This is the webpage for Math 1A, Sections 103 and 104. I'll basically use this website to post the documents I send via bspace.

Other resources you can use are under Prof. Christ's Homepage or under bspace


Solutions to a couple of problems

Solution to 3.3.51 (the arclength problem)

A picture of the through in 3.9.24

Solution to 3.9.44 (the clock/law of cosines problem)

Solution to 3.10.36 (the paint problem)

Solutions to 4.4.14, 4.4.15, 4.4.49, 4.4.71

Solution to 4.8.38 (last Newton Method problem)

Hints for Problem Set 12

Solution to 5.1.26 (The polygon problem)

Solution to 5.2.67, 5.2.68 (Functions that are not Riemann integrable)


Study Guides

Study Guide for Quiz 1

Study Guide for Quiz 2

Study Guide for Midterm 1

Study Guide for Quiz 3

Study Guide for Quiz 4

Study Guide for Midterm 2

Study Guide for Quiz 5

Study Guide for the Final

A List of Definitions, Theorems, and Proofs for the Final


Other notes

Notes for Sep. 23 Section (Derivatives)

A Worksheet about epsilons and deltas (thanks to Chris Peterson)

Derivation of the formula for the derivative of arccos (detailed version)

Derivative of arccos (what you would need to write on the exam)

A handout about slant asymptotes and how to find them

A handout about the area problem

A fun handout about the FTC (just for fun, won't be on the exam)

Proof of the FTC (what you would need to write on the exam)

Proof of the FTC (detailed version with lots of explanations)

A fun handout about non-integrable functions and the Lebesgue integral (just for fun, won't be on the exam)


Practice exams

Midterm 1

Midterm 1 (Borcherds)

Midterm 1 (Christ)

Midterm 1 (Haiman)

Midterm 1 (Ribet)

Midterm 1 (Vojta)

Midterm 1 (Weinstein)

Midterm 2 (also look at Prof. Vojta's and Prof. Borcherds' Midterm 1)

Midterm 2 (Borcherds)

Midterm 2 (Christ)

Midterm 2 (Haiman)

Midterm 2 (Ribet)

Midterm 2 (Vojta)

Midterm 2 (Weinstein)

Final Exam

Final (Borcherds)   Answer Key

Final (also from Borcherds)   Answer Key

Final (Christ)

Final (Vojta)

Final (Ribet)

Final (Agol)

Final (Weinstein)

Final (Adiredja)

Final (Bergman)

Final (also from Bergman)

Final (Dales)

Final (Froehle)

Final (Jones)