Week 1 material

• What will we do here
• Review and a little bit more
  • Derivatives and their approximation
  • Computing derivatives
• Code testing
• More accurate and one sided derivatives
• Class assignmets
• Class assignmets
• Class assignmets
• What will we be doing
• Recall Gradients
• Numerical Computation of derivatives
• Testing the gradient
• Class/homeworek assignmets
• Class/homeworek assignmets
• Plotting the gradients and visualizing things
• Numerical ODES
  • The forward Euler method
  • Stability of the solution
  • The backward Euler and the trapezoidal methods
  • Class assignment
  • Using Implicit Methods to solve a linear system of ODEs
  • Quick review - solving linear systems
  • Class assignment
  • Back to the backward Euler method
  • Class assignment
  • Homework assignment