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Preface | p. ix |
Conventions and Notations | p. xiv |
An Introduction to Mathematica“ | p. 1 |
The Very Basics | p. 1 |
Basic Arithmetic | p. 4 |
Lists and Matrices | p. 9 |
Expressions versus Functions | p. 12 |
Plotting and Animations | p. 14 |
Solving Systems of Equations | p. 24 |
Basic Programming | p. 28 |
Linear Systems of Equations and Matrices | p. 31 |
Linear Systems of Equations | p. 31 |
Augmented Matrix of a Linear System and Row Operations | p. 44 |
Some Matrix Arithmetic | p. 54 |
Gauss-Jordan Elimination and Reduced Row Echelon Form | p. 69 |
Gauss-Jordan Enmination and rref | p. 69 |
Elementary Matrices | p. 81 |
Sensitivity of Solutions to Error in the Linear System | p. 92 |
Applications of Linear Systems and Matrices | p. 105 |
Applications of Linear Systems to Geometry | p. 105 |
Applications of Linear Systems to Curve Fitting | p. 115 |
Applications of Linear Systems to Economics | p. 122 |
Applications of Matrix Multiplication to Geometry | p. 127 |
An Application of Matrix Multiplication to Economics | p. 135 |
Determinants, Inverses, and Cramer's Rule | p. 143 |
Determinants and Inverses from the Adjoint Formula | p. 143 |
Finding Determinants by Expanding along Any Row or Column | p. 161 |
Determinants Found by Triangularizing Matrices | p. 173 |
LU Factorization | p. 185 |
Inverses from rref | p. 192 |
Gramer's Rule | p. 197 |
Basic Vector Algebra Topics | p. 207 |
Vectors | p. 207 |
Dot Product | p. 221 |
Cross Product | p. 233 |
Vector Projection | p. 242 |
A Few Advanced Vector Algebra Topics | p. 255 |
Rotations in Space | p. 255 |
"Rolling" a Circle along a Curve | p. 265 |
The TNB Frame | p. 275 |
Independence, Basis, and Dimension for Subspaces of Rn | p. 281 |
Subspaces of Rn | p. 281 |
Independent and Dependent Sets of Vectors in Rn | p. 298 |
Basis and Dimension for Subspaces of Rn | p. 310 |
Vector Projection onto a Subspace of Rn | p. 320 |
The Gram-Schmidt Orthonormalization Process | p. 331 |
Linear Maps from Rn to Rm | p. 341 |
Basics about Linear Maps | p. 341 |
The Kernel and Image Subspaces of a Linear Map | p. 353 |
Composites of Two Linear Maps and Inverses | p. 361 |
Change of Bases for the Matrix Representation of a Linear Map | p. 368 |
The Geometry of Linear and Affine Maps | |
The Effect of a Linear Map on Area and Arclength in Two Dimensions | p. 383 |
The Decomposition of Linear Maps into Rotations, Reflections, and Rescalings in R2 | p. 401 |
The Effect of Linear Maps on Volume, Area, arid Arclength in R3 | p. 409 |
Rotations, Reflections, and Rescalings in Three Dimensions | p. 421 |
Affine Maps | p. 431 |
Least-Squares Fits and Pseudo inverses | p. 443 |
Pseudoinverse to a Nonsquare Matrix and Almost Solving an Overdetermined Linear System | p. 443 |
Fits and Pseudoinverses | p. 454 |
Least-Squares Fits and Pseudoinverses | p. 469 |
Eigenvalues and Eigenvectors | p. 481 |
What Are Eigenvalues and Eigenvectors, and Why Do We Need Them? | p. 481 |
Summary of Definitions and Methods for Computing Eigenvalues and Eigenvectors as Well as the Exponential of a Matrix | p. 496 |
Applications of the Diagonalizability of Square Matrices | p. 500 |
Solving a Square First-Order Linear System of Differential Equations | p. 516 |
Basic Facts about Eigenvalues, Eigenvectors, and Diagonalizability | p. 552 |
The Geometry of the Ellipse Using Eigenvalues and Eigenvectors | p. 566 |
A Mathematica Eigen-Function | p. 586 |
Bibliographic Material | p. 591 |
Indexes | p. 593 |
Keyword Index | p. 593 |
Index of Mathematica Commands | p. 597 |
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