| 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 = ATCA |
| 8 |
Least Squares: ATAx = ATb |
| 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 |