Lecture 01 Describing Inverse Problems
Lecture 02 Probability and Measurement Error, Part 1
Lecture 03 Probability and Measurement Error, Part 2
Lecture 04 The L₂ Norm and Simple Least Squares
Lecture 05 A Priori Information and Weighted Least Squared
Lecture 06 Resolution and Generalized Inverses

Lecture 07 Backus-Gilbert Inverse and the Trade Off of Resolution and Variance
Lecture 08 The Principle of Maximum Likelihood
Lecture 09 Inexact Theories

Lecture 10 Prior Covariance and Gaussian Process Regression
Lecture 11 Non-uniqueness and Localized Averages
Lecture 12 Vector Spaces and Singular Value Decomposition

Lecture 13 Equality and Inequality Constraints
Lecture 14 L₁ , L_∞ Norm Problems and Linear Programming
Lecture 15 Nonlinear Problems: Grid and Monte Carlo Searches
Lecture 16 Nonlinear Problems: Newton’s Method
Lecture 17 Nonlinear Problems: MCMC and Bootstrap Confidence Intervals
Lecture 18 Factor Analysis
Lecture 19 Varimax Factors, Empirical Orthogonal Functions
Lecture 20 Backus-Gilbert Theory for Continuous Problems; Radon’s Problem
Lecture 21 Linear Operators and Their Adjoints
Lecture 22 Fréchet Derivatives

Lecture 23 Estimating a Parameter in a Differential Equation
Lecture 24 Exemplary Inverse Problems, incl. Filter Design
Lecture 25 Exemplary Inverse Problems, incl. Earthquake Location
Lecture 26 Exemplary Inverse Problems, incl. Vibrational Problems