Previous Material |
Integration Techniques |
Integration summary |

Chapter 1 |
Classification of Differential equations |
Linear vs. Nonlinear Differential Equations |

SLOPe Fields |
Introduction to Slope Fields
Slope Field Example 2 (Section 1.3, Problem 21) |

Separable Equations |
Separation of Variables Example 1 with u sub (Section 1.4 Problem 4)
Separation of Variables Example 2 with Trig Functions (Section 1.4 Problem 8)
Separation of Variables Example 3 with Partial Fraction Decomposition (Section 1.4, Problem 9)
Separation of Variables Example 4 with Integration By Parts |

Integrating Factor |
Integrating Factor Example |

Newton's Law of Cooling |
Newton's Law of Cooling Example 1 (Section 1.4 Problem 26)
Newton's Law of Cooling Example 2 (Section 1.6 Problem 24) |

Mixing Problems |
Mixing Problem Example 1 - Separation of Variable (Section 1.7 Problem 5)
Double Tank Problem (Section 1.7, #8, Part A)
Double Tank Problem (Section 1.7, #8, Part B) |

RLC Circuits |
RC Circuit - Integrating Factor (Section 1.7 Problem 13)
RL Circuit - Separation of Variable (Section 1.7 Problem 16) |

Chapter 2 |
Row Operations |
Row Echelon/Rank Example
Reduced Row Echelon/Rank Example |

Gauss Jordan Elimination |
Gauss Jordan Elimination - One Solution (Section 2.5 Section 1)
Gauss Jordan Elimination - No Solutions (Section 2.5 Problem 3) |

Matrix inverse |
Matrix Inverse Using Gauss Jordan Technique (Section 2.6 Problem 8) |

Chapter 3 |
Determinants |
Adjoint Method to find Matrix Inverse (Section 3.4 Problem 9)
Cramer's Rule to find Solutions (Section 3.4 Problem 13)
Properties of Determinants |

Chapter 4 |
Vector/Subspaces |
Vector Space Axioms 1-4 (Section 4.2 Problem16)
Vector Space Axioms 5-10 (Section 4.2 Problem 16)
Subspace Example 1 (Section 4.3 Problem 5)
Subspace Example 2 (Section 4.3 Problem 16)
Subspace Example 3 (Matrix)
Subspace Example 4 (Functions) |

Spanning Sets |
"Show that the set spans..." with n-tuples (Section 4.4 Problem 9)
"Determine if it lies in the span..." with Polynomials (Section 4.4 Problem 25)
"Find the span..." with Matrices (Section 4.4 Problem 26) |

Bases |
Extending a Basis from Subspace to Vector Space (Section 4.6 Problem 32) |

Nullspace |
Finding the Basis and Dimension of a Nullspace (Section 4.6 Problem 11)
Nullspace, Basis, and Nullity (Section 4.9 Problem 4) |

Chapter 5 |
Eigenvalue/Eigenvectors |
Eigenvalues and Eigenvectors (Section 5.6 Problem 16)
Introduction to Complex Numbers
Complex Eigenvalues and Eigenvectors
Multiplicity, Eigenspace Basis and Dimension, Defective/Nondefective (Section 5.7 Problem 7) |

Diagonalization |
Intro to Diagonalization
Diagonalization Example (Section 5.8 Problem 5)
Diagonalization Example (Section 5.8 Problem 15) |

Chapter 6 |
Homogeneous Equations |
Intro to Linear, Constant Coeff, Homogeneous Equations
Example 1 (Repeated Roots, Section 6.2)
Example 2 (Distinct, Real Roots and Complex Roots)
Example 3 Repeated Complex Roots (Section 6.2 Problem 21) |

NonHomogeneous Equations |
Intro to Method of Undetermined Coefficients (MOUC)
MOUC Example 1 (F(x) = exponential, need to modify)
MOUC Example 2 (F(x) = trig function)
MOUC Example 3 (F(x) = polynomial)
MOUC Example 4 (F(x) = product of exponential and trig function) |

Spring Mass Systems |
Overdamped, Free Oscillation (Section 6.5 Problem 5)
Critically damped, Free Oscillation (Section 6.5 Problem 7)
Underdamped, Forced Oscillation (Section 6.5 Problem 23)
Pendulum Problem (Section 6.5 Problem 17) |

Chapter 7 |
First order linear Systems of differential equations |
Using Differential Operators and Substitution (Homogeneous - Section 7.1 Problem 2)
Using Differential Operators and Substitution (Nonhomogeneous - Section 7.1 Problem 13)
Vector Differential Equations with Nondefective Matrices (Section 7.4 Problem 12)
Vector Differential Equations with Nondefective Matrices IVP (Section 7.4 Problem 16) |