Study guide for the Final Exam

$\let\b=\mathbf$ Here is a non-exhaustive list of questions you should be able to answer as you prepare for the final.

Past chapters

See the

• Study guide for examlet 1
• Study guide for examlet 2
• Study guide for examlet 3
• Study guide for examlet 4
• Study guide for examlet 5
• Study guide for examlet 6
• Study guide for examlet 7

(Recall from the course policies that our examlets are cumulative.)

The final will have its questions drawn evenly from the entirety of the class. (This is in contrast to examlets 1 through 6 that had a somewhat heavy focus on recent material.)

There is also not very much material that is new compared to examlet 7. Some guidelines on that new material are below.

(Nonlinear) Equation Solving

• What is a Jacobian matrix? What are its entries? its properties?

• How does Newton's method for equation solving work in 1D? How would you set it up for a given problem?

  • What is its rate of convergence?
  • Is it locally/globally convergent?

• What is the secant method? How would you set it up for a given problem?

  • What are its advantages/disadvantages compared to Newton's method?
  • Is it locally/globally convergent?

• How does Newton's method for equation solving work in $n$D? How would you set it up for a given problem?

  • What is its rate of convergence?
  • Is it locally/globally convergent?

Optimization

• What is a local/global minimum?
• What are necessary and sufficient conditions for a local minimum? in 1D? in $n$D?
• What is a Hessian matrix? What are its entries? its properties?

• How does Newton's method for optimization work in 1D? How would you set it up for a given problem?

  • What is its rate of convergence?
  • Is it locally/globally convergent?

  • How does Newton's method for optimization work in $n$D? How would you set it up for a given problem?

  • What is its rate of convergence?

  • Is it locally/globally convergent?