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Visual linear algebra

Visual linear algebra (8회 대출)

자료유형
단행본
개인저자
Herman, Eugene A. Pepe, Michael D. Schulz, Eric P.
서명 / 저자사항
Visual linear algebra / Eugene A. Herman, Michael D. Pepe, with contributions by Eric P. Schulz.
발행사항
Hoboken, NJ :   Wiley ,   c2005.  
형태사항
xix, 550 p. : col. ill. ; 27 cm. + 1 CD-ROM (4 3/4 in.).
ISBN
0471682993 (acid-free paper) 0471706280 (CD-ROM)
일반주기
Includes index.  
일반주제명
Algebras, Linear -- Computer-assisted instruction.
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001 000045215748
005 20051229145604
008 041027s2005 njua 001 0 eng
010 ▼a 2004059088
020 ▼a 0471682993 (acid-free paper)
020 ▼a 0471706280 (CD-ROM)
035 ▼a (KERIS)REF000010816368
040 ▼a DLC ▼c DLC ▼d DLC ▼d 211009
042 ▼a pcc
050 0 0 ▼a QA185.C65 ▼b H47 2005
082 0 0 ▼a 512/.5 ▼2 22
090 ▼a 512.5 ▼b H551v
100 1 ▼a Herman, Eugene A.
245 1 0 ▼a Visual linear algebra / ▼c Eugene A. Herman, Michael D. Pepe, with contributions by Eric P. Schulz.
260 ▼a Hoboken, NJ : ▼b Wiley , ▼c c2005.
300 ▼a xix, 550 p. : ▼b col. ill. ; ▼c 27 cm. + ▼e 1 CD-ROM (4 3/4 in.).
500 ▼a Includes index.
538 ▼a System requirements for accompanying CD-ROM: Windows/Macintosh and Unix/Linux compatible.
630 0 0 ▼a Maple (Computer file)
630 0 0 ▼a Mathematica (Computer file)
650 0 ▼a Algebras, Linear ▼x Computer-assisted instruction.
700 1 ▼a Pepe, Michael D.
700 1 ▼a Schulz, Eric P.
945 ▼a KINS

소장정보

No. 소장처 청구기호 등록번호 도서상태 반납예정일 예약 서비스
No. 1 소장처 과학도서관/Sci-Info(2층서고)/ 청구기호 512.5 H551v 등록번호 121118942 도서상태 대출가능 반납예정일 예약 서비스 B M

컨텐츠정보

목차

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


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