Cover
Contents
Series Page
Title Page
Copyright
Conventions and Notations
Preface
Chapter 1: An Introduction to Mathematica®
1.1 The Very Basics
1.2 Basic Arithmetic
1.3 Lists and Matrices
1.4 Expressions versus Functions
1.5 Plotting and Animations
1.6 Solving Systems of Equations
1.7 Basic Programming
Chapter 2: Linear Systems of Equations and Matrices
2.1 Linear Systems of Equations
2.2 Augmented Matrix of a Linear System and Row Operations
2.2 Some Matrix Arithmetic
Chapter 3: Gauss-Jordan Elimination and Reduced Row Echelon Form
3.1 Gauss-Jordan Elimination and rref. 3.2 Elementary Matrices3.3 Sensitivity of Solutions to Error in the Linear System
Chapter 4: Applications of Linear Systems and Matrices
4.1 Applications of Linear Systems to Geometry
4.2 Applications of Linear Systems to Curve Fitting
4.3 Applications of Linear Systems to Economics
4.4 Applications of Matrix Multiplication to Geometry
4.5 An Application of Matrix Multiplication to Economics
Chapter 5: Determinants, Inverses, and Cramer's Rule
5.1 Determinants and Inverses from the Adjoint Formula
5.2 Finding Determinants by Expanding along Any Row or Column. 5.3 Determinants Found by Triangularizing Matrices5.4 LU Factorization
5.5 Inverses from rref
5.6 Cramer's Rule
Chapter 6: Basic Vector Algebra Topics
6.1 Vectors
6.2 Dot Product
6.3 Cross Product
6.4 Vector Projection
Chapter 7: A Few Advanced Vector Algebra Topics
7.1 Rotations in Space
7.2 "Rolling" a Circle along a Curve
7.3 The TNB Frame
Chapter 8: Independence, Basis, and Dimension for Subspaces of Rn
8.1 Subspaces of Rn
8.2 Independent and Dependent Sets of Vectors in Rn
8.3 Basis and Dimension for Subspaces of Rn
8.4 Vector Projection onto a Subspace of Rn. 8.5 The Gram-Schmidt Orthonormalization ProcessChapter 9: Linear Maps from Rn to Rm
9.1 Basics about Linear Maps
9.2 The Kernel and Image Subspaces of a Linear Map
9.3 Composites of Two Linear Maps and Inverses
9.4 Change of Bases for the Matrix Representation of a Linear Map
Chapter 10: The Geometry of Linear and Affine Maps
10.1 The Effect of a Linear Map on Area and Arclength in Two Dimensions
10.2 The Decomposition of Linear Maps into Rotations, Reflections, and Rescalings in R2
10.3 The Effect of Linear Maps on Volume, Area, and Arclength in R3. 10.4 Rotations, Reflections, and Rescalings in Three Dimensions10.5 Affine Maps
Chapter 11: Least-Squares Fits and Pseudoinverses
11.1 Pseudoinverse to a Nonsquare Matrix and Almost Solving an Overdetermined Linear System
11.2 Fits and Pseudoinverses
11.3 Least-Squares Fits and Pseudoinverses
Chapter 12: Eigenvalues and Eigenvectors
12.1 What Are Eigenvalues and Eigenvectors, and Why Do We Need Them
12.2 Summary of Definitions and Methods for Computing Eigenvalues and Eigenvectors as Well as the Exponential of a Matrix
12.3 Applications of the Diagonalizability of Square Matrices.