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E-raamat: Exploring Linear Algebra: Labs and Projects with Mathematica

(Elon University, North Carolina, USA)
  • Formaat: 151 pages
  • Sari: Textbooks in Mathematics
  • Ilmumisaeg: 13-Nov-2014
  • Kirjastus: Chapman & Hall/CRC
  • Keel: eng
  • ISBN-13: 9781482241501
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  • Formaat: 151 pages
  • Sari: Textbooks in Mathematics
  • Ilmumisaeg: 13-Nov-2014
  • Kirjastus: Chapman & Hall/CRC
  • Keel: eng
  • ISBN-13: 9781482241501
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Exploring Linear Algebra: Labs and Projects with Mathematica® is a hands-on lab manual for daily use in the classroom. Each lab includes exercises, theorems, and problems that guide your students on an exploration of linear algebra.

The exercises section integrates problems, technology, Mathematica® visualization, and Mathematica CDFs, enabling students to discover the theory and applications of linear algebra in a meaningful way. The theorems and problems section presents the theoretical aspects of linear algebra. Students are encouraged to discover the truth of each theorem and problem, to move toward proving (or disproving) each statement, and to present their results to their peers.

Each chapter also contains a project set consisting of application-driven projects that emphasize the material in the chapter. Students can use these projects as the basis for further undergraduate research.

Arvustused

"The presented book provides readers with a set of interesting exercises and problems regarding linear algebra. The book covers the scope of an undergraduate course excellent supplementary material for a linear algebra course " Zentralblatt MATH 1320

Preface ix
Acknowledgments xi
1 Matrix Operations
1(28)
Lab 0 An Introduction to Mathematica®
1(3)
Lab 1 Matrix Basics and Operations
4(3)
Lab 2 A Matrix Representation of Linear Systems
7(3)
Lab 3 Powers, Inverses, and Special Matrices
10(3)
Lab 4 Graph Theory and Adjacency Matrices
13(3)
Lab 5 Permutations and Determinants
16(5)
Lab 6 4 X 4 Determinants and Beyond
21(8)
Project Set 1
23(6)
2 Invertibility
29(18)
Lab 7 Singular or Nonsingular? Why Singularity Matters
29(3)
Lab 8 Mod It Out, Matrices with Entries in Zp
32(3)
Lab 9 It's a Complex World
35(2)
Lab 10 Declaring Independence: Is It Linear?
37(10)
Project Set 2
40(7)
3 Vector Spaces
47(24)
Lab 11 Vector Spaces and Subspaces
47(3)
Lab 12 Basing It All on Just a Few Vectors
50(3)
Lab 13 Linear Transformations
53(4)
Lab 14 Eigenvalues and Eigenspaces
57(3)
Lab 15 Markov Chains: An Application of Eigenvalues
60(11)
Project Set 3
62(9)
4 Orthogonality
71(26)
Lab 16 Inner Product Spaces
71(4)
Lab 17 The Geometry of Vector and Inner Product Spaces
75(5)
Lab 18 Orthogonal Matrices, QR Decomposition, and Least Squares Regression
80(5)
Lab 19 Symmetric Matrices and Quadratic Forms
85(12)
Project Set 4
90(7)
5 Matrix Decomposition with Applications
97(20)
Lab 20 Singular Value Decomposition (SVD)
97(6)
Lab 21 Cholesky Decomposition and Its Application to Statistics
103(5)
Lab 22 Jordan Canonical Form
108(9)
Project Set 5
112(5)
6 Applications to Differential Equations
117(16)
Lab 23 Linear Differential Equations
117(5)
Lab 24 Higher-Order Linear Differential Equations
122(3)
Lab 25 Phase Portraits, Using the Jacobian Matrix to Look Closer at Equilibria
125(8)
Project Set 6
128(5)
Mathematica Demonstrations and References 133(4)
Index 137
Crista Arangala