# 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