150A

Office Hours: Tuesday 3:30-5:30 in Skye 281

Please feel free to email for any questions or appointments.

Week 1 (Jul 30) - Notes of review of bounded sets and convergence

Key Takeaways:

• Formal definition of sets bounded from above, bounded from below, bounded, and unbounded.

• Formal definition of convergence using epsilon-N.

Week 2 (Aug 6) - Notes of HW1 solutions and some examples

Key Takeaways:

• Showing limits exist with limit theorems and lemmas.

• Limit laws (i.e. sum, quotient law).

Week 3 (Aug 13) - HW2 solutions and half of HW3 solutions (no pdf file).

Key Takeaways:

• Limits example problems

• Induction

• Monotone and bounded sequences

• Closed sets, limit points, limit set

Week 4 (Aug 20) - HW3 solutions and part of HW4 (no pdf file).

Key Takeaways:

• How to use algebraic properties of continuous functions to show more complicated functions are continuous.

• How to use theorem 2.2 to compute complicated limits.

Week 5 (Aug 27) - HW4 and HW5 solutions and if time permits some final review (no pdf file).

Key Takeaways:

• How to show a function is monotone increasing or decreasing.

• Practice on using IVT