**Instructor:** Jack Shotton, Eckhart 333, jshotton@math.uchicago.edu.

**Texts:**

- Michael Spivak, Calculus, ISBN 978-0914098911, chapters 24--27.
- Michael Spivak, Calculus on Manifolds, ISBN 978-0805390216, chapters 1--3.

**Lectures:** MWF Ryerson 358, 9:30-10:20.

**Problem sessions:** Fridays 15:00-16:00, Ryerson 358.

**Office hours:** Wednesdays 17:00-18:00, Thursdays 17:00-18:00 or by appointment.

**Important dates:**

- Final exam: Wednesday 7th June, 10:30-12:30.
- Midterm 1: Friday 21st April
- Midterm 2: Friday 19th May

**General policy:** There will be two in-class hour tests (midterms) and a final
exam, as well as weekly homework. You should feel free (encouraged!) to work on homework together,
but writeups must be independent. The material for the hour-tests will be theorems, definitions and
proofs that I did in class, any assigned reading, and questions similar to those on the homework
sheets. For the determination of the final grade, the weighting will be: 50% on the final, 20% on
each hour test, and 10% on the homework. Late homework will receive a grade of zero no matter what
the reason, but the two lowest scoring homeworks for each student will be discarded.

The final exam must occur at the time and place designated on the College Final Exam Schedule. In particular,no final examinations may be given during the tenth week of the quarter, except in the case of graduating seniors.- Instructors are not permitted to excuse students from the scheduled time of the final exam except in the case of an incomplete.

**Homework:** This will be posted weekly, and due each Monday at noon in the
pigeonhole in Eckhart basement (or in class).

**Readers:**
Jin Woo Sung, jins@uchicago.edu

Week 2 due 4/10.

Week 3 due 4/17.

Week 4 due 5/1.

Week 5 due 5/8.

Week 6 due 5/15.

Week 7 due 5/26.

Week 8 due 5/31.

Problem numbers from week 4 on refer to Spivak, Calculus on Manifolds. Note that for some multi-part problems you will want to use, say, the result of part (ii) to prove part (vii); in that case, you should include a solution of part (ii) in your write-up even if the homework only asks for part (vii). You should feel free to use results from class (but state what you are using), unless the question says something like `prove from the definition that...' in which case you have to work straight from the definition.

Midterm 2 sat 5/19. The median score was 24/40. Solutions.

Final sat 6/7. The median score was 61/120. Solutions.

Practice problems for first midterm.

Chain rule proof.

Practice problems for second midterm.

Basic properties of integrals and their proofs.

Practice final.