Appendix D Commands Used in Maple Tutorials 521
Appendix E Advice for Using Mathematica with Visual Linear Algebra 527
Appendix F Commands Used in Mathematica Tutorials 530
Appendix G Answers and Hints for Selected Pencil and Paper Problems 537
Index 545
| Erscheint lt. Verlag | 8.4.2005 |
|---|---|
| Verlagsort | New York |
| Sprache | englisch |
| Maße | 209 x 257 mm |
| Gewicht | 1223 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| ISBN-13 | 9780471682998 / 9780471682998 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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