Chapter One: First-Order Differential Equations.

1.1 Differential Equations Everywhere.

1.2 Basic Ideas and Terminology.

1.3 The Geometry of First-Order Differential Equations.

1.4 Separable Differential Equations.

1.6 First-Order Linear Differential Equations.

1.7 Modeling Problems Using First-Order Linear Differential Equations.

1.8 Change of Variables.

Chapter 5: Inner Product Spaces.

5.1 Definition of an Inner Product Space.

5.2 Orthogonal Sets of Vectors and Orthogonal Projections.

5.3 The Gram-Schmidt Process.

Chapter 9: Systems of Differential Equations.

9.1 First-Order Linear Systems.

9.2 Vector Formulation.

9.3 General Results for First-Order Linear Differential Systems.

9.4 Vector Differential Equations: Non-defective Coefficient Matrix.

9.5 Vector Differential Equations: Defective Coefficient Matrix.

9.6 Variation-Of-Parameters for Linear Systems.

Coming soon

Chapter Two: Matrices and Systems of Linear Equations.

2.1 Matrices: Definitions and Notation.

2.2 Matrix Algebra.

2.3 Terminology for Systems of Linear Equations.

2.4 Row-Echelon Matrices and Elementary Row Operations.

2.5 Gaussian Elimination.

2.6 The Inverse of a Square Matrix.

Chapter 6: Linear Transformations.

6.1 Definition of a Linear Transformation.

6.3 The Kernel and Range of a Linear Transformation.

6.4 Additional Properties of Linear Transformations

Chapter Three: Determinants.

3.1 The Definition of the Determinant.

3.2 Properties of Determinants.

3.3 Cofactor Expansions.

Chapter 7: Eigenvalues and Eigenvectors.

7.1 The Eigenvalue/Eigenvector Problem.

7.2 General Results for Eigenvalues and Eigenvectors.

7.3 Diagonalization.

7.5 Orthogonal Diagonalization and Quadratic Forms.

Chapter 4: Vector Spaces.

4.1 Vectors in R^n .

4.2 Definition of a Vector Space.

4.3 Subspaces.

4.4 Spanning Sets.

4.5 Linear Dependence and Linear Independence.

4.6 Bases and Dimension.

4.8 Row Space and Column Space.

Chapter 8: Linear Differential Equations of Order n.

8.1 General Theory for Linear Differential Equations.

8.2 Constant Coefficient Homogeneous Linear Differential Equations.

8.3 The Method of Undetermined Coefficients: Annihilators.

8.7 The Variation of Parameters Method.

8.8 A Differential Equation with Nonconstant Coefficients.