Topics (tentative):

• Part 1: Models and Simulation
  • Introduction to differential equations (DE), the exponential, numerical methods.
  • Systems of equations, elimination, implicit methods for systems of DE.
  • Nonlinear models, root-finding and Newton's method, implicit methods for nonlinear DE.
• Part 2: Optimization and Control
  • Constrained and unconstrained formulations
  • Classification of minima
  • Iterative methods
• Part 3: Uncertainty Quantification
  • Probability: random variable, distribution, moments, conditional probabilities
  • Estimation of the mean and standard deviation, confidence intervals
  • Probabilistic DE and Monte Carlo sampling

Many examples from mechanics (robotics, planetary motion), chemistry, Earth and climate science, biology (epidemiology), etc.