Calendar

SES # TOPICS
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