Chaos and Differential Equations

Undamped Forced Motion and Resonance

The Eigenvectors for a Matrix Are Not Unique

Quadratic Forms

Solving Homogeneous Linear Systems with Constant Coefficients

Diagonalization of Symmetric Matrices

The Wronskian for a System of Differential Equations

Linear Systems of Differential Equations in Normal Form

Orthogonal Projections

Gram–Schmidt Orthogonalization and 𝑄𝑅 Factorization

Power Series Solutions of First-Order Differential Equations

Ordinary Points and Singular Points for a Differential Equation

Orthogonal Sets

Finding Power Series

Orthogonal Complement of a Set of Vectors

Solving Differential Equations with an Initial Value Using Taylor Series

Laplace Transform of a Second-Order Differential Equation with a Step Function

Analyzing Owl Population Growth with Matrices

Laplace Transforms

Complex Eigenvalues

Finding Eigenvalues and Eigenvectors Using Mathematica or WolframAlpha

Finding Eigenvalues on a TI-83 or TI-84

Diagonalization

Predator-Prey Models

Change of Basis

The Dimension of a Vector Space

Rank of a Matrix

Solving Systems of Differential Equations Using Elimination

Solving Systems of Differential Equations Using Substitution

Damped Forced Motion