by Sandra Z. Keith, St. Cloud University
Note: Exercises will open in a new browser window.
Chapter 0: Learning Maple
Project 0: A “Do-It-Yourself” Guide to Maple (hands-on experience for the beginner)
Chapter 1: Linear Equations
Project 1: Solving Systems of Linear Equations and Graphing Results
Project 2: Exploring Lines, Curves, Planes, and Translations
Project 3: Using Matrix Equations for Curve Fitting
Project 4: Symmetries of a Square
Project 5: Reflections
Chapter 2: Linear Transformations
Project 1: An Encyclopedia of Rotations, Reflections, Shears, Projections
Project 2: Matrix Products Visualized (an animation project)
Project 3: Using a Projection Matrix as a Camera
Project 4: A Quick Tour of Elementary Matrices
Project 5: LU Factorization of Matrices
Project 6: Affine Maps as Matrices
Project 7: An Exploration of Complex Numbers—Roots of Unity
Chapter 3: Subspaces of R and Their Dimensions
Project 1: Exploring Linear Combinations and Subspaces
Project 2: Exploring Kernel and Image (Part 1)
Project 3: Kernel and Image, a Demonstration (Part 2)
Project 4: Bases and Change of Basis
Chapter 4: Vector Spaces
Project 1: Function Spaces—Legendre Polynomials and Fourier Series
Chapter 5: Orthogonality and Least Squares
Project 1: Orthogonal Projections, Orthogonal Transformations
Project 2: Orthogonal Projections and Orthonormal Bases—Gram Schmidt Process
Project 3: QR Factorization of Matrices
Chapter 6: Determinants
Project 1: Determinants
Project 2: Using Cross Product to Rotate about an Axis
Chapter 7: Eigenvalues and Eigenvectors
Project 1: Eigenvalues and Eigenvectors
Project 2: Change of Basis to Perform a Rotation and Reflection
Project 3: The Eigenvector Mystery Game, a Demonstration
Project 4: Illustrating Diagonalization with the Change of Basis Matrix
Chapter 8: Coordinate Systems
Project 1: Rotation of Axes (2-dimensional)
Project 2: Applications to Geometry using Eigenvectors
(3-dimensional)
Applications:
Application 1: Linear Programming, The Simplex Method
Application 2: The Leontiev Economic Model
Application 3: Glimpses into 4-Space
Application 4: The Method of Least Squares
Application 5: Fibonacci Sequences (an example of a recurrence relation)
Application 6: Population Models and Markov Processes
Application 7: Eigenvectors in Differential Equations
Application 8: A Little Graph Theory with the Characteristic Polynomial
Application 9: The Lorentz-Einsteinian Transformation
Application 10: Fractal Images
