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 |