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E-raamat: Exploring Linear Algebra: Labs and Projects with MATLAB(R)

  • Formaat: 156 pages
  • Sari: Textbooks in Mathematics
  • Ilmumisaeg: 07-Mar-2019
  • Kirjastus: CRC Press
  • Keel: eng
  • ISBN-13: 9781351664073
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Exploring Linear Algebra: Labs and Projects with MATLAB(R)Suurem pilt
  • Formaat: 156 pages
  • Sari: Textbooks in Mathematics
  • Ilmumisaeg: 07-Mar-2019
  • Kirjastus: CRC Press
  • Keel: eng
  • ISBN-13: 9781351664073
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Exploring Linear Algebra: Labs and Projects with MATLAB® is a hands-on lab manual that can be used by students and instructors in classrooms every day to guide the exploration of the theory and applications of linear algebra. For the most part, labs discussed in the book can be used individually or in a sequence. Each lab consists of an explanation of material with integrated exercises. Some labs are split into multiple subsections and thus exercises are separated by those subsections.

The exercise sections integrate problems using Mathematica demonstrations (an online tool that can be used with a browser with Java capabilities) and MATLAB® coding. This allows students to discover the theory and applications of linear algebra in a meaningful and memorable way.

Features:











The books inquiry-based approach promotes student interaction





Each chapter contains a project set which consists of application-driven projects emphasizing the chapters materials





Adds a project component to any Linear Algebra course





Explores many applications to a variety of fields that can promote research projects





Employs MATLAB® to calculate and explore concepts and theories of linear algebra
Preface vii
Acknowledgments ix
1 Matrix Operations
1(30)
Lab 0 An Introduction to MATLAB®
1(4)
Lab 1 Matrix Basics and Operations
5(3)
Lab 2 A Matrix Representation of Linear Systems
8(3)
Lab 3 Powers, Inverses, and Special Matrices
11(3)
Lab 4 Graph Theory and Adjacency Matrices
14(3)
Lab 5 Permutations and Determinants
17(5)
Lab 6 4 × 4 Determinants and Beyond
22(9)
Project Set 1
24(7)
2 Invertibility
31(18)
Lab 7 Singular or Nonsingular? Why Singularity Matters
31(3)
Lab 8 Mod It Out, Matrices with Entries in Zp
34(4)
Lab 9 It's a Complex World
38(2)
Lab 10 Declaring Independence: Is It Linear?
40(9)
Project Set 2
43(6)
3 Vector Spaces
49(24)
Lab 11 Vector Spaces and Subspaces
49(3)
Lab 12 Basing It All on Just a Few Vectors
52(3)
Lab 13 Linear Transformations
55(4)
Lab 14 Eigenvalues and Eigenspaces
59(3)
Lab 15 Markov Chains: An Application of Eigenvalues
62(11)
Project Set 3
65(8)
4 Orthogonality
73(26)
Lab 16 Inner Product Spaces
73(3)
Lab 17 The Geometry of Vector and Inner Product Spaces
76(5)
Lab 18 Orthogonal Matrices, QR Decomposition, and Least Squares Regression
81(5)
Lab 19 Symmetric Matrices and Quadratic Forms
86(13)
Project Set 4
92(7)
5 Matrix Decomposition with Applications
99(20)
Lab 20 Singular Value Decomposition (SVD)
99(6)
Lab 21 Cholesky Decomposition and Its Application to Statistics
105(5)
Lab 22 Jordan Canonical Form
110(9)
Project Set 5
114(5)
6 Applications to Differential Equations
119(18)
Lab 23 Linear Differential Equations
119(5)
Lab 24 Higher-Order Linear Differential Equations
124(3)
Lab 25 Phase Portraits, Using the Jacobian Matrix to Look Closer at Equilibria
127(10)
Project Set 6
130(7)
Matlab Demonstrations and References 137(6)
Index 143
Dr. Crista Arangala holds a PhD in mathematics from the University of Cincinnati. She is now at Elon University in North Carolina teaching and researching in a variety of fields including mathematical modeling and service learning education. She was chosen to be a Fulbright Scholar in 2014. She runs a traveling science museum with her Elon University students in Kerala, India. She is also the author of Exploring Calculus: Labs and Projects with Mathematica published by CRC Press.
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