Syllabus
Part 1: Applied Linear Algebra
Four Special Matrices
Differences, Derivatives, and Boundary Conditions
Elimination Leads to K = LDLT
Inverses and Delta Functions
Eigenvalues and Eigenvectors
Positive Definite Matrices
Numerical Linear Algebra: LU, QR, SVD
Part 2: A Framework for Applied Mathematics
Equilibrium and the Stiffness Matrix
Oscillation by Newton’s Law
Least Squares for Rectangular Matrices
Graph Models and Kirchhoff’s Laws
Networks and Transfer Functions
Nonlinear Problems
Structures in Equilibrium
Part 3: Boundary Value Problems
Differential Equations of Equilibrium
Cubic Splines and Fourth Order Equations
Gradient and Divergence
Laplace’s Equation
Finite Differences and Fast Poisson Solvers
The Finite Element Method
Elasticity and Solid Mechanics
Part 4: Fourier Series and Integrals
Fourier Series for Periodic Functions
Chebyshev, Legendre, and Bessel
The Discrete Fourier Transform and the FFT
Convolution and Signal Processing
Fourier Integrals
Deconvolution and Integral Equations
Wavelets and Signal Processing