Introduction | 1 | Handouts | 3-4 |

Fundamentals of Differential Equation | 2 | Handouts | 5-8 |

Separable Equations | 3 | Handouts | 9-17 |

Homogeneous Differential Equations | 4 | Handouts | 18-25 |

Exact Differential Equations | 5 | Handouts | 26-33 |

Integrating Factor Technique | 6 | Handouts | 34-43 |

First Order Linear Equations | 7 | Handouts | 44-50 |

Bernoulli Equations and Practice Examples | | Handouts | 51-77 |

Applications of First Order Differential Equations | 10 | Handouts | 78-88 |

Radioactive Decay | 11 | Handouts | 89-94 |

Application of Non Linear Equations | 12 | Handouts | 95-102 |

Higher Order Linear Differential Equations and their Solutions | | Handouts | 103-126 |

Construction of a Second Solution | 15 | Handouts | 127-133 |

Homogeneous Linear Equations with Constant Coefficients | 16 | Handouts | 134-144 |

Method of Undetermined Coefficients Superposition Approach | 17 | Handouts | 145-158 |

Undetermined Coefficient Annihilator Operator Approach | | Handouts | 159-179 |

Variation of Parameters | 20 | Handouts | 180-189 |

Introduction and Overview of Linear Algebra | 21 | Elementary Linear Algebra and its Application | 1-5 |

Introduction to Matrices. | 22 | (3rd edition) | 6-17 |

System Of Linear Equations. | 23 | By David C. Lay | 18-29 |

Row reduction and Echelon Form of a Matrix. | 24 | | 30-43 |

Vector Equations. | 25 | | 44-55 |

Matrix Equations. | 26 | | 56-65 |

Solution Set of Linear Equations. | 27 | | 66-73 |

Linearly Dependent and Linearly Independent Sets. | 28 | | 81-88 |

Linear Transformations. | 29 | | 89-225 |

The Matrix of Linear Transformations. | 30 | | 98-107 |

Matrix Algebra. | 31 | | 121-133 |

Inverse of a Matrix. | 32 | | 134-143 |

Characterization of Invertible Matrices. | 33 | | 144-149 |

Partitioning of a Matrix. | 34 | | 150-157 |

Matrix Factorization. | 35 | | 158-167 |

Iterative Solution of Linear Systems. | 36 | | 168-201 |

Introduction to Determinants. | 37 | | 202-207 |

Properties of Determinants. | 38 | | 208-216 |

Cramer"s rule, Volume and Linear Transformations. | 39 | | 217-222 |

Vector Spaces. | 40 | | 232-241 |

Null Spaces, Column Spaces and Linear Transformations. | 41 | | 242-252 |

Bases for a vector Space. | 42 | | 253-261 |

Coordinate systems | 43 | | 262-271 |

Dimension of a Vector Space | 44 | | 272-278 |

The Rank Theorem and Invertible Matrix Theorem | 45 | | 279-286 |