**Positive Definite Matrices** |

1 |
Four Special Matrices |

2 |
Differences, Derivatives, and Boundary Conditions |

3 |
Elimination and Inverse Matrices |

4 |
Eigenvalues and Eigenvectors |

5 |
Positive Definiteness and Minimization |

6 |
Numerical Linear Algebra: LU, QR, and SVD |

**Applied Linear Algebra** |

7 |
Springs and Masses: K = A^{T}CA |

8 |
Least Squares: A^{T}Ax = A^{T}b |

9 |
Weighted Least Squares and Statistics |

10 |
Graphs and Electrical Networks |

11 |
Structures in Equilibrium: Determinate or Indeterminate |

12 |
Instability: Rigid Motion and Mechanism |

13 |
Review for Exam 1 |

14 |
Exam 1: Chapters 1 and 2 |

**Equilibrium Equations: Continuous Case** |

15 |
Equilibrium of an Elastic Bar: Finite Elements in One Dimension |

16 |
Equilibrium of an Elastic Beam and Spline Approximations |

17 |
Potential Flow and Laplace's Equation |

18 |
Divergence Theorem, Green's Theorem, Boundary Conditions, and Poisson's Equation |

19 |
The Finite Element Method |

20 |
Calculus of Variations: Introduction |

21 |
Line Integrals, Potentials, Curl, and Gradient in 3D |

22 |
Fluid Mechanics |

23 |
Review for Exam 2 |

24 |
Exam 2: Chapter 3 |

**Fourier Series and Transforms** |

25 |
Fourier Coefficients |

26 |
Sine and Cosine Series, Parseval's Formula |

27 |
Fourier Solution to Laplace Equation and Convergence |

28 |
Orthogonal Functions; Bessel Functions |

29 |
Discrete Fourier Series and the *n* Roots of Unity |

30 |
Convolution Rule and Signal Processing |

31 |
Constant-diagonal Matrices |

32 |
Fourier Transforms: Plancherel's Formula and Uncertainty Principle |

33 |
Transform Rules |

34 |
Solutions of ODE's and Green's Function |

35 |
Review for Exam 3 |

36 |
Exam 3: Chapter 4 |

37 |
Wavelets |