### Instructor Key

DF = Prof. Dan Frey

GS = Prof. Gilbert Strang

### Session Key

L = Lecture

R = Recitation

E = Quiz or Exam

SES # | TOPICS | INSTRUCTORS | KEY DATES |
---|---|---|---|

L1 | Course introduction: What are differential equations and linear algebra? How do engineers use them? Four examples of first order differential equations. | DF |
Problem Set 1 Assigned |

L2 | First-order equations: Constant source, step function (Heaviside), delta (Dirac), exponentials, real and complex sinusoids. | GS | |

R1 | Recitation | ||

L3 | First-order equations (continued): Separable equations, exact equations. | GS |
Problem Set 1 Due Problem Set 2 Assigned |

L4 | Second-order equations: Second derivatives in engineering, complex numbers, constant coefficient equations. | GS | |

E1 | Quiz 1 | ||

L5 | Second-order equations (continued): Forced oscillations, examples in electrical and mechanical systems, Laplace transforms. | GS | Problem Set 3 Assigned |

L6 | Laplace transforms (continued): Graphical Methods: Direction fields, nonlinear equations, sources, sinks, saddles, and spirals. | DF | Problem Set 2 Due |

R2 | Recitation | ||

L7 | Graphical and numerical methods: Linearization, stability, Euler’s method. | DF | |

L8 | Linear systems of equations: Gaussian elimination, matrix multiplication. | DF | |

R3 | Recitation | ||

L9 | Linear systems of equations: Matrix inverse. Existence and uniqueness of solutions. Column, row, null space. | DF |
Problem Set 3 Due Problem Set 4 Assigned |

L10 | Linear systems of equations (continued): Mechanical engineering examples. | DF | |

R4 | Recitation | ||

E2 | Quiz 2: Oral exams scheduled throughout the week. | ||

L11 | Eigenvalues and eigenvectors: The eigenvalue problem. Diagonalization, exponentiation of a matrix. | DF |
Problem Set 4 Due Problem Set 5 Assigned |

L12 | Least squares and projection: Positive definite matrices. Singular value decomposition. | DF | Problem Set 5 Due |

L13 | Review session for the final exam. | DF | |

R5 | Review session for the final exam (continued). | ||

E3 | Final Exam |